NMTC 2026 Comes to Kolkata: Cheenta Hosts the Preliminary Round at Mitra Institution

On 30th August 2026, young mathematics enthusiasts across Kolkata gathered at Mitra Institution (Main) for the preliminary round of the National Mathematics Talent Contest (NMTC) — one of India's longest-running mathematical olympiads. Cheenta took charge of conducting the exam in the city, with invigilation handled by Deepan Dutta, Raghunath J V, Shilpa Bera, Taniya Das and Sukdeb Mahato.

A Contest Rooted in History

NMTC is organised annually by the Association of Mathematics Teachers of India (AMTI), founded in 1965 to strengthen mathematics teaching and spot young talent nationwide. The contest itself has run since 1968, making 2026 roughly its 58th edition. What began as a regional initiative out of Tamil Nadu has grown into a national event, with well over a hundred thousand students from hundreds of schools sitting the screening test each year.

Over the decades, NMTC has become a recognised stepping stone in India's olympiad pipeline. Strong performers, especially at the Junior and Inter levels, often go on to represent their states at the Indian National Mathematics Olympiad (INMO), and from there to India's international olympiad teams.

Inside the Competition

NMTC is split into five age-based categories, each named after a mathematician: Primary (Gauss), Sub-Junior (Kaprekar), Junior (Bhaskara), Inter (Ramanujan), and Senior (Aryabhata), covering students from Standard V all the way through undergraduate level. The Preliminary Test — the round held this weekend — is a two-hour paper mixing multiple-choice and fill-in-the-blank questions, deliberately weighted toward difficulty: roughly a fifth of the questions are straightforward, while the rest demand real problem-solving. Only the top tenth of performers make it through to the Final Test, a longer three-hour paper that pushes further into advanced territory.

Kolkata's leg of this national exercise played out at Mitra Institution (Main), with Cheenta's invigilators ensuring the paper ran smoothly for the city's participating students.

How Cheenta Prepares Students

The exam day itself was only the visible part of a longer effort. In the weeks leading up to it, Cheenta ran a series of offline workshops at its Lake Place centre, giving students structured practice with the kind of unconventional, creative problems NMTC is built around — quite different from the routine drilling most school classrooms focus on.

This reflects Cheenta's broader approach to olympiad training: mathematical creativity is a skill that has to be practised through discussion, mistakes, and mentor feedback, not just picked up from a textbook. Through small-group problem-solving sessions at Lake Place, Cheenta has been helping students build the instincts they need — not just for NMTC, but for the longer olympiad journey that follows it, from RMO to INMO and beyond.

What the Curriculum Covers

NMTC draws its syllabus from pre-degree college mathematics, organised broadly around four areas: Algebra, Geometry, Number Theory, and Graph Theory & Combinatorics. Algebra questions typically involve polynomials, equations, inequalities, and complex numbers. Geometry centres on triangles and circles, and can often be approached through trigonometric, vector, complex-number, or transformation methods — giving students room to choose the technique that suits them best. Number theory and combinatorics round out the paper, rewarding pattern recognition and clean logical argument over formula recall.

Looking Ahead

With the preliminary round complete, Kolkata's NMTC aspirants now wait for results, while qualifiers begin preparing for the Final Test. For Cheenta, the Lake Place workshops and the exam day at Mitra Institution are two halves of the same effort — helping local students engage with mathematics as a creative pursuit, one contest at a time.

NMTC 2026 in Kolkata: Cheenta Runs a Month of Prep Workshops

Cheenta is hosting the National Mathematics Talent Contest (NMTC) 2026 Preliminary Round on 30th August 2026 at Mitra Institution (Main), Kolkata. In the weeks leading up to it, Cheenta ran an offline workshop at its Lake Place Road center, from 8th to 29th August to get students ready for the kind of thinking NMTC actually rewards.

A Talent Search Since 1968

NMTC is organised by the Association of Mathematics Teachers of India (AMTI), founded in 1965. The contest itself began in 1968, making 2026 its 58th edition, one of India's longest-running olympiad-style talent searches, predating even the Indian National Mathematical Olympiad. Its founding aim has stayed constant: to identify students capable of original, creative thinking on unfamiliar, non-routine problems, not just fast recall of textbook methods. Last year alone, over 82,000 students across India sat the screening round, with the top 10% at each level advancing to the final.

Inside NMTC 2026

NMTC runs in two stages, organised by grade:

Primary (Gauss, Classes 5–6), Sub-Junior (Kaprekar, 7–8), Junior (Bhaskara, 9–10), Inter (Ramanujan, 11–12), Senior (Aryabhata, first-year college).

Stage 1 — Preliminary Test: 30th August 2026, 10 AM–12 Noon. A 2-hour objective paper: 20 questions for Primary, 30 for the rest, with 80% of questions set at a distinctly Olympiad-like difficulty. Each school shortlists its own top 10% to advance.

Stage 2 — Final Test: 25th October 2026, a 3-hour subjective paper (at most 8 questions) pitched at IOQM/RMO/INMO level. Senior-level students skip the preliminary and go straight to this. Results and cash prizes for top scorers are announced in December.

How Cheenta Is Helping Students

Cheenta is hosting the preliminary exam itself at Mitra Institution (Main), giving Kolkata students a local, straightforward way to sit NMTC, continuing its long-standing role as a host center for olympiads like NMTC, the Australian Mathematics Competition, and the Sharygin Geometrical Olympiad.

Alongside that, Cheenta ran a dedicated prep workshop at its Lake Place Road center every weekend from 8th to 29th August. Rather than syllabus revision, sessions focused on working through non-routine, NMTC-style problems in person with mentors, building exactly the kind of reasoning the screening test is designed to reward.

What the Contest Tests

The syllabus is layered, each level building on the one below:

Primary: Fractions, ratios, divisibility, basic mensuration and geometry.
Sub-Junior: Adds surds, equations, 3D mensuration, and early number theory.
Junior: Adds circle theorems, modular arithmetic, and combinatorics (permutations, pigeonhole principle).
Inter: Adds inequalities, functional equations, and Diophantine equations.
Senior: A subjective paper at typical B.Sc. mathematics level.

Across every level, the emphasis stays on creative problem-solving over formula recall — exactly what Cheenta's Lake Place Road sessions were built to sharpen ahead of the 30th August exam.

NMTC 2023 Stage I - Gauss (Grade 5 & 6) - Problems

Question 1

The value of $\frac{999 \times 999 \times 999}{(999+999) \times 111 \times 111}$, when simplified, is

(a) $\frac{999}{2}$

(b) $\frac{111}{3}$

(d) 1000

Question 2

When $4 \frac{1}{2}$ is divided by $3 \frac{1}{4}$, the result is x. When $3 \frac{3}{4}$ is divided by $2 \frac{1}{8}$, the result is y. Then the numerical value of $13 x+17 y$ is

(a) 38

(b) 40

(d) 48

Question 3

There are 5 cards numbered as shown. In the figure. The number of ways in which one can choose 3 or less cards which contain only odd numbers is.

(a) 8

(b) 7

(d) 21

Question 4

ABC is a triangle. The bisector of $\angle \mathrm{C}$ meets AB at D. The bisectors of $\angle \mathrm{A}$ and $\angle \mathrm{BDC}$ meet at E. Then the measure of $\angle A E D$ is.

(a) $\frac{\angle \mathrm{C}}{2}$

(b) $\frac{\angle \mathrm{C}}{3}$

(d) $\frac{\angle \mathrm{C}}{5}$

Question 5

Samrud secures 20% of the marks but fails by 30 marks. Saket gets 32% marks which is 42 marks more than the minimum pass marks. The maximum marks in the test would be

(a) 100

(b) 200

(d) 600

Question 6

The greatest number that divides 25, 73 and 97 to leave the same remainder is

(a) 19

(b) 22

(d) 37

Question 7

If $\frac{19}{7}=a+\frac{2}{a+\frac{b}{c}}$ where $a b c$, are natural numbers, then the numerical value of $(a+b+c)$ is

(a) 8

(b) 13

(d) 9

Question 8

In the adjoining figure, two equilateral triangles ABP, CDP are placed such that AB is parallel to CD. If $\mathrm{AB}=3 \mathrm{ cm}, \mathrm{CD}=1 \mathrm{ cm}$, the area (in $\mathrm{cm}^{2}$ ) of trapezium ABCD is.

(a) $\sqrt{3}$

(b) $\frac{2}{\sqrt{3}}$

(d) $4 \sqrt{3}$

Question 9

Siva found the average of 5 numbers. He got an answer 40 which is wrong because, while listing, instead of writing the number 43 he wrote 48. The correct average must be

(a) 38

(b) 39

(d) 31

Question 10

In the adjoining figure, ABCD is a square. Also $\mathrm{BE}=\mathrm{BF}$. Then the value of 2x (in degrees) is

(a) 210

(b) 220

(d) 225

Question 11

If the numerator and denominator of a fraction are increased by 20% and 30% respectively, then the fraction becomes $\frac{9}{13}$. If the original fraction is $\frac{p}{q}$, where $p$ and $q$ have no common factors, then $p+q$ is

(a) 3

(b) 6

(d) 9

Question 12

Gita divided 360 into 4 parts such that twice the first part, thrice the second part, five times the third part and six times the fourth part are all equal. Then the difference between the third and fourth parts is

(a) 20

(b) 15

(d) 7

Question 13

In the adjoining figure, the degree measure of $\angle \mathrm{FAB}$ is.

(a) 95°

(b) 105°

(d) 125°

Question 14

Consider the following sequence: 1, 3, 5, 7, 9, 7, 5, 3, 1, 3, 5, 7, 9, 7, 5, 3, 1, 3, 5, 7, 9, 7, 5, 3, 1,  The digit in the $2023{ }^{\text {rd }}$ place is

(a) 3

(b) 5

(d) 1

Question 15

In the two figures, there is a pattern of numbers which are same. Then the number in the head of the second figure,

(a) 6

(b) 13

(d) 10

Fill in the blanks

Question 16

There are two cars $\mathrm{C}_{1}$ and $\mathrm{C}_{2}$. The speed of $\mathrm{C}_{1}$ is 20% less than that of $\mathrm{C}_{2}$. They travel a certain equal distance. The percentage of time does $\mathrm{C}_{1}$ need to travel than $\mathrm{C}_{2}$ is x%. Then x is = (____)

Question 17

Six equal unit squares are arranged in different shapes as shown in the diagram below:

[] In diagram (1), the perimeter is $A B C D$, which equals 10 . Similarly the perimeters of the other shapes also are found out. Let the perimeters be denoted by $P_{1}, P_{2}, P_{3}$ and $P_{4}$. Then the value of $\left(P_{1}+P_{4}\right)-\left(P_{2}+P_{3}\right)$ is_.

