MATHEMATICS

Quiz from 1 to 5
QUIZ-1
Q.1 In the diagram, ABCD is a parallelogram, and BFDE is a square. If
AB = 20 cm and CF = 16 cm, what is the perimeter of the
parallelogram ABCD?
(A) 86 cm (B) 92 cm
(C) 96 cm (D) 106 cm

Q.2 Given three segments of length x, 11 – x, and x – 4, respectively. Which of the following indicates the set
of all numbers x such that the three segments could be the lengths of the sides of a triangle?
(A) x > 4 (B) 5 < x < 7 (C) 4 < x < 11 (D) 0 < x < 11

Q.3 A rhombus is formed by two radii and two chords of a circle whose radius is 16 cm. Find the area of the
rhombus.
(A) 128 3 cm2 (B) 128 cm2 (C) 256 cm2 (D) 256 3 cm2

Q.4 Two congruent 30° – 60° – 90° triangles are placed, as shown, so that
they overlap partly and their hypotenuses coincide. If the hypotenuse is
12cm, find the area common to both triangles.
(A) 6 3 cm2 (B) 8 3 cm2
(C) 9 3 cm2 (D) 12 3 cm2

Q.5 A circular arch having width 24m and height 9m is to be constructed. What is the radius of the circle of
which the arch is an arc?
(A) 10m (B) 12.5 m
(C) 13.5m (D) 14m

QUIZ-2

Q.1 The minute hand of a clock travels k radians from 1 pm to 2.35pm. The value of k is ________.

Q.2 The number palindrome 1 2 3 4 3 2 1 is a perfect square. Its positive root is _____.
2
The real number  75  12 
3
Q.3 when expressed in the simplest form is equal to
 
(A) 1/2 (B) 1/3 (C) 1/4 (D) 1/5

Q.4 The sum of the solutions on the interval (0, 2] to the equation:

 
 sin 3 x  sin x 
0 = – 2 sin 2 x  2 cos 2 x 
cos x
 , is (cos x  0 )

 
(A) 3 (B) 4 (C) 5 (D) 6
Q.5 Twice the measure of the supplement of an angle is added to three times the measure of the complement
of the same angle. The sum is the measure of an interior angle of a regular nine-sided polygon. The
measure of the supplement of the angle, is
(A) 82° (B) 72° (C) 98° (D) 108°
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Q.6 Let XOY be a right triangle with XOY = 90°. Let M and N be the midpoints of legs OX and OY
respectively. If XN = 19 and YM = 22, then XY equals
(A) 26 (B) 13 5 (C) 32.5 (D) 41

QUIZ-3

Q.1 If (1, 2) is one of the points of intersection of the graphs of ax 2 + by2 = 5 and bx2 + ay2 = 5, then find
a + b.
(A) 2 (B) 3 (C) 4 (D) 5

Q.2 Given parallelogram ABCD, with AB = 10, AD = 12 and BD = 2 13 . The length of (AC) is
(A) 10 (B) 2 13 (C) 12 3 (D) 2 109

1
Q.3 The continued fraction 2  , has the value equal to
1
2
1
2
2  ...........
(A) 1 (B) 5/4 (C) 3/2 (D) 7/4

Q.4 If x2 – xy + y2 = a and x3 + y3 = b then xy =

b2 b2 b b2  a 3 a 2  2b 3
(A) –1 (B) 2  (C) (D)
a2 3a 3 3a 2 3a

Q.5 A square and an equilateral triangle have the same perimeter. Let A be the area of the circle circumscribed
about the square and B be the area of the circle circumscribed about the triangle. The ratio A/B equals
(A) 9 : 16 (B) 3 : 4 (C) 27 : 32 (D) 3 6 : 8

Q.6 ABC is a right triangle with hypotenuse AB and AC = 15 cm. Altitude

CH divides AB into segments AH and HB, with HB = 16cm. The area
of ABC, is
(A) 120 cm2 (B) 144cm2 (C) 150cm2 (D) 216cm2

QUIZ-4

Q.1 Three identical squares are place side-by-side as indicated in the figure.
Lines are then drawn from O to A and from O to B. Find the measure of
angle AOC plus angle BOC, is ________.

