This document contains an admission test paper for Class X subjects of Physics and Mathematics. The Physics section consists of 20 multiple choice questions covering topics like scalar and vector quantities, forces, pressure, heat, light, electricity and magnetism. The Mathematics section consists of 10 questions and covers topics like ratios, percentages, profit and loss, simple and simultaneous equations, trigonometry, geometry, logarithms and trigonometric functions. It directs students to answer questions from specified sections and provides the full time duration and marking scheme for the test paper.

1. Admission test paper
Class – X
Subject – Physics and maths
Set – II
Section – I (40 Marks)
Note :- This section is compulsory. Answer all the questions from this section.
Question – 1.
(a) Distinguish between scalar and vector quantities.
(b) An aeroplane touches down at 225 km hr-1 and stops after 2 minutes. Calculate (i)
acceleration (ii) length of runway. [Ans. (i) – 0.52 ms-2 (ii) 3756 m]
(c) State four effects which a force can bring about. Give two examples in each case.
(d) State two disadvantages of friction.
(e) A force of 525 N, produces a moment of force of 420 N-m. Calculate the shortest
distance between the point of application of force and the turning point. [Ans. 0.8 m]
(f) Explain, why passengers are not allowed to stand in a boat in midstream.
(g) The atmospheric pressure at a place is 650 mm of Hg. Calculate this pressure in
Pascals (Pa). [Ans. 88400 Pa]
(h) An inflated balloon is placed inside a big glass jar which is connected to an
evacuating pump. What will you observe when the evacuating pump starts working ?
Give a reason for your answer.
(i) Convert 108 º F into Celcius scale. [Ans. 42.22 º C]
(j) A metal cube of side 5 cm at 20 º C is heated, when its each side becomes 5.05 cm at
820 º C. Calculate the values of coefficients of linear, superficial and cubical expansion.
[Ans. α = 0.0000125 / º C, β = 0.0000250 / º C, γ = 0.0000375 / º C]
(k) At what temperature does water have maximum density?
(l) Why are double glass window panes used in cold countries?
(m) State the factors that determine the size of an image in a pin hole camera.
(n) Give two uses of a concave mirror.
(o) An electric tuning fork completes one oscillation in 0.000125 s. Calculate the
frequency of tuning fork. Will the sound emitted by tuning fork be audible? Give reason.
[Ans. 8000 Hz]
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2. (p) Explain why lightning flash is seen before thunder is heard?
(q) What are insulators? Give four examples of insulators.
(r) A dry cell can supply a charge of 50 C. If the current drawn from the cell is 750 μA,
find the time in which the cell completely discharges.
[Ans. 6.67×104 s]
(s) Briefly describe the theory of simple voltaic cell.
(t) What do you understand by the term magnetic declination?
SECTION – II (40 Marks)
Answer ANY FOUR questions from this section.
Question – 2.
(a) Draw a diagram to show the motion of body whose speed remains constant, but
velocity changes continuously.
(b) Prove : v2 – u2 = 2aS, where u = initial velocity, v = final velocity, a = acceleration
and S = distance covered. How is dyne related to Newton?
(c) Why are passengers traveling in a double-decker bus allowed to stand in the lower
deck, but not in the upper deck?
Question – 3.
(a) State four advantages of aneroid barometer.
(b) State Archimedes’ Principle.
(c) A block of mass 7 kg and volume 0.07 m3 floats in a liquid of density 140 kg/m3.
Calculate : (i) Volume of block above the surface of liquid, (ii) Density of block.
[Ans. (i) 0.02 m3 (ii) 100 kg m-3]
Question – 4.
(a) Give six reasons for using mercury as thermometric liquid.
(b) State two advantages and two disadvantages of thermal expansion of solids.
(c) What do you understand by the term anomalous expansion of water? How do fishes
survive in frozen lakes?
Question – 5.
(a) Why does a metal chair feels much colder than a wooden chair in winter?
(b) Why does the land become warmer than water during the day?
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3. (c) Why is a vessel containing liquid always heated from below rather than from the
sides?
Question – 6.
(a) Why are the shadows produced by fluorescent tubes far lighter than the shadows
produced by filament bulb?
(b) Draw a diagram to show reflection of a ray of light using plane mirror. In the diagram
label the incident ray, the reflected ray, the normal, the angle of incidence and angle of
reflection. State the laws of reflection.
(c) What is a real image? What type of mirror is used to obtain a real image of an object?
Does the mirror named by you above gives real image for all locations of object?
Question – 7.
(a) A continuous disturbance is created on the surface of water in a ripple tank with a
small piece of cork floating on it. Describe the motion of the cork. What does the motion
of the cork tell about the disturbance?
(b) Charging by friction is accompanied by loss or gain of electrons. In the following
cases which body loses the electrons and which body gains the electrons when :
(i) the glass rod is rubbed with the silk
(ii) an ebonite rod is rubbed with fur.
(c) How will you differentiate between an insulator and a conductor by using charged
electroscope?
Question – 8.
(a) Describe an experiment to prove that electric charge resides on the outer surface of
conductor.
(b) What do you understand by the term electric potential?
(c) What do you understand by the term parallel circuit ? State two characteristics of
resistance in the parallel circuit. Draw a diagram showing two bulbs connected in parallel
to a dry cell.