Question 18

In a two digit number, the digit in the tens place is twice the digit in the units place. If we swap the places of these two digits, a new two-digit number is formed. The sum of these two numbers is 132. The original number is. (____)

Question 19

An ant starts from A and wants to go to D. It isallowed to go along the lines and pass a line and a point only once. The number of different routes that it can take to go from A to D is (____).

Question 20

Three consecutive natural numbers are taken from 1 to 6 . With these three numbers, three digit numbers are formed. The total number of such 3-digit numbers is (____)

Question 21

In the adjoining figure, $\angle B A C=20^{\circ}, \angle B C A=10^{\circ}, \angle A C D=90^{\circ}$ and $\angle C D B=55^{\circ}$. If $\angle A B D=x^{\mathrm{o}}$, then $x=$ (____)

Question 22

The number of 5-digit numbers of the form $34 a 5 b$ (where $a, b$ are digits), each of which is divisible by 36 is (____)

Question 23

The units digit of the sum of all 2-digit numbers is (____)

Question 24

A natural number is taken. One sixth of this number is subtracted from it. From the resulting number, half of the number is taken and from this number one fifth is taken. If the resulting number is 3 , then the original number taken is (____).

Question 25

The least number that is added to 2716321 to make it exactly divisible by 3456 is (____)

NSEJS 2017 Question Paper

Question 1

Two wave pulses I and II have the same wavelength. They are travelling in the directions as shown by the single headed arrows. The resultant sketch of the two wave pulses at some instant of time when $P$ coincides with $R$ is ____ .

Question 2

The equivalent resistance of two resistances in series is ' $S$ '. These resistances are now joined in parallel. The parallel equivalent resistance is ' $P$ '. If $S =n P$. Then the minimum possible value of $n$ is

(a) 2

(b) 4

(d) 5

Question 3

A copper disc of radius $a_{0}$ has a hole of radius $b_{0}$ at the centre, at $0^{\circ} \mathrm{C}$. The disc is now heated and maintained at $200^{\circ} \mathrm{C}$. The new radii of disc and hole are $a_{t}$ and $b_{t}$ respectively. For the heated disc it can be concluded that

(a) $a_{0}<a_{t}, b_{0}>b_{t}$ and density of disc increases

(b) $a_{0}<a_{t}, b_{0}>b_{t}$ and density of disc decreases

(d) $a_{0}<a_{t}, b_{0}<b_{t}$ and density of disc decreases

Question 4

A liquid, whose density doesn't change during the motion, is flowing steadily through a pipe of varying cross sectional area as shown in the given figure. If $a_{1}, a_{2}$ are the cross sectional areas, $v_{1}, v_{2}$ are the values of velocities (or speeds) at $L$ and $H$ respectively, then the correct relation between $a_{1}, a_{2}$ and $v_{1}, v_{2}$ is

(a) $a_{1} v_{1}=a_{2} v_{2}$

(b) $a_{1} v_{2}=a_{2} v_{1}$

(d) $a_{1} v_{1}^{2}=a_{2} v_{2}^{2}$

Question 5

A common hydrometer has a uniform scale and its stem is graduated downwards from 0 to 20 . While floating in water, it reads 0 and while floating in a liquid of density $1.40 \mathrm{ g} / \mathrm{cm}^{3}$, it reads 20 . Then the density of the liquid in which it will read 10 is ____ .

(a) $0.7 \mathrm{ g} / \mathrm{cm}^{3}$

(b) $0.85 \mathrm{ g} / \mathrm{cm}^{3}$

(d) $2.8 \mathrm{ g} / \mathrm{cm}^{3}$

Question 6

A boy throws a steel ball straight up. Consider the motion of the ball only after it has left the boy's hand but before it touches the ground and assume that forces exerted by the air are negligible. For these conditions, the force(s) acting on the ball is (are)

(a) A downward force of gravity along with a steadily decreasing upward force.

(b) A steadily decreasing upward force from the moment it leaves the boy's hand until it reaches its highest point; on the way down there is a steadily increasing downward force of gravity as the object gets closer to the earth.

(c) Constant downward force of gravity along with an upward force that steadily decreases until the ball reaches its highest point; on the way down there is only a constant downward force of gravity.

(d) Constant downward force of gravity only

Question 7

In bringing a $\alpha$-particle towards another $\alpha$-particle, the electrostatic potential energy of the system ____ .

(a) Increases

(b) Decreases

(d) Becomes zero

Question 8

An empty office chair is at rest on a floor. Consider the following forces

I. A downward force of gravity

II. An upward force exerted by the floor,

III. A net downward force exerted by the air

Then, which of the force(s) is (are) acting on the office chair?

(a) I only

(b) I and II

(d) None of the forces. (Since the chair is at rest there are no forces acting upon it.)

Question 9

If $x, v$ and $t$ represent displacement (m), velocity (m/s) and time (s) respectively for a certain particle then which pair of the following figures can be best correlated to each other?

(a) I and II

(b) I and III

(d) None

Question 10

In rural areas, an indigenous way of keeping kitchen materials cool is to put them in a box and wrap the box with wet blanket; the blanket is kept wet as tap is allowed to drip in to its corner Choose the correct statement:

(a) This method works because the water from the tap is cold. If one uses room temperature water, it will not work.

(b) Method will work only if the box is a bad conductor of heat. If one uses tin box, it will not work.

(d) This method works because the latent heat necessary for evaporation of water in the blanket is taken from the box so the box and its content remain cool.

Question 11

An electron and $\alpha$-particle enter a region of uniform magnetic field (of induction $B$ ) with equal velocities. The direction of $B$ is perpendicular and into the plane of the paper. Then qualitatively identify the direction of paths of electron and the $\alpha$-particle.

(a) I for $\alpha$-particle, III for electron

(b) I for electron, II for $\alpha$-particle

(d) I for electron, III for $\alpha$-particle

Question 12

A concave mirror of radius of curvature 1 m is placed at the bottom of a water tank. The mirror forms an image of the sun when it is directly overhead. If the depth of water in the tank is 80 cm , then the distance of the image formed is ____ . (refractive index of water is 1.33 )

(a) 50 cm above mirror

(b) On surface of water

(d) Image cannot be formed

Question 13

As shown in adjacent figure, two plane mirrors $M_{1}$ and $M_{2}$ are inclined to each other at an angle $70^{\circ}$ (angle $M_{1} O M_{2}$ ). Incident ray $A B$ makes an angle of incidence $\theta$ on $M_{1}$. This ray after reflection at $B$ on $M_{1}$ and further at $C$ on $M_{2}$ travels along the direction $C D$, such that path $C D$ is parallel to $M_{1}$. Then angle $\theta$ is ____ -

(a) $45^{\circ}$

(b) $50^{\circ}$

(d) $60^{\circ}$

Question 14

For the same angle of incidence, the angle of refraction in three different media $A, B, C$ are $15^{\circ}$, $25^{\circ}$ and $35^{\circ}$ respectively. Then which statement is correct? $\left(\mu_{A}\right.$ is refractive index of $\left.A\right)$

(a) $\mu_{A}$ is maximum and velocity of light is minimum in medium $A$

(b) $\mu_{A}$ is minimum and velocity of light is maximum in medium $A$

(d) $\mu_{A}$ is minimum and velocity of light is minimum in medium $A$

Question 15

A large truck collides head-on with a small compact car. During the collision

(a) The truck exerts a greater force on the car than the car exerts on the truck

(b) The car exerts a greater force on the truck than the truck exerts on the car

(d) The truck exerts the same force on the car as the car exerts on the truck

Question 16

A magnet is placed between two coils $A B$ and $C D$ as shown. It is being moved in the direction as shown by the arrow, then which of the following statements is correct?

(a) Looking from end $A$, current in coil $A B$ will be anticlockwise and looking from end $D$ the direction of current in coil $C D$ will be clockwise

(b) Looking from end $A$, current in coil $A B$ will be clockwise and looking from end $D$, the direction of current in coil CD will be clockwise

(c) Looking from end $A$, current in coil $A B$ will be clockwise and looking from end $D$, the direction of current in coil CD will be anticlockwise

(d) Looking from end $A$, current in coil $A B$ will be anticlockwise and looking from end $D$, the direction of current in coil CD will be anticlockwise

Question 17

The ability of eye to focus both near and distant objects, by adjusting its focal length, is called

(a) Myopia

(b) Presbyopia

(d) Tyndall effect

Question 18

The take-off speed of Airbus A340 is $288 \mathrm{ km} / \mathrm{hr}$. From the taxi track it comes to the main runway and waits for a while for the final clearance from Air Traffic Control. The aircraft then achieves this speed within 50 seconds, Neglecting the effect of the wind direction and friction, what should be the minimum length of main runway decided by civil engineers for this aircraft for a take-off?

(a) 1800 m

(b) 2000 m

(d) 2400 m

Question 19

In the adjacent circuit what is the current flowing from $N$ to $K$ ?

(a) 3 A

(b) 2 A

(d) 0.5 A

Question 20

The positions of two blocks at successive 0.20 second time intervals are represented by the numbered squares in the figure below. The blocks are moving towards right.

The accelerations of the blocks are related as follows :

(a) Acceleration of 'a' is greater than acceleration of 'b'

(b) Acceleration of 'a' equals acceleration of 'b', both accelerations are greater than zero

(d) Acceleration of 'a' equals acceleration of 'b', both acceleration are zero

Question 21

If $x^{2}-3 x+2$ is a factor of $x^{4}-p x^{2}+q$, then $p, q$ are

(a) 0,0

(b) 2,3

(d) 5,4

Question 22

If the roots of the equation $\frac{x^{2}-b x}{a x-c}=\frac{m-1}{m+1}$ are equal and of opposite signs, then the value of $m$ is -.