Q.2 The number 18  308 can be written in the form a  b where a and b are whole numbers and
a > b. The value of (a – b), is
(A) 4 (B) 12 (C) 16 (D) 18

Q.3 Consider the eight digit number N = 11115556. Which of the following statements are true?
I. N is divisible by 11
II. N – 9 is a prime
III N is a perfect square
(A) I (B) II (C) III (D) I, II and III
Q.4 If 0 < x < 2 and 2tan x = 4sin x then the number of value of x is ________.
(A) 1 (B) 2 (C) 3 (D) 4

Q.5 The value of the series

1 + 2 – 3 – 4 + 5 + 6 – 7 – 8 + 9 + ... – 99 – 100, is
(A) –100 (B) 0 (C) 1 (D) 100

QUIZ-5
Q.1 The sum of the digits of the integral solution of the equation 14  32  x  1 = 4 is
(A) 785 (B) 765 (C) 20 (D) 18

Q.2 Given the following system of equations

1 1 1 1 1 1 1 1 1
  ;   ;  
x y 3 x z 5 y z 7
z
The value of the ratio is
y
(A) 17 (B) 23 (C) 29 (D) 31

2
Q.3 The equation 2 x = 162x – 3 has two solutions. Their sum is
(A) 0 (B) 2 (C) 6 (D) 8

Q.4 If sin2x + sin x cos x – 6cos2x = 0 and   x  0 , then the value of tan x, is
2
(A) 0 (B) – 3 (C) 2 (D) –6

5 
Q.5 If sin  =  and  is in Quadrant III, then the value of cos  , is
13 2
6 1 5 26
(A)  (B) (C)  (D) 
13 26 12 26

ANSWERS
QUIZ-1
Q.1 C Q.2 B Q.3 A Q.4 D Q.5 B
QUIZ-2
57
Q.1 Q.2 1111 Q.3 B Q.4 A Q.5 A
18
Q.6 A
QUIZ-3
Q.1 A Q.2 D Q.3 A Q.4 C Q.5 C
Q.6 C
QUIZ-4
Q.1 45° Q.2 A Q.3 C Q.4 B Q.5 D
QUIZ-5
Q.1 C Q.2 C Q.3 D Q.4 B Q.5 D
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 MATHEMATICS
Quiz from 6 to 9
QUIZ-6 (CLASS-XI)
cos 5x  cos 3x
Q.1 The value of the expression at x = /8, is _______.
sin 5x  sin 3x

 
Q.2 If y = 2 sin  2x   – 1 then the largest possible value of y for all real x, is
 2
(A) 1 (B) 2 (C) 3 (D) 0
Q.3 Which of statements I, II and III and IV below are true?
I cos  = cos(–) for all angles .
II sin  = sin(–) for all angles .
III cos  = cos(–) for some angles .
IV sin  = sin(–) for some angles .
(A) I, III, IV but not I (B) I and III but not II or IV
(C) I and IV but not II or III (D) III and IV but not II or III
Q.4 Number of sides in a polygon if the sum of its interior angles is 2520°, is
(A) 14 (B) 16 (C) 18 (D) 20
Q.5 Suppose ABCD is a quadrilateral inscribed in a circle. Then among the following identities how many are
always true.
I sinA = sinC
II sinA + sinC = 0
III cosB + cosD = 0
IV cosB = cosD
(A) 0 (B) 1 (C) 2 (D) 3
Q.6 Value of sin 705° is
6 2 2 6 3 2 1 3
(A) (B) (C) (D)
4 4 4 2
QUIZ-7 (CLASS-XI)

Q.1 If the base of a triangle is increased 66. 6 % and the altitude to this base is decreased 40% then the
change in the area of the triangle, is
(A) 1% increase (B) 0% increase (C) 1/2% decrease (D) 1% decrease

x2 2x  1
Q.2 The value of the parameter m for which the equation = has no solution for x, is
3x  1 6 x  m
(A) 12 (B) 18 (C) 14 (D) 13
Q.3 The value of x such that 4(1 + y)x2 – 4x + 1 – y = 0 is true for all real values of y, is
(A) – 1/2 (B) – 2/3 (C) 2/3 (D) 1/2
Q.4 Knowing that 2 is a solution of the equation 6x 3 – 25x2 + 32x – 12 = 0, the sum of the other two
solutions, is
(A) – 12/5 (B) 12/5 (C) – 13/6 (D) 13/6

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Q.5 Suppose that x & y are numbers such that sin (x + y) = 3/10 and sin (x – y) = 1/2. The value of sinx·cosy
is
(A) 0.1 (B) 0.2 (C) 0.3 (D) 0.4
Q.6 A circle of area 20 is centered at the point indicated by a solid dot in the
accompanying figure. Suppose that ABC is inscribed in that circle and
has area 8. The central angles ,  and  are as shown. What is the value
of sin  + sin  + sin ?
4 3 2 
(A) (B) (C) (D)
5 4 3 2
QUIZ-8 (CLASS-XI)
Q.1 Solve for x, given that 3x + 2 = 3x + 216.