Question – 9.
(a) Repulsion is a surest test of magnetic condition of a body than attraction. Explain.
(b) Give the various methods for demagnetizing a magnet.
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4. (c) Draw a clearly labelled diagram, to show how a steel bar is magnetized by a divided
touch method and explain the process.
Subject – Mathematics
[Time – Two hours and a half]
SECTION – I (40 Marks)
Note :- This section is compulsory. Answer all the questions from this section.
Question – 1.
(a) Insert a rational number between 2/9 and 3/8 and arrange them in ascending order.
(b) Find the square root of 5 correct to three significant figure.
(c) Convert 4/5 into percentage.
(d) Find a single discount equivalent to three successive discounts of 20%, 10% and 5%.
(e) Calculate the simple interest on Rs1200 for 3 years 9 months at 5% p.a.
Question – 2.
(a)If x + 1/x = 3, find the value of x2 + 1/x2.
(b) Factorize : x2 + 5x + 6.
(c) P = m/(m + n), make ‘m’ as a subject and write the formula.
(d) Solve the equation : x + 1 = √2 (1 – x).
(e) Solve the simultaneous equation :
2/x + 2/3y = 1/6 ; 3/x + 2/y = 0
Question – 3.
(a) Simplify the following :
(xa + b/xc)a – b(xb + c/xa)b – c(xc + a/xb)c – a .
(b) In the figure given below, AB and CD intersect at O. Find the value of x, LAOC and LCOB.
Fig.
(c) In the figure given below AB is parallel to CD. Find the value of x.
Fig.
(d) In the figure given below, D, E and F are mid-points of the sides BC, CA and AB respectively of Δ ABC. If AB = 6
cm, BC = 4.8 cm and CA = 5.6 cm, find the perimeter of the triangle DEF.
Fig.
(e) In the figure given below, DE is parallel to BC , AD = 3 cm, BD = 4 cm and BC = 5 cm, find DE.
Fig. Q.1(ii)/page 272 [TB]
Question – 4.
(a) Find the measure in degree of an angle of a regular hexagon.
(b) If the height of an equilateral Δ is 8 cm, calculate its area.
(c) If the total surface area of a cube is 384 cm2, find its volume.
(d) In the figure given below, ABC is a right angled triangle, right angle at B and tan A = 3/4. If AC = 15 cm, find the
length of AB and BC.
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5. Fig.
(e) Evaluate the following :
(sin 31º/cos 59º)2 + (cos 59º/sin 31º)2 – 4sin2 45º.
SECTION – II (40 Marks)
Answer ANY FOUR questions from this section.
Question – 5.
(a) Prove that √3 is an irrational number. Hence show that √3 + √2 is an irrational number.
(b) A candidate who gets 20% marks in an examination fails by 30 marks, but another candidate, who gets 32% marks,
gets 42 more marks than the minimum pass marks. Find the pass percentage of marks.
(c) A sum lent on simple interest becomes Rs7890 in 3 years and Rs10410 in 7 years. Find the sum and the rate of
interest.
(d) If a2 + b2 + c2 = 125 and ab + bc + ca = 50, find a + b + c.
Question – 6.
(a) Factorize : a6 – b6.
(b) Make v the subject of the formula 1/f = 1/u + 1/v. Find the value of v when f = 6 and u = 14.
(c) If p = 3x + 1, q = 1/3(9x + 13) and p:q = 6:5, find x.
(d) Solve the following equations graphically :
2y – x = 8 ; y – 2x = 1.
Question – 7.
(a) A two digit number is seven times the sum of its digits. The number formed by interchanging the digits is 18 less
than the original number. Find the number.
(b) If a = b2x, b = c2y and c = a2z, prove that xyz = 1/8.
Question – 8.
(a) Use log table to evaluate the following :
(10.23)3/502.0.
(b) Draw a straight line AB = 5.5 cm. Mark a point C on AB such that AC = 2 cm. Draw a perpendicular to AB at C.
(c) In the figure given below, AB is parallel to CD. Find the value of x, y and z.
Fig
(d) Construct a triangle ABC such that AB = 5 cm, BC = 5.5 cm and CA = 4.6 cm.
Question – 9.
(a) In Δ ABC, LA = 90º and AD is perpendicular to BC. Calculate DC and AC given that AB = 5 cm and AD = 3 cm.
(b) Construct a quadrilateral ABCD such that AB = 4 cm, BC = 2.8 cm, AD = 4.1 cm, LA = 90º and LB = 120º.
(c) Prove that area of a trapezium = 1/2(sum of parallel sides)×height.
Question – 10.
(a) The parallel sides AB and DC of a trapezium ABCD are 51 cm and 30 cm respectively. The sides AD and BC are
20 cm and 13 cm respectively. Find the distance between parallel sides and the area of the trapezium.
(b) The radius and height of a cylinder are in the ratio 2:7. The volume of the cylinder is 704 cm3, Find the total surface
area of the cylinder. [Tale π = 22/7].
(c) If 4 sin2 θ – 1 = 0 and θ is less than 90º, find the value of θ and hence the values
(i) cos2 θ + tan2 θ (ii) cos 2θ (iii) sin 3θ.
Best of luck
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