(a) $\frac{a b}{a+b}$

(b) $\frac{a+b}{a b}$

(d) $\frac{a+b}{a-b}$

Question 23

If $p+q+r=2, p^{2}+q^{2}+r^{2}=30$ and $p q r=10$, the value of $(1-p)(1-q)(1-r)$ will be

(a) -18

(b) -24

(d) -35

Question 24

What is the radius of the circumcircle of a triangle whose sides are $30 \mathrm{ cm}, 36 \mathrm{ cm}$ and 30 cm ?

(a) 15 cm

(b) 16 cm

(d) 18 cm

Question 25

If $A B C D$ is a cyclic quadrilateral, $A B=204, B C=$ 104, $C D=195, D A=85$ and $B D=221$, then $A C=$

(a) 240

(b) 225

(d) 210

Question 26

By which smallest number we should divide 198396198 to get a perfect square?

(a) 14

(b) 18

(d) 28

Question 27

If $(a+b+c+d)=4$, then $\frac{1}{(1-a)(1-b)(1-c)}+\frac{1}{(1-b)(1-c)(1-d)}+$ $\frac{1}{(1-c)(1-d)(1-a)}+\frac{1}{(1-d)(1-a)(1-b)}=$ ____

(a) 0

(b) 0.25

(d) 4

Question 28

In triangle $A B C$, segment $A D$, segment $B E$ and segment $C F$ are altitudes. If $A B \times A C=172.8 \mathrm{ cm}^{2}$ and $B E \times C F=108.3 \mathrm{ cm}^{2}$ then $A D \times B C=$ ____

(a) $136.8 \mathrm{ cm}^{2}$

(b) $132.4 \mathrm{ cm}^{2}$

(d) $128.6 \mathrm{ cm}^{2}$

Question 29

$1 \frac{1}{2}+1 \frac{1}{6}+1 \frac{1}{12}+1 \frac{1}{20}+1 \frac{1}{30}+\ldots \ldots .+1 \frac{1}{380}=$ ____

(a) 19.85

(b) 19.95

(d) 20.25

Question 30

If $x=(\sqrt{21}-\sqrt{20})$ and $y=(\sqrt{18}-\sqrt{17})$, then

(a) $x=y$

(b) $x+y=0$

(d) $x<y$

Question 31

If $\left(x+\frac{1}{x}\right)=5$, then $\left(x^{3}+\frac{1}{x^{3}}\right)-5\left(x^{2}+\frac{1}{x^{2}}\right)+ \left(x+\frac{1}{x}\right)=$ ____ .

(a) 0

(b) 5

(d) 10

Question 32

The mean of the following frequency distribution is ____ .

__TABULAR__:W1siQ2xhc3MiXSxbImludGVydmFsIl1d	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
Frequency	4	6	8	10	12

(a) 25

(b) 28

(d) 32

Question 33

On seventy first 'Independence Day' there was Tuesday. After how many years there will be Tuesday on 'Independence Day'?

(a) 4 yrs .

(b) 5 yrs .

(d) 7 yrs .

Question 34

If $x^{2}+x y+x z=135, y^{2}+y z+x y=351$ and $x^{2}+x z+y z=243$, then $x^{2}+y^{2}+z^{2}=$ ____

(a) 225

(b) 250

(d) 300

Question 35

What will be the remainder if the number $(7)^{2017}$ is divided by 25 ?

(a) 1

(b) 7

(d) 24

Question 36

The sum of two numbers is 13 and the sum of their cubes is 1066 . Find the product of those two numbers.

(a) 26

(b) 27

(d) 29

Question 37

Diagonals of a quadrilateral bisect each other. Therefore the quadrilateral must be a ____

(a) Parallelogram

(b) Rhombus

(d) Square

Question 38

A train is running at a speed of $54 \mathrm{ km} / \mathrm{hr}$. It is not stopping at a certain station. It crosses the person showing green flag in 20 seconds and crosses the platform in 36 seconds. What is the length of the train?

(a) 240 m

(b) 300 m

(d) 360 m

Question 39

What is the sum of all odd numbers between 500 and 600 ?

(a) 29500

(b) 27500

(d) 2600

Question 40

How many four digit numbers are there such that when they are divided by 101, they have 99 as remainder?

(a) 90

(b) 98

(d) 101

Question 41

An open vessel contains air at $27^{\circ} \mathrm{C}$. The vessel is heated till two-fifth of the air in it has been expelled. Assuming the volume of the vessel remains constant, find the temperature to which the vessel has to be heated?

(a) 500 K

(b) 550 K

(d) 750 K

Question 42

Rajiv, Nikhil, Shubha and Nilima wanted to establish a relationship between loss in weight of a solid with weight of water displaced by immersing it in tap water and sea water. After performing their experiment, they noted their observations for the same solid as follows: Rajiv : Loss of weight of solid is more in tap water. Nikhil : Loss of weight of solid is more in sea water. Shubha : Loss of weight of solid is equal in the tap water and the sea water. Nilima : Loss of weight of solid may be more in tap water or sea water, depending upon how deeply it is immersed. Identify the correct observation.

(a) Nikhil

(b) Nilima

(d) Rajiv

NSEJS 2016 Question Paper

Question 1

Rod AB of radius 2 r is joined with rod BC of radius r . They are of same material and are of same length. The combination carries a current I. Choose the correct statement.

(a) $V_{A B}=4 V_{B C}$

(b) Current per unit in AB and BC are equal

(d) $\mathrm{V}_{\mathrm{BC}}=4 \mathrm{ V}_{\mathrm{AB}}$ Ans. (d) Sol. $\frac{\mathrm{V}_{\mathrm{AB}}}{\mathrm{V}_{\mathrm{BC}}}=\frac{\mathrm{IR}_{\mathrm{AB}}}{\mathrm{IR}_{\mathrm{BC}}}=\frac{\mathrm{I} \rho \ell / \pi(2 \pi)^{2}}{\mathrm{I} \rho \ell / \pi \mathrm{r}^{2}}=\frac{1}{4}$ or $\mathrm{V}_{\mathrm{BC}}=4 \mathrm{ V}_{\mathrm{AB}}$

Question 2

The statement "a is not less than 4 " is correctly represented by

(a) $a<4$

(b) a $>4$

(d) $\mathrm{a} \leq 4$

Question 3

In the figure shown, the current carrying loop is fixed, where as current carrying straight conductor is free to move. Then straight wire will (ignore gravity)

(a) remain stationary

(b) move towards the loop

(d) rotate about the axis perpendicular to plane of paper

Question 4

Two friends A and B watched a car from the top of their buildings. Angle of depression for A was $10^{\circ}$ more than angle of depression for B , then

(a) A's apartment is taller than B's apartment

(b) B's apartment is taller than A's apartment

(d) We cannot compare the heights of the two apartments

Question 5

A convex mirror of focal length $f$ produces an image of size equal to $\frac{1}{n}$ times the size of the object. Then the object distance is

(a) nf

(b) $\frac{\mathrm{f}}{\mathrm{n}}$

(d) (n - 1)f

Question 6

Total surface area of a sphere $S$ with radius $\sqrt{2}+\sqrt{3} \mathrm{ cm}$ is

(a) $400 \pi(5+2 \sqrt{6}) \mathrm{sq} \mathrm{mm}$

(b) $\pi(\sqrt{2}+\sqrt{3})^{2}$ sq cm

(d) $40 \pi(5+2 \sqrt{6}) \mathrm{sq} \mathrm{mm}$

Question 7

The angle between the hour arm and the minute arm of a clock at 2:10 a.m. is

(a) Zero

(b) $4^{\circ}$

(d) $6^{\circ}$

Question 8

A craft teacher reshapes the wax from a cylinder of candle with section diameter 6 cm and the height 6 cm into a sphere. The radius of this sphere will be

(a) $r=6 \sqrt{3 / 2} \mathrm{ cm}$

(b) $r=6 \mathrm{ cm}$

(d) $\mathrm{r}=6 \sqrt[3]{2} \mathrm{ cm}$

Question 9

A point object O is kept at origin. When a concave mirror $\mathrm{M}_{1}$ placed at $\mathrm{x}=6 \mathrm{ cm}$, image is formed at infinity. When $\mathrm{M}_{1}$ is replaced by another concave mirror $\mathrm{M}_{2}$ at same position, image is formed at $\mathrm{x}=$ 30 cm , then ratio of the focal length of $\mathrm{M}_{1}$ to that of $\mathrm{M}_{2}$ is

(a) $\frac{3}{4}$

(b) $\frac{4}{3}$

(d) $\frac{1}{5}$

Question 10

The number $3^{8}\left(3^{10}+6^{5}\right)+2^{3}\left(2^{12}+6^{7}\right)$ is

(a) A perfect square and a perfect cube

(b) Neither a perfect squre nor a perfect cube

(d) A perfect square but not a perfect cube

Question 11

Melting point of a substance is $10^{\circ} \mathrm{C}$. What does this mean?

(a) The substance is a liquid at $10^{\circ} \mathrm{C}$.

(b) The substance is a solid at $10^{\circ} \mathrm{C}$.

(d) The substance is $50 %$ solid and $50 %$ liquid at $10^{\circ} \mathrm{C}$.