Q.2 A rectangular closed box (shown) with dimensions a, 2a and 1

has a surface area of 54, where a is an integer. Determine the
volume of the box.

Q.3 Compute the sum of the first 99 terms of the series (a > 0, a  1)
logaa – logaa2 + logaa3 – logaa4 + logaa5 – logaa6 + ...........

Q.4 In the figure, each region T represents an equilateral triangle

and each region S a semicircle. The complete figure is a semicircle
of radius 6 with its centre O. The three smaller semicircles touch
the large semicircle at points A, B and C. What is the radius of
a semicircle S?

Q.5 The lengths of the sides of triangle ABC are 60, 80 and 100
with  A= 90°. The line AD divides triangle ABC into two
triangles of equal perimeter. Calculate the length of AD.

QUIZ-9 (CLASS-XI)

Q.1 If a + b = 1 and a2 + b2 = 85, then the value of (a3 + b3), is

(A) 127 (B) 173 (C) 154 (D) 321
Q.2 The set of values of k for which the sum of the roots of P(x) = 4x2 + k2x + k is equal to twice the product
of the roots is
(A) {–2} (B) {–2, 0} (C) {0} (D) {2}

Q.3 If a b = 3 4 and b c = 8 9 and c d = 2 3 , then ad b 2 is equal to

64 61 81 84
(A) (B) (C) (D)
81 84 64 61
Q.4 Number of diagonals in a regular polygon with 20 sides, is
(A) 170 (B) 180 (C) 190 (D) 200
Q.5 If two real numbers x and y satisfy the equation x y = x – y, then which of the following is true?
(A) Both x and y must be rational. (B) It is possible that y = 1.
(C) Both x and y must be irrational. (D) x  4 or x  0

3
Q.6 Solve 6 x  28  3 6 x  28 = 2.
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 QUIZ-10 (CLASS-XI)
Q.1 John has taken n tests. If he receives 71 on the next test, his average will be exactly 83. If he receives 99,
then the average will be exactly 87 then the the value of n, is
(A) 6 (B) 5 (C) 8
(D) there is not enough information provided to answer the question

Q.2 If x + y = 1 and x2 + y2 = 4, then what x3 + y3 equal?

11 5 5 11
(A) or (B) 10 (C) (D)
2 2 2 2
Q.3 Find the number of triangles with sides of integer length whose perimeter is 10.
(A) 4 (B) 3 (C) 2 (D) 0
Q.4 If a and b are positive real numbers such that b > a, and c and d are negative real numbers such that
d > c, then which of the following statements must be true?
b a
I > II b – d > a – c III (a + d)(b + c) > (a + c)(b + d)
d c
(A) only I (B) only II (C) only III (D) only II and II
Q.5 A and B are points on the circumference of a circle of radius r and centre O. If the distance between A
and B is r, find the measure of angle AOB in radian.

Q.6 Three mutually tangent circles of equal radius two, are shown in the
figure. Find the area of the shaded portion between the three circles.

QUIZ-11 (CLASS-XI)

1 1
Q.1 If x > 0 such that x + = 4 then the value of x3 + 3 is
x x
(A) 60 (B) 52 (C) 64 (D) 12 (E) none
1
Q.2 Simplify: 2  .
1
3
1
2
1
3


2 3 29  1 14 15
(A) 1 + (B) (C) 1 (D) 1 +
3 2 3 3
Q.3 A marble of diameter 2 is dropped into a conical cup of height 4 and radius 3. When it gets stuck, how
high is the bottom of the marble above the vertex of the cone?
(A) 1/3 (B) 2 3 (C) 2 3 (D) 3 3

(2  1)(2 2  1)(24  1)(28  1)(216  1)  1

Q.4 Evaluate:
233
(A) 1/4 (B) 1/2 (C) 1 (D) 2
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x 1 x
4  8  2
Q.6 Solve system of equations
x + 2y – z = 5
3x + 2y + z = 11
(x + 2y)2 – z2 = 15

ANSWERS KEY

Quiz-10 (Class-XI)

Q.1 A Q.2 D Q.3 C

Q.4 C Q.5 /3 Q.6 4 3  2

Quiz-11 (Class-XI)

Q.1 B Q.2 D Q.3 C

Q.4 B Q.5 2 Q.6 x = 4; y = 0; z = – 1

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