NSTSE Sample Paper Class 12 PCM

Class : 12_PCM Mathematics
1. A cylindrical gas container is closed at the top and
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open at the bottom. If the iron plate of the top is
4
times as thick as the plate forming the cylindrical
sides, the ratio of the radius to the height of the
cylinder using minimum material for the same
capacity is:
4 1 4 20
(A) (B) (C) (D)
1 5 5 1

x3 + x x +1 x -2
2x 3 + 3x 1 3x 3x 3
2. If = x A + B, then A = ____
3
x + 2x + 3 2x 1 2x 1

1 1 1 0 1 2
4 0 0 4 0 0
(A) (B)
3 3 3 3 3 3

1 2 3 1 0 0
4 0 1 0 1 0
(C) (D)
3 3 3 0 0 1

3. Which of the following is a root of the following equation ?
0 x a x b
x+a 0 x c =0
x+b x+c 0
(A) a (B) b (C) 0 (D) 1

1

1 0
4. If A = 1 , then A100 is equal to:
1
2

1 0
100 1 0
(A) 1 (B)
1 25 1
2

1 0 1 0
(C) 50 1 (D) 100 1

a1 b1 c1
5. If Δ = a2 b2 c2 , then find the value of
a3 b3 c3

2a1 + 3b1 + 4c1 b1 c1
2a2 + 3b2 + 4c2 b2 c2
2a3 + 3b3 + 4c3 b3 c3
1
(A)  (B) 2  (C)  (D) (2×3×4) 
2

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Class : 12_PCM Physics
6. A conducting loop, carrying a current I is placed in a
uniform magnetic field pointing into the plane as shown.
What tendency will the loop have ?
B
X

(A) It contracts
(B) It expands
(C) It moves towards positive X-axis
(D) It moves towards negative X-axis
7. Study the given information.
When a rod of certain substance ‘X’ is suspended
in a magnetic field, it quickly aligns itself along
the direction of the magnetic field. Secondly, the
substance ‘X’ moves from weaker part of the
magnetic field to the stronger part.
Based on the above information, what could
substance ‘X’ be ?
(A) Aluminium (B) Gold
(C) Oxygen (D) Gadolinium
8. A current of 20 A is maintained in a conductor of cross
section 0.0001 m2. If the number of free electrons is
9 × 1030 m-3, calculate the drift velocity of free electrons.
(Take e = 1.6 × 10–19C.)
(A) 0.138 × 10-6 m s-1 (B) 0.1125 × 10-6 m s-1
(C) 0.35 × 10-6 m s-1 (D) 6.94 × 10-6 m s-1

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9. The image obtained with a convex lens is erect and its
length is four times the length of the object. If the
focal length of the lens is 20 cm, calculate the object
and image distance.
(A) + 10 m, + 20 m (B) – 15 cm, – 60 cm
(C) – 10 m, + 40 m (D) + 12 cm, – 24 cm.
10. Calculate the potential at the centre of a square PQRS
of each side 2 m due to charges 2, –2, –3 and 6  C at
four corners of it.
(A) 2.7 × 104 V (B) 3.8 × 106 V
(C) 4.5 × 107 V (D) 5.3 × 108 V

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Class : 12_PCM Chemistry

11. Identify how is the monomer used for the manufacture
of PVC obtained.
(A) Addition of HCl to acetylene in the presence of Hg+2 salts
(B) Addition of HCl to ethylene in the presence of Hg+2 salts
(C) A d d i t i o n o f Cl 2 to acetylene
(D) Addition of Cl2 to ethylene
12. Which of the following is the ideal condition for the
manufacture of H2SO4 by contact process ?
(A) Low temperature, high pressure and high concentration
of reactants.
(B) Low temperature, low concentration of reactants and
low pressure.
(C) High temperature, high pressure and high concentration
of reactants.
(D) Low temperature, low pressure and high concentration
of reactants.
13. What is tempering ?
(A) The process of heating steel to bright red heat and
then cooling it slowly.
(B) The process of heating the quenched steel to a
temperature much below redness and cooling it slowly.
(C) The process of heating to bright red heat and then
cooling suddenly by plunging it in oil or water.
(D) The process of giving a thin coating of hardened steel
to a strong flexible, mild steel by heating in contact
with charcoal and quenching in oil.

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14. Why are amorphous solids considered to be super
cooled liquids ?
(A) As they melt sharply at their melting points.
(B) As they exist in a solid state.
(C) As they soften on heating.
(D) As long range order is absent in them.
15. Study the given description of a complex ion.
• It is an octahedral complex ion which is
paramagnetic in nature
• It has an inner orbital complex ion
Based on the given information identify the complex
ion.
(A) [Fe(H2O)6]3+ (B) [FeF6]3-
(C) [CuCl4]3- (D) [Fe(CN)6]3-

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Class : 12_PCM Critical Thinking
16. Recognize the tool in the question and choose the
most closely related tool or object from the given
choices.

(A) (B)

(C) (D)

17. You are interviewd for a new job. Which of the
following questions is most important to you ?
(A) Opportunities for promotions.
(B) Remuneration you will be paid.
(C) Scope to develop your ideas and use them to improve
the working of the organisation.
(D) All the above are equally important.

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18. Identify the 3-dimensional object from the given three
views.

(A) (B) (C) (D)

19. Recognize the tool in the question and choose the
most closely related tool or object from the given
choices.

(A) (B) (C) (D)

20. Three pencils cost the same as two erasers.
Four erasers cost the same as one ruler.
Pencils are more expensive than rulers.
If the first two statements are true, the third statement is
(A) True (B) False
(C) Uncertain (D) None of these

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