Question 12

Let the number of rectangles formed by 6 horizontal and 4 vertical lines be n and those formed by 5 vertical and 5 horizontal lines be m then we have

(a) $n=m$

(b) $\mathrm{n} \geq \mathrm{m}+1$

(d) $m>n+5$

Question 13

The effective resistance between $A$ and $D$ in the circuit shown in the adjacent figure is

(a) $5 \Omega$

(b) $10 \Omega$

(d) $20 \Omega$

Question 14

If ABCD is a rhombus and $\angle \mathrm{ABC}=60^{\circ}$ then

(a) The points $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$ are concyclic

(b) The quadrilateral has exactly half the area of the square with same sides as ABCD

(d) The diagonals of the quadrilateral ABCD are equal and bisect each other at right angle

Question 15

Three bulbs $\mathrm{B}_{1}, \mathrm{ B}_{2}$ and $\mathrm{B}_{3}$ having rated powers $100 \mathrm{ W}, 60 \mathrm{ W}$ and 60 W at 250 V are connected in a circuit as shown in the adjacent figure. If $\mathrm{W}_{1}, \mathrm{ W}_{2}$ and $\mathrm{W}_{3}$ are the output powers of the bulbs $\mathrm{B}_{1}, \mathrm{ B}_{2}$ and $\mathrm{B}_{3}$ respectively, then

(a) $\mathrm{W}_{1}>\mathrm{W}_{2}=\mathrm{W}_{3}$

(b) $\mathrm{W}_{1}>\mathrm{W}_{2}>\mathrm{W}_{3}$

(d) $\mathrm{W}_{1}<\mathrm{W}_{2}<\mathrm{W}_{3}$

Question 16

If $\mathrm{a}, \mathrm{b}>0$ then

(a) $a+b \leq \sqrt{a b}$

(b) a + b $>\sqrt{\text { ab }}$

(d) None of the above inequalities will hold

Question 17

Following diagram shows refraction of parallel beam of light through a spherical surface. Identify the correct ray diagram

Question 18

Tenth term in the sequence $12,18,20,28, \ldots$ is

(a) 336

(b) 63

(d) 68

Question 19

In the diagram $\mathrm{M}_{1}$ and $\mathrm{M}_{2}$ are two plane mirrors at right angles to each other. O is a luminous point object. Consider two images formed due to first reflection at $\mathrm{M}_{1}$ and $\mathrm{M}_{2}$. The area of the triangle formed by the object and two images is

(a) $4 \mathrm{ cm}^{2}$

(b) $2 \mathrm{ cm}^{2}$

(d) $16 \mathrm{ cm}^{2}$

Question 20

The probability of a point within an equilateral triangle with side 1-unit lying outside its in-circle (inscribed circle) is

(a) $1-\frac{1}{2(\sqrt{3})}$

(b) $1-\frac{\pi}{3 \sqrt{3}}$

(d) $1-\frac{2 \pi}{3 \sqrt{3}}$

Question 21

A fisherman of height $h$ is standing on the bank of a lake. A fish in the water perceives his height as $h$ '. Then

(a) $\mathrm{h}^{\prime}>\mathrm{h}$

(b) $h^{\prime}<h$

(d) $h^{\prime}>h$ or $h^{\prime}<h$ depending on position of fish

Question 22

A triangle has perimeter 316 and its sides are of integer length. The maximum possible area for such a triangle is achieved for

(a) Single triangle

(b) Two triangles

(d) More than three triangle

Question 23

Object A is completely immersed in water. True weight of object A is $\mathrm{W}_{\mathrm{A}}$. Weight of water with beaker is $\mathrm{W}_{\mathrm{B}}$. Let B be the buoyant force. $\mathrm{W}_{1}$ and $\mathrm{W}_{2}$ are scale readings of spring balance and weighing scale respectively.

(a) $\mathrm{W}_{1}=\mathrm{W}_{\mathrm{A}}$

(b) $\mathrm{W}_{1}=\mathrm{W}_{\mathrm{A}}+\mathrm{B}$

(d) $\mathrm{W}_{2}=\mathrm{W}_{\mathrm{B}}+\mathrm{B}$

Question 24

Number of numbers less than 40 having exactly four divisors is

(a) 15

(b) 12

(d) 14

Question 25

Velocity of a particle moving along a straight line varies with time as shown in the figure. Net forces acting on the aprticle are $\mathrm{F}_{1}, \mathrm{ F}_{2}, \mathrm{ F}_{3}, \mathrm{ F}_{4}$ and $\mathrm{F}_{5}$ in the intervals $\mathrm{OA}, \mathrm{AB}, \mathrm{BC}, \mathrm{CD}$ and DE respectively. Indentify the correct statement

(a) $\mathrm{F}_{1}$ increases with time

(b) $\mathrm{F}_{5}$ is initially positive and then becomes negative

(d) $\mathrm{F}_{3}$ is negative

Question 26

If set $X$ consists of three elements then the number of elements in the power set of power set of $X$ is

(a) $3^{3}$

(b) $2^{3}$

(d) $2^{8}$

Question 27

A wooden block $(\mathrm{W})$ is suspended by using a cord from a heavy steel ball (B). The entire system is dropped from a height. Neglecting air resistance, the tension in the cord is

(a) Zero

(b) The difference in the masses of B and W

(d) The weights of $B$

Question 28

In a n - sided regular polygon, the radius of the circum-circle is equal in length to the shortest diagonal. the number of values of $\mathrm{n}<60$ for which this can happen is

(a) 0

(b) 1

(d) 2

Question 29

A circus performer of weight W is standing on a wire as shown in the figure. The tension in the wire is

(a) Approximately $\frac{\mathrm{W}}{4}$

(b) Approximately $\frac{\mathrm{W}}{2}$

(d) Much less than $\frac{W}{2}$

Question 30

Number of integers $n$ such that the number $1+n$ is a divisor of the number $1+n^{2}$ is :

(a) 0

(b) 1

(d) 2

Question 31

In the following diagrams O is point object and I is its image formed by a concave mirror. Identify the diagram. In which position of image I is nearly correct.

Question 32

If for $\mathrm{x}, \mathrm{y}>0$ we have $\frac{1}{\mathrm{x}}+\frac{1}{\mathrm{y}}=2$ then the minimum value of xy is

(a) 2

(b) 1

(d) $\sqrt{2}$

Question 33

Two bodies $A$ and $B$ are charged with equal magnitude of charge but $A$ with positive charge and $B$ with negative. If $M_{A}$ and $M_{B}$ are masses before charging and $M^{I}{ }_{A}$ and $M^{I}{ }_{B}$ are the masses after charging the ( $\mathrm{m}_{0}$ is some constant mass)

(a) $\mathrm{M}_{\mathrm{A}}^{\mathrm{I}}=\mathrm{M}_{\mathrm{A}}+\mathrm{m}_{0}$ and $\mathrm{M}_{\mathrm{B}}^{\mathrm{I}}=\mathrm{M}_{\mathrm{B}}-\mathrm{m}_{0}$

(b) $\mathrm{M}_{\mathrm{A}}^{\mathrm{I}}=\mathrm{M}_{\mathrm{A}}-\mathrm{m}_{0}$ and $\mathrm{M}_{\mathrm{B}}^{\mathrm{I}}=\mathrm{M}_{\mathrm{B}}+\mathrm{m}_{0}$

(d) $M^{I}{ }_{A}=M_{A}-\frac{m_{0}}{2}$ and $M_{B}^{I}=M_{B}+m_{0}$

Question 34

The number of natural numbers $\mathrm{n} \leq 30$ for for which $\sqrt{\mathrm{n}+\sqrt{\mathrm{n}+\sqrt{\mathrm{n}+\ldots . .}}}$ is a natural number is

(a) 30

(b) Zero

(d) 5

Question 35

A conductor of length $L$ has a varying cross section with area $2 A$ at $P$ and $A$ at $Q$ as shown in the figure. If it carries a steady current I, then

(a) Net charge per unit volume near P is more than net charge per unit volume near Q .

(b) Net charge per unit volume near Q is less than net charge per unit volume.

(d) Current per unit area near P is less than current per unit area near Q .

Question 36

The number of natural numbers $n \leq 30$ for which $\sqrt{n+\sqrt{n+\sqrt{n+\ldots \ldots . .}}}$ is a prime number is

(a) Three

(b) Zero

(d) Two

Question 37

Vessels A and B are made of conducting material. Both contain water. Vessel A floats in B. Vessel B is now heated at a uniform rate, then

(a) Water in A boils first.

(b) Water in A boils some time after water in B starts boiling.

(d) Water in A does not boil.

Question 38

The number of squares formed by 5 vertical and 4 horizontal lines (all are equispaced) is

(a) 60

(b) 20

(d) 46

Question 39

Every major city in India has a pollution control board to monitor air and water pollution. The following data is from three different localities in Bangalore city from the year 2015.

ppb stands for parts per billion and ppm stands for parts per million. These are different units to express concentration. They are very similar to percentage (which is actually parts per hundred). Based on the above data, which place will you choose to live in?

(a) All localities are equally polluted, so I have no preference.

(b) P is more polluted than Y and Z , hence I will live in either Y or Z .

(d) Z and Y are more polluted than P , hence I will live in P .

Question 40

A body thrown vertically up reaches a maximum height and returns back. Its acceleration is

(a) Downward during both ascent and descent.

(b) Downward at all positions except at the highest point, where it is zero.

(d) Downward during ascent and upward during descent.

Question 41

The number of integers $a, b, c$ for which $a^{2}+b^{2}-8 c=3$ is

(a) 2

(b) Infinite

(d) 4

NSEJS 2020 Question Paper

Question 1

Gravitational collapse is the contraction of an astronomical object under its own gravity. This draws the matter inwards towards the centre of gravity. A neutron star is an example of the collapsed core of a giant star. A certain neutron star of radius 10 km is of mass $1.5 M_{\odot}$. The acceleration due to gravity on the surface of the neutron star is nearly

(a) $2.0 \times 10^{8} \mathrm{ m} / \mathrm{s}^{2}$

(b) $2.0 \times 10^{12} \mathrm{ m} / \mathrm{s}^{2}$

(d) $2.6 \times 10^{20} \mathrm{ m} / \mathrm{s}^{2}$

Question 2

Two illuminated point objects $\mathrm{O}_{1}$ and $\mathrm{O}_{2}$ are placed at a distance 24 cm from each other along the principal axis of a thin convex lens of focal length 9 cm such that images of both the objects are formed at the same position. Then the respective distances of the lens from $\mathrm{O}_{1}$ and $\mathrm{O}_{2}$ (in cm ) are

(a) 12 and 12

(b) 18 and 6

(d) 16 and 8

Question 3

A nuclear reactor is working at $30 %$ efficiency (i.e. conversion of nuclear energy to electrical energy). In this reactor ${ }_{92}^{235} \mathrm{U}$ nucleus undergoes fission and releases 200 MeV energy per atom. If 1000 kW of electrical power is obtained in this reactor, then the number of atoms disintegrated (undergone fission) per second in the reactor is

(a) $1.04 \times 10^{17}$

(b) $6.5 \times 10^{12}$

(d) $3.25 \times 10^{32}$

Question 4

Two blocks $A$ and $B$ are in contact with each other and are placed on a frictionless horizontal surface. A force of 90 N is applied horizontally on block A (situation I ) and the same force is applied horizontally on block B (situation II). Mass of A is 20 kg and B is 10 kg . Then the correct statement is

(a) Since both the blocks are in contact, magnitude of force by block A on B will be 90 N (situation I) and magnitude of force by block B on A will also be 90 N (situation II).

(b) Magnitude of force by block A on B is 30 N (situation I) and magnitude of force by block B on $A$ is 60 N (situation II).

(c) Magnitude of force by block A on B is 60 N (situation I) and magnitude of force by block B on A is 30 N (situation II).

(d) The 90 N force will produce acceleration of different magnitudes in A and B .

Question 5

In the adjoining circuit, $R=5 \Omega$. It is desired that the voltage across $R_{x}$ should be 6 V , then the value of $R_{x}$ should be

(a) $4 \Omega$

(b) $12 \Omega$

(d) $20 \Omega$

Question 6

If $x^{2}+a x+b=0$ and $x^{2}+b x+a=0$ have one common root, then

(a) $a+b=0$

(b) $a+b=1$

(d) $a^{2}+b^{2}=1$

Question 7

Six circles each of radius 3 cm are inscribed in an equilateral triangle ABC such that they touch each other and also touch the sides of the triangle as shown in the adjacent figure. Then height of triangle $A B C$ is

(a) $6(2 \sqrt{3}+3)$

(b) $3(2 \sqrt{3}+6)$

(d) $6(2+\sqrt{3})$

Question 8

Find the remainder when $x^{51}$ is divided by $x^{2}-3 x+2$

(a) $X$

(b) $\left(2^{51}-2\right) x+2-2^{51}$

(d) 0

Question 9

If $\frac{3}{x-2}<1$, where $x$ is a real number, then

(a) $2<x<5$

(b) $x<2$ or $5<x$

(d) None of these

Question 10

If $100^{25}-25$ is written in decimal notations, then the sum of its digits is

(a) 444

(b) 442

(d) 422

Question 11

$A B C$ is a triangle, the bisector of angle $A$ meets $B C$ in $D$. The relation between $A D, A B$ and $A C$ is

(a) $A D>\sqrt{A B \cdot A C}$

(b) $A D>A B \cdot A C$

(d) $A D<\sqrt{A B \cdot A C}$ PART: A - 2 MORE THAN ONE CORRECT OPTIONS. BUBBLE ALL CORRECT OPTIONS ONLY.

Question 12

An infinitely long conductor when carrying current $I$, produces a magnetic field $B$ around it. If such a conductor is placed along the X-axis, then the magnitude of $B$ at a distance $r$ is given by the relation $B=\frac{\mu_{0}}{4 \pi} \frac{2 I}{r}$, (where $\frac{\mu_{0}}{4 \pi}=10^{-7} \mathrm{NA}^{-2}$ is a constant). The following figure shows such an infinitely long conductor placed along X -axis carrying current $I$ and $B$ at $S$ is $2 \times 10^{-4} \mathrm{ T}$, directed into the plane of the paper at S . Given $r=1 \mathrm{ cm}$. Then, the correct statements are

(a) $I=10 \mathrm{ A}$

(b) The number of electrons transported across the cross section of the conductor during time 1s is $6.25 \times 10^{19}$

(d) The electrons will flow in the direction $X_{2}$ to $X_{1}$.

Question 13

The ratio of the charge of an ion or subatomic particle to its mass $(q / m)$ is called specific charge. Then the correct options are

(a) SI unit of specific charge can be written as $\mathrm{A} \cdot \mathrm{s} / \mathrm{kg}$.

(b) If all the isotopes of hydrogen are ionized then tritium will have least specific charge among them.

(d) specific charge ratio of an electron is $1.75 \times 10^{11} \mathrm{C} / \mathrm{kg}$.

Question 14

If $0 \leq x \leq \pi$ and $81^{\sin ^{2} x}+81^{\cos ^{2} x}=30$, then $x=$

(a) $\frac{\pi}{6}$

(b) $\frac{\pi}{3}$

(d) $\frac{2 \pi}{3}$ [0pt] [Useful information: $\pi^{c}=180^{\circ}, \sin (180-\theta)=\sin \theta, \sin \theta \geq 0$ when $0 \leq \theta \leq 180^{\circ}$ ]

Question 15

Given $(a-b)^{2}+(a-c)^{2}=(b-c)^{2}$, then which of the following statements are true?

(a) equation is valid when $b=c$ and $a \neq c$

(b) equation is valid when $a=b$

(d) Given equation is not valid when $a, b$ and $c$ are distinct.

NSEJS 2021 Question Paper

Question 1

The axes of a coordinate system $\mathrm{S}_{2}$ are inclined at an angle $\theta$ to those of another coordinate system $\mathrm{S}_{1}$. The origins of both the systems are coinciding. A particle $\mathrm{P}_{1}$ at rest in system $\mathrm{S}_{1}$, starts from point ($-2,0$) and travels along positive direction of $\mathrm{X}_{1}$ axis with uniform acceleration of $1.25 \mathrm{ m} / \mathrm{s}^{2}$ for 4 s and stops. In system $\mathrm{S}_{2}$, particle $\mathrm{P}_{2}$, starts from rest from the origin and travels for 2 s along positive direction of $\mathrm{X}_{2}$ axis with uniform acceleration $5 \mathrm{ m} / \mathrm{s}^{2}$ and stops. If the final distance between $P_{1}$ and $P_{2}$ is 6 m , then the angle between $+\mathrm{Y}_{1}$ axis and $+\mathrm{X}_{2}$ axis is

(a) $36.8^{\circ}$

(b) $53.2^{\circ}$

(d) $126.8^{\circ}$

Question 2

The variation of a certain physical parameter $Z$ with variable $u$ is given by the relation $\mathrm{Z}=A\left(\frac{R}{R+u}\right)^{3}$, where $R$ and $A$ are constants and the maximum value of $u \ll R$. Then to find $R$, a student plots a graph of variation of $Z$ ( Y axis) against $u$ ( X axis). The graph is a

(a) straight line passing through origin and slope $=\frac{R}{3}$

(b) straight line with intercept $\frac{3 A}{2}$ and slope $=-\frac{R}{3 A}$

(d) straight line with intercept $-\frac{A}{2}$ and slope $=-3 R$

Question 3

A submarine $S_{1}$ is parked at a depth of 200 m in an ocean on earth. Assume oceans exist on Mars. At about what depth a submarine $\mathrm{S}_{2}$ has to be parked in an ocean on Mars so that $\mathrm{S}_{2}$ will experience same pressure as that of $\mathrm{S}_{1}$ ? Acceleration due to gravity on Mars is $3.7 \mathrm{ m} / \mathrm{s}^{2}$. (Assume that sea water density on Earth and Mars is same, $\rho=1.03 \times 10^{3} \mathrm{ kg} / \mathrm{m}^{3}$ )

(a) 158 m

(b) 435 m

(d) 616 m

Question 4

In an oscillating system, damping results in dissipation of the stored energy. The following figure shows the variation of displacement x with time t for an oscillating system. Which of the following statements best describes this physical phenomenon.

(a) Oscillatory motion of an object without damping

(b) Oscillatory motion of an object with damping such that time measurement was started when the system was at the mean position.

(d) Oscillatory motion of an object with damping such that time measurement was started when the system had maximum potential energy.

Question 5

In the adjacent circuit, the galvanometer $G$ does not show any deflection. If $R=2 \Omega$, the current drawn from the cell is

(a) 1 A

(b) 9 A

(d) $\frac{9}{4} \mathrm{ A}$

Question 6

'Gear' is a mechanical system used to transfer mechanical and rotary motion from one mechanical system to another. As shown in the figure below the driving wheel A drives the driven wheel B without slipping and thus forms the gear system. The wheel A has 16 teeth and B has 24 teeth. Wheel B has a projection (shown by white ring in Fig. 1 and also in the side view of Fig. 2) of radius $\frac{14}{11} \mathrm{ cm}$.

A long massless, inextensible string can be wound / unwound over this circular projection. A mass $m$ is attached to the free end of this long string. If the wheel A makes 6 revolutions per second in the clockwise direction, without slipping, then in $\frac{1}{2}$ second the potential energy of the mass $m$ in CGS unit

(a) increases by $32 m g$

(b) decreases by 32 mg

(d) decreases by 16 mg

Question 7

Canopus is the second brightest star in the night sky. It is about 300 light years away. The energy is produced inside the star through nuclear reactions. If we receive $5.0 \times 10^{-8} \mathrm{ W} / \mathrm{m}^{2}$ energy from Canopus, how much mass does it lose per second?

(a) $1.70 \times 10^{-6} \mathrm{ kg}$

(b) $1.91 \times 10^{9} \mathrm{ kg}$

(d) $6.34 \times 10^{31} \mathrm{ kg}$

Question 8

An average human adult radiates about 100 W energy mainly in infra-red region of the electromagnetic spectrum. 50 persons are sitting in a hall with an air conditioning system which is $50 %$ efficient. How much electricity must be used to maintain temperature of the hall at $25^{\circ} \mathrm{C}$ for 4 hours?

(a) 5 units

(b) 10 units

(d) 40 units

ANY NUMBER OF OPTIONS 4, 3, 2 or 1 MAY BE CORRECT IN THE FOLLOWING QUESTIONS.

Question 9

According to Einstein's theory, light can be assumed to be in the form of a large number of discrete energy packets called 'photons'. In case of light of frequency $v$, each photon carries energy $E=h v$. In a certain surgical procedure a surgeon uses LASER beam of wavelength 650 nm in pulses of 30.0 ms duration. The average power of each pulse is 0.6 W . Here h is Planck's constant. Then

(a) the frequency of this LASER photon is $4.6 \times 10^{14} \mathrm{ Hz}$

(b) the energy in each pulse is $1.1 \times 10^{17} \mathrm{eV}$

(d) number of photons in each pulse is $5.9 \times 10^{16}$

Question 10

In the following circuit, $\mathrm{R}_{1}=6 \Omega, \mathrm{R}_{2}=12 \Omega, \mathrm{ V}=16 \mathrm{ V}$. The currents $\mathrm{I}_{1}$ and $\mathrm{I}_{2}$ flow through the resistances $\mathrm{R}_{1}$ and $\mathrm{R}_{2}$ respectively

(a) power generated across $\mathrm{R}_{1}$ is 42.6 watt

(b) the ratio of $\frac{I_{1}}{I_{2}}=2$

(d) as $R_{2}=2 R_{1}$, the voltage across $R_{2}$ will be twice the voltage across $\mathrm{R}_{1}$

Question 11

A glass plate of uniform thickness $t$ and refractive index $\mu$ is as shown in the diagram. AB is the incident ray and FG is the emergent ray. The angles of incidence and refraction are $i$ and $r$ respectively. The perpendicular distance $\mathrm{FC}=x$ between the incident and the emergent rays is called the lateral shift. Then

(a) $x=t\left(\sin i-\frac{\cos i \sin r}{\cos r}\right)$

(b) $x$ depends on refractive index $\mu$

(d) Maximum value of $x=t$ when $i$ is close to $90^{\circ}$

NSEJS 2025 Question Paper

Question 1

A student, intending to catch a bus on the bus stand, finds that the bus starts and accelerates away from him/her with uniform acceleration $a=2 m s^{-2}$ when he is 16 m far from the bus. He runs fast enough with a uniform speed so as just to catch the bus. The minimum speed with which the student must run, is

(a) $2.0 \mathrm{ ms}^{-1}$

(b) $4.0 \mathrm{ ms}^{-1}$

(d) $16.0 \mathrm{ ms}^{-1}$

Question 2

A block of mass 2.0 kg is suspended from the ceiling by a massless string. The string is taut bearing a definite tension when the block is stationary. Suddenly, the string breaks and the block start falling freely. The difference in the tension in string just before and after it breaks is

(a) 9.8 N

(b) 19.6 N

(d) zero

Question 3

Having been paddled continuously on a horizontal road, the speed of a bicycle is increasing, the force of friction exerted by the ground on the wheels is

(a) in the backward direction on both the wheels

(b) in the forward direction on both the wheels

(d) in the backward direction on the front wheel and in forward direction on the rear wheel

Question 4

A current $\mathrm{i}=2 \mathrm{amp}$ is established through the long straight conductors which are the arms of a hairpin like structure placed in the plane of paper as shown in the figure. Knowing that a current carrying conductor produces magnetic field represented by the lines of force, analyze the situations described

The correct option is

(a) The magnetic field at point P is directed outward, normal to the plane of paper

(b) The magnetic field at point Q is directed inward, normal to the plane of paper

(d) No magnetic field is produced outside the hair pin that is at points M and N

Question 5

A certain water pump rated 500 watt lifts water from ground level to a height $h=10$ meter at a rate of $240 \mathrm{ kg} /$ minute . Ignoring the kinetic energy gained by water, the efficiency of water pump is

(a) $74.8 %$

(b) $78.4 %$

(d) $87.4 %$

Question 6

An electric kettle consists of two filaments $\mathrm{F}_{1}$ and $\mathrm{F}_{2}$ of different resistances $R_{1}$ and $R_{2}$ respectively, connected in parallel with separate switches. With a certain fixed amount of water in the kettle pot to prepare the tea, when only $F_{1}$ is switched on, it takes 4 minute to boil the water. When $F_{1}$ and $F_{2}$ both are switched on simultaneously, it takes 3 minute to boil the same amount of water up to the same temperature. The time taken to boil the same amount of water when only $F_{2}$ is switched on (assume that entire heat radiated by filaments is used in boiling the water starting from the same room temperature in each case) is

(a) 7.0 min

(b) 8.4 min

(d) 12.0 min

Question 7

Two filament bulbs $B_{1}(100 \mathrm{ W}, 220 \mathrm{ V})$ and $B_{2}(60 \mathrm{ W}, 220 \mathrm{ V})$ are connected in series with a 440 V supply voltage source as shown. When switched on, the bulb

(a) $B_{1}$ will fuse: $B_{2}$ will not fuse

(b) $B_{1}$ will not fuse: $B_{2}$ will fuse

(d) $\mathrm{B}_{1}$ and $\mathrm{B}_{2}$ both will not fuse

Question 8

The volume of water, spilled out of a completely filled cubic container of side 4 m when the container has been accelerated horizontally with $1.96 \mathrm{ m} / \mathrm{s}^{2}$, is

(a) 0

(b) $12.8 \mathrm{ m}^{3}$

(d) $3.2 \mathrm{ m}^{3}$

Question 9

Two athletes, A and B, run in the ground on an oval track of length L (say) at $8.0 \mathrm{ m} / \mathrm{s}$ and $6.0 \mathrm{ m} / \mathrm{s}$ respectively in the same direction starting from same initial point. How many laps (rounds) will the athlete A complete on the track before overtaking athlete B for the first time?

(a) 2

(b) 3

(d) 5

Question 10

A wooden solid cylinder (density $0.80 \mathrm{ kg} / \mathrm{m}^{3}$ ), a plastic ball (density $0.90 \mathrm{ kg} / \mathrm{m}^{3}$ ) and a rubber cube (density $0.95 \mathrm{ kg} / \mathrm{m}^{3}$ ) all of equal mass M float partly immersed in a trough containing water (density $1.00 \mathrm{ kg} / \mathrm{m}^{3}$ ) as shown below (ignore any tilt during floatation) You may conclude that

(a) The buoyant force is largest on the wooden cylinder

(b) The buoyant force is largest on the Plastic ball

(d) The buoyant force is equal on all the three

Question 11

A stone is thrown vertically down into a well, the splash is heard after a time $t_{1}$. If the stone is thrown vertically up with the same speed from the same point, the splash is heard after a time $t_{2}$. The common initial speed ( $u$ ) of the stone in both the cases is given by (the time taken by the splash sound to reach the observer is ignored)

(a) $u=g\left(t_{2}-t_{1}\right)$

(b) $u=g\left(t_{2}+t_{1}\right)$

(d) $u=\frac{1}{2} g\left(t_{2}-t_{1}\right)$

Question 12

A 80 kg man skating with a speed of $10 \mathrm{ m} / \mathrm{s}$ on a smooth horizontal surface collides with a 20 kg skater at rest, as a result the two cling to each other. What percentage of initial kinetic energy of skaters is lost during the collision? (Ignore any friction)

(a) $12 %$

(b) $18 %$

(d) $25 %$

Question 13

A beam of light is incident parallel to principal axis on a convex lens (L) of focal length $\mathrm{f}=20 \mathrm{ cm}$. A plane mirror PQ (See figure), inclined at $60^{\circ}$ with the principal axis, is placed a distance ' d ' behind the lens so as to form a real image 1 of the distant object at a distance ' $d$ ' from the optical center of the lens as shown in the figure. The value of ' $d$ ' is

(a) 5 cm

(b) 10 cm

(d) 20 cm

Question 14

Two cylindrical vessels $V_{1}$ and $V_{2}$ are placed on the same horizontal level. Each vessel contains the same liquid of density $\rho$. Initially the vessels are not connected (valve closed). The height of liquid in vessel $\mathrm{V}_{1}$ is $h_{1}$ and that in vessel $V_{2}$ is $h_{2}$. The diameter of vessels $V_{1}$ and $V_{2}$ are $2 d$ and $d$ respectively. When vessels are interconnected (valve opened) at the bottom, the height h of liquid in each vessel (neglecting the volume of liquid in connecting tube) will be

(a) $\frac{2 \mathrm{ h}_{1}+\mathrm{h}_{2}}{3}$

(b) $\frac{4 \mathrm{ h}_{1}+\mathrm{h}_{2}}{5}$

(d) $\frac{\mathrm{h}_{1}+2 \mathrm{ h}_{2}}{4}$

Question 15

Two vertical object pins are located on the principal axis of a thin lens at distances of $x_{1}=9.0 \mathrm{ cm}$ and $x_{2}=18.0 \mathrm{ cm}$ from the lens on the two sides of the lens. The images of the two pins formed by the lens are at the same position (overlap). The focal length and the nature of the lens are

(a) 15 cm , convex

(b) 12 cm , convex

(d) 12 cm , concave

Question 16

A steam boat goes across a lake up to a distance of 1200 meter and comes back. There is a uniform wind blowing with velocity $v$ so as to help the onward journey and to impede the journey back. If the uniform speed of launch of the boat is $5 \mathrm{ ms}^{-1}$ and total time taken by the boat in going and coming back is 500 s , the velocity $v$ of the wind blow is

(a) $0.6 \mathrm{ ms}^{-1}$

(b) $0.8 \mathrm{ ms}^{-1}$

(d) $1.2 \mathrm{ ms}^{-1}$

Question 17

A trolley of mass 240 kg is initially at rest on the frictionless horizontal straight rails lying in east-west direction. The length of the trolley is 20 meter. A man of mass 60 kg is standing at the eastern end of the trolley. The man starts moving on the trolley from eastern end towards west with velocity $1.0 \mathrm{ m} / \mathrm{s}$ relative to the trolley. Assume the displacement and the velocity in eastward direction to be positive. Choose the correct option.

(a) The velocity of man relative to ground is $-1 \mathrm{ ms}^{-1}$

(b) The recoil velocity of the trolley relative to ground is $+0.2 \mathrm{ ms}^{-1}$ -(c)

(d) Displacement of trolley over the ground when the man reaches the other end of trolley is +4.0 m.

Question 18

A homogeneous column of water $\left({ }_{a} \mu_{w}=\frac{4}{3}\right)$ of height 8.0 cm fills the space above a 9.0 cm thick glass $\left({ }_{a} \mu_{g}=\frac{3}{2}\right)$ slab. Observers A and B are in air just outside the top and the bottom whereas the observers C and D are inside just below the top and above the bottom. The total thickness of glass plus water observed by these observers are

(a) Observer A measures it as 12.0 cm

(b) Observer B measures it as 12.0 cm

(d) Observer D measures it as 18.0 cm

Question 19

In abn experiment performed using a cloud chamber (a device that can show the tracks of subatomic particle) the nature of a particle can be analysed. Under the influence of a strong perpendicular magnetic field $\mathbf{B}$ directed into the plane of the paper, a particle track like the one shown beside as $p q$ was obtained. The track shown may depict

(a) a proton (charge +e ) moving from point p to q

(b) an alpha particle (charge $+2 \mathrm{e})$ moving from point

(d) a neutron (charge zero) moving from point p to q

Question 20

Several resistances of $2 \Omega$ and $3 \Omega$ are used to form a typical electric network as shown in the figure below. A de supply of emf 18 volt and negligible internal resistance has been connected between points $A$ and $B$.

Choose the correct option(s)

(a) Total resistance between A and B is $6 \Omega$

(b) The power consumed in the network is 60 W

(d) The current through resistance of $3 \Omega$ in the branch CK is 2 A

NSEJS 2022 Question Paper

Question 1

A particle of mass 0.3 kg starts moving from rest, in one dimension, under a force that delivers constant power $\mathrm{P}=1.5$ watt. The kinetic energy of the particle will be $\mathrm{KE}=15$ Joule after a time of

(a) 5 S

(b) 10 S

(d) 15 S

Question 2

A trolley of mass 200 kg carrying a sandbag of mass 20 kg is moving on a frictionless horizontal track with speed $36 \mathrm{ km} / \mathrm{hr}$. After a while, sand starts leaking out of the bag on the floor of trolley at the rate $0.04 \mathrm{ kg} / \mathrm{sec}$. What is the speed of trolley after the entire sand bag is empty?

(a) $8 \mathrm{ m} / \mathrm{s}$

(b) $9.2 \mathrm{ m} / \mathrm{s}$

(d) $10.8 \mathrm{ m} / \mathrm{s}$

Question 3

A particle, initially at rest at origin, starts moving under acceleration $a$ along +x direction. The acceleration versus time graph is shown in figure. The displacement and the velocity of the particle after 6 second are

(a) 51 meter, $6 \mathrm{ m} / \mathrm{s}$

(b) 33 meter, $6 \mathrm{ m} / \mathrm{s}$

(d) 27 meter, $24 \mathrm{ m} / \mathrm{s}$

Question 4

Gravitational potential energy of a system of two particles of masses $\mathrm{m}_{1}$ and $\mathrm{m}_{2}$, separated by distance r , is given by $\mathrm{U}=-\frac{\mathrm{Gm}_{1} \mathrm{ m}_{2}}{\mathrm{r}}$, where G is the universal Gravitational constant. Consider two stars, each of mass M , initially separated by distance d and at rest with respect to each other. The two stars start moving towards each other under their mutual gravitational attraction. The stars can be treated as point objects and motion is assumed non-relativistic. As measured from the laboratory frame, the speed of each star when they are at a distance $\frac{d}{2}$ apart from each other is

(a) $\sqrt{\frac{\text { GM }}{\text { d }}}$

(b) $\sqrt{\frac{2 G M}{d}}$

(d) $\sqrt{\frac{G M}{4 d}}$

Question 5

An engine approaches a vertical cliff with constant speed $72 \mathrm{ km} /$ hour . When the engine is at a distance of 0.7 km from the cliff, it blows a whistle. The driver hears the echo after a time (Speed of sound in air is $330 \mathrm{ m} / \mathrm{s}$.)

(a) 3.88 S

(b) 4.00 S

(d) 4.24 S

Question 6

A vessel contains a liquid-1 of density $0.8 \mathrm{gm} / \mathrm{cm}^{3}$ over a liquid-2 of density $13.6 \mathrm{gm} / \mathrm{cm}^{3}$. The two liquids are immiscible. A homogeneous solid sphere floats with half of its volume immersed in liquid-1 and other half in liquid-2. The density of the material of the sphere in gm/ $\mathrm{cm}^{3}$ is

(a) 3.3

(b) 6.4

(d) 12.8

Question 7

One fine morning, Mr. Ravi visited Gandhi park with his grandson. When he was just on a bridge over the lake in the park, an old wooden toy 'just' dropped from his hand. The toy went straight down to hit surface of calm water, then sinked into water to a certain depth below water surface and returns back due to upthrust of water to the hands of Mr. Ravi in the same position from where it was dropped. Assuming this position to be at height 19.6 meter above the surface of water, and density of material of toy to be just half the density of water in lake, the total time in which toy is received back to the hand of Mr. Ravi is calculated to be

(a) 2 second

(b) 4 second

(d) 16 second

Question 8

Two plane mirrors OA and OB are inclined at an angle $\theta$ as shown in figure. A ray of light incident parallel to BO strikes the mirror OA at point P . It gets reflected from mirror OA and then reflected from the mirror OB , the ray finally emerges parallel to OA . The value of angle $\theta$ is

(a) $90^{\circ}$

(b) $60^{\circ}$

(d) $30^{\circ}$

Question 9

A long solenoid of length 2 m and radius 10 cm having 2000 turns per meter carries a current of 1.0 A . The strength of magnetic field (B) is maximum at point

(a) A at the left end

(b) C at the right end

(d) P outside the solenoid

Question 10

A tank with a square base of area 2.0 meter $^{2}$ is divided by a vertical partition in the middle. The bottom of the partition has a small hinged door of area $10 \mathrm{ cm}^{2}$. The tank is filled with water in one compartment and a liquid of relative density 1.8 in other compartment, both to a height 5.0 meter. The force necessary to keep the door close is approximately $\left(\mathrm{g}=9.8 \mathrm{ m} / \mathrm{s}^{2}\right)$

(a) 0.04 N

(b) 3.9 N

(d) Zero

Question 11

An electron is projected horizontally towards east in uniform magnetic field B . The electron is deflected towards north by the magnetic field. The magnetic field is directed

(a) East wards

(b) West wards

(d) Downward

Question 12

Sir CV Raman announced the discovery of Raman Effect on February 28, 1928. He received 1930 Nobel Prize in Physics for this discovery. Raman Effect is the discovery of

(a) Dispersion of light

(b) Total Internal Reflection of light

(d) Inelastic scattering of light

Question 13

Figures (i) to (v) show graphical representation of motion in one-dimension. Here $s, v, a$ and $t$ represent the displacement, the velocity, the acceleration and the time respectively.

Which of the above graphs represent uniform motion?

(a) (i) only

(b) (ii) only

(d) (iv) and (v)

Question 14

Three identical electric bulbs $\mathrm{A}, \mathrm{B}$ and C having specification 60 W , 220 V are connected across a 220 V supply as shown. The total power dissipated in three bulbs is close to

(a) 180 W

(b) 60 W

(d) 40 W

Question 15

A copper wire is stretched to decrease its radius by $0.15 %$. The percentage change in the resistance of wire is

(a) $+0.3 %$

(b) $-0.3 %$

(d) $-0.6 %$

Question 16

Speed of sound in air is directly proportional to square root of absolute temperature of air (keeping other parameters constant). The speed of sound in air at 273 K and 1 atom is $332 \mathrm{ m} / \mathrm{s}$. On a clear day, when temperature in the laboratory was $27^{\circ} \mathrm{C}$, an experiment was performed to measure speed of sound in air in the laboratory. The measured value comes out to be $352 \mathrm{ m} / \mathrm{s}$. the percentage error in this measurement is

(a) $0.2 %$

(b) $1.15 %$

(d) $6.02 %$ A - 2

ANY NUMBER OF OPTIONS 4, 3, 2 or 1 IN THE FOLLOWING QUESTIONS MAY BE CORRECT.

Question 17

Two blocks $\mathrm{M}_{1}$ and $\mathrm{M}_{2}$ of masses 3 kg and 6 kg respectively are connected through a string and spring balance $\mathrm{B}_{1}$. The string passes over a massless and frictionless pulley P . The pulley is suspended from a rigid support through spring balance $\mathrm{B}_{2}$. Strings are massless and inextensible. Masses of spring balances are negligible. The system is released from rest. At the instant when masses $\mathrm{M}_{1}$ and $\mathrm{M}_{2}$ are moving with same speed ( $\mathrm{g}=9.8 \mathrm{ m} / \mathrm{sec}^{2}$ )

(a) reading of $\mathrm{B}_{1}$ is 4.5 kg wt.

(b) reading of $B_{1}$ is 4.0 kg wt .

(d) acceleration of $\mathrm{M}_{1}$ is $\frac{9.8}{3} \mathrm{mS}^{-2}$

Question 18

Focal length of a thin convex lens is 10 cm . An object is placed at a distance 15 cm in front of the lens and a plane mirror is kept at 20 cm on the other side as shown in figure.

(a) The final image is formed at distance 10 cm from lens towards the mirror

(b) The final image is formed at a distance 30 cm from lens means 10 cm behind the mirror

(d) The final image has magnification $\mathrm{m}=+2$

Question 19

Given network of 18 resistors, each equal to $\mathrm{R}=3$ ohm, is connected in series with resistor $\mathrm{R}_{0}$ to a source of $\mathrm{emf}=9$ volt. Choose the correct option.

(a) Current drawn from battery is 1.5 A

(b) Potential difference between A and B is 7.5 V

(d) Electrical power dissipated in network between A and B is 12.25 watt.

Question 20

Two bodies of masses $\mathrm{m}_{1}=2 \mathrm{ kg}$ and $\mathrm{m}_{2}=1 \mathrm{ kg}$ are moving towards each other in the same straight line with speed $12 \mathrm{ m} / \mathrm{s}$ and $6 \mathrm{ m} / \mathrm{s}$ respectively as shown in figure. The bodies can be assumed as point masses. After some time, the two bodies undergo elastic collision. After the collision

(a) the two bodies mearly exchange their velocities

(b) $m_{1}$ comes to rest

(d) $m_{1}$ and $m_{2}$ move with same speeds but they reverse their directions of motion. Rough Work

NSEJS 2023 Question Paper

Question 1

Select the correct order of dielectric constant, refractive index and intermolecular forces for water $\left(\mathrm{H}_{2} \mathrm{O}\right)$ and heavy water $\left(\mathrm{D}_{2} \mathrm{O}\right)$ at 293 K respectively among those given below

(i) Dielectric constant $-\mathrm{H}_{2} \mathrm{O}>\mathrm{D}_{2} \mathrm{O}$ (ii) Dielectric constant $-\mathrm{D}_{2} \mathrm{O}>\mathrm{H}_{2} \mathrm{O}$ (iii) Refractive index $-\mathrm{H}_{2} \mathrm{O}>\mathrm{D}_{2} \mathrm{O}$ (iv) Refractive index $-\mathrm{D}_{2} \mathrm{O}>\mathrm{H}_{2} \mathrm{O}$

(v) Intermolecular forces $-\mathrm{H}_{2} \mathrm{O}>\mathrm{D}_{2} \mathrm{O}$ (vi) Intermolecular forces - $\mathrm{D}_{2} \mathrm{O}>\mathrm{H}_{2} \mathrm{O}$ The option containing all correct statements is

(a) (i), (iii), (vi)

(b) (i), (iv), (v)

(d) (i), (iv), (vi)

Question 2

Among the elements of atomic number (Z) from 1 to 92 (i.e., from H to U), the elements having atomic number ____ and ____ are not found in nature.

(a) 89, 92

(b) 83,89

(d) None of these

Question 3

Which state of matter exists at very high temperature and at very low temperature (near absolute zero) respectively? BEC stands for Bose Einstein Condensate.

(a) BEC, fermionic condensate

(b) Plasma, BEC

(d) Gas, BEC

Question 4

Two blocks A and B of masses 1 kg and 4 kg respectively are moving with equal kinetic energies Read the following statements $\mathrm{S}_{1}$ and $\mathrm{S}_{2}$ Statement $\mathrm{S}_{1}$ : Ratio of speed of the block A to that of B is $1: 2$ Statement $S_{2}$ : Ratio of magnitude of linear momentum of $A$ to that of $B$ is $1: 2$ Now choose the correct option:

(a) Both $\mathrm{S}_{1}$ and $\mathrm{S}_{2}$ are true

(b) Both $\mathrm{S}_{1}$ and $\mathrm{S}_{2}$ are false

(d) $\mathrm{S}_{1}$ is false, $\mathrm{S}_{2}$ is true

Question 5

The mass of a straight copper wire is 20.95 g and its electrical resistance is $0.065 \Omega$. If the density and resistivity of copper are $\mathrm{d}=8900 \mathrm{ kg} / \mathrm{m}^{3}$ and $\rho=1.7 \times 10^{-8}$ ohm-meter respectively, the length of the copper wire is

(a) 3 m

(b) 6 m

(d) date is insufficient

Question 6

It is known that the speed of sound in a gas is directly proportional to square root of its absolute temperature T measured in Kelvin i.e. $v \propto \sqrt{T}$ Speed of sound in air at $0^{\circ} \mathrm{C}$ is $332 \mathrm{ m} / \mathrm{s}$. On a hot day, the speed of sound was measured $360 \mathrm{ m} / \mathrm{s}$ in NCR Delhi, the temperature of air in Delhi on that very day must have been close to

(a) $40^{\circ} \mathrm{C}$

(b) $42^{\circ} \mathrm{C}$

(d) $48^{\circ} \mathrm{C}$

Question 7

A small bar magnet is allowed to fall vertically through a metal ring lying in a horizontal plane. During its fall, the acceleration of the magnet in the region close to the ring must be (g is the acceleration due to gravity)

(a) equal to g

(b) less than $g$ and uniform

(d) greater than g and uniform

Question 8

An object pin is placed at a distance 10 cm from first focus of a thin convex lens on its principal axis, the lens forms a real and inverted image of this object pin at a distance 40 cm beyond the second focus. The focal length of the lens is

(a) 16 cm

(b) 20 cm

(d) 40 cm

Question 9

A bullet of mass 0.25 kg moving horizontally with velocity $v(\mathrm{ m} / \mathrm{s})$ strikes a stationary block of mass 1.00 kg suspended by a long inextensible string of negligible mass and length $\ell$. The bullet gets embedded in the block and the system rises up to maximum height $\mathrm{h}=19.6 \mathrm{ cm}$ (as shown in the figure. The string still remains taut). The value of initial speed $v$ of the bullet is

(a) $5.9 \mathrm{ m} / \mathrm{s}$

(b) $7.8 \mathrm{ m} / \mathrm{s}$

(d) $11.8 \mathrm{ m} / \mathrm{s}$

Question 10

The equivalent resistance between points A and B in the following electrical network is

(a) $\frac{3}{4} \Omega$

(b) $\frac{4}{3} \Omega$

(d) $\frac{9}{14} \Omega$

Question 11

The order of magnitude of the pressure (in pascal) exerted by an adult human on the Earth when he stands bare footed on the Earth on both of his legs, is

(a) $10^{2}$

(b) $10^{4}$

(d) $10^{9}$

Question 12

On the board of an experiment, three bulbs $\mathrm{B}_{1}(100 \mathrm{ W}, 200 \mathrm{ V})$, $\mathrm{B}_{2}(60 \mathrm{ W}, 200 \mathrm{ V})$ and $\mathrm{B}_{3}(40 \mathrm{ W}, 200 \mathrm{ V})$ are connected to a 200 V fluctuating supply with a fuse in series as shown in the figure. The electric current rating of the fuse required in the circuit to protect all the three bulbs must be

(a) 0.2 Amp

(b) 0.3 Amp

(d) 1.0 Amp

Question 13

An ant is sitting on the principal axis of a convex mirror of focal length f , at a distance 2 f from the pole in front of the mirror. It starts moving on principal axis towards the mirror. During the course of motion, the distance between the ant and its image

(a) throughout increases

(b) throughout decreases

(d) first decreases, then increases

Question 14

You are given three resistance of values $2 \Omega, 4 \Omega$ and $6 \Omega$. Which of the following values of equivalent resistance is not possible to get by using/arranging these three resistors in any circuit?

(a) Less than $2 \Omega$

(b) Equal to $4.4 \Omega$

(d) Equal to $7.6 \Omega$

Question 15

ABC is a 0.8 meter long curved wire track in a vertical plane. A bead of mass 3 g is released from rest at A . It slides along the wire and comes to rest at C . The average frictional force opposing the motion in a single trip from A to C is

(a) $18.40 \times 10^{-3} \mathrm{ N}$

(b) $29.4 \times 10^{-3} \mathrm{ N}$

(d) $7.36 \times 10^{-3} \mathrm{ N}$

Question 16

Two long straight conductors 1 and 2, carrying parallel currents $\mathrm{I}_{1}$ and $\mathrm{I}_{2}$ in the same direction, are lying parallel and close to each other, as shown in the figure. $\mathrm{F}_{\mathrm{e}}$ and $\mathrm{F}_{\mathrm{m}}$ respectively represent the electric and the magnetic forces, applied by conductor 1 on conductor 2 . Choose the correct alternative regarding nature of $\mathrm{F}_{\mathrm{e}}$ and $\mathrm{F}_{\mathrm{m}}$

(a) $F_{e}$ is repulsive while $F_{m}$ is attractive

(b) $\mathrm{F}_{\mathrm{e}}$ is repulsive and $\mathrm{F}_{\mathrm{m}}$ is repulsive too

(d) $\mathrm{F}_{\mathrm{e}}$ is zero and $\mathrm{F}_{\mathrm{m}}$ is attractive

Question 17

A doctor measures the temperature of a patient by a digital thermometer as $37.3^{\circ} \mathrm{C}$. As a Physics student you will record his temperature in Kelvin as

(a) 310.30 K

(b) 310.45 K

(d) 310.31 K

Question 18

Two planets $P_{1}$ and $P_{2}$ are moving around the Sun, in circular orbits of radii $10^{13} \mathrm{ m}$ and $10^{12} \mathrm{ m}$ respectively. The ratio of the orbital speeds of planets $\mathrm{P}_{1}$ and $\mathrm{P}_{2}$ in their respective orbits is

(a) $\sqrt{10}$

(b) 10

(d) $\frac{1}{\sqrt{10}}$

Question 19

Select the correct statement(s) pertaining to Bohr model of an atom.

(a) An electron near the nucleus is attracted more by the nucleus; thereby has lower potential energy.

(b) An electron continuously radiates energy as long as it revolves in a discrete orbit.

(d) This is the first atomic model based on quantization of energy.

Question 20

The correct order(s) of first ionization energy for the following pairs is/are:

(a) $\mathrm{Ag}<\mathrm{Au}$

(b) $\mathrm{Pd}<\mathrm{Pt}$

(d) $\mathrm{Sb}>\mathrm{Bi}$

Question 21

Crane A and crane B take 1 minute and 2 minute respectively to lift a car of mass 2 ton ( 2000 kg ) upward through a vertical height $h=3$ meter. If the efficiencies of the engines (defined as the ratio of work output to fuel energy input) of both the cranes are equal, your inference is that

(a) the power supplied by crane B is 1000 kW

(b) the crane A and the crane B consume equal amount of fuel

(d) the crane A consumes more fuel in lifting the car than the crane B

Question 22

Two tungsten filament bulbs with rating 100 watt, 200 volt and 60 watt, 200 volt are connected in series with a variable supply of $0-400 \mathrm{ V}$ range, as shown. The supply voltage is gradually increased from 0 to 400 V . Choose the correct statement(s).

(a) When supply voltage is 200 volt, 60 W bulb glows brighter

(b) When supply voltage is 200 volt, total power dissipated in both the bulbs is greater than 37.5 W

(d) When supply voltage becomes 400 V , none of the bulbs glow

Question 23

A solid sphere of radius $R=10 \mathrm{ cm}$ floats in water with $60 %$ of its volume submerged. In an oil, this sphere floats with $80 %$ of its volume submerged. If the density of water is $1000 \mathrm{ kg} / \mathrm{m}^{3}$. The correct statement(s) is/are that

(a) the density of the material of sphere is $600 \mathrm{ kg} / \mathrm{m}^{3}$

(b) the density of the oil is $750 \mathrm{ kg} / \mathrm{m}^{3}$

(d) the loss in weight of the sphere when floating in oil is close to 30.82 N

Question 24

A particle starts moving from origin O along $x$ axis. The velocity-time graph of motion of particle is given below. The positive values of $v$ refer to direction of motion along $+x$ axis, the negative values of $v$ refer to direction of motion along $-x$ direction. Choose the correct statement(s).

(a) Initial acceleration of the particle is $4 \mathrm{ m} / \mathrm{s}^{2}$

(b) The displacement of particle from origin is 130 m after 16 second

(d) Somewhere during the motion for $0-16$ second, the retardation of the particle is $10 \mathrm{ m} / \mathrm{s}^{2}$ Rough Work