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NAS-X_Cycle 2 : : 2017-18 MATHEMATICS Test Form-23 1
NAS-X_Cycle 2 : : 2017-18 MATHEMATICS Test Form-23
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NAS-X_Cycle 2 : : 2017-18 MATHEMATICS Test Form-23
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Q.1 The roots of the equation ax2 + bx + c = 0 are
1.
2 4
2
± −b b ac
a
2.
4
2
± −b b ac
c
2
3.
4
2
− ± −b b ac
a
2
4.
2
4− ± −
a
b b ac2
Q.2 The mean of x –2a, x – a, x , x + a, x + 2a is
1. x
2. 5x
3. a
4. not possible to find unless value of a is given
Q.3 Which one of the following statements is true?
1. Every integer is a whole number
2. Every rational number is an integer
3. Every irrational number is a real number
4. Every real number is an irrational number
Q.4 The value cos 30o . cos 60
o – sin 30
o . sin 60
o is
1. 2
2. 1
3. 0
4. 3
2
Q.5 If A (– 5, 7), B (– 4, – 5), C (– 1, – 6) and D (4, 5) are the vertices of a quadrilateral, then
the area of the quadrilateral ABCD is:
1. 53 sq. units
2. 72 sq. units
3. 27 sq. units
4. 35 sq. units
NAS-X_Cycle 2 : : 2017-18 MATHEMATICS Test Form-23
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Q.6 In the given figure, O is the centre of the circle. If ∠ACB = 30°, then ∠AOB is equal to
1. 30°
2. 45°
3. 60°
4. 75°
Q.7 In the given figure, PQRS is a quadrilateral which circumscribes a circle with centre O.
If PA = 4 cm, QB = 3 cm, RC = 6 cm and SD = 5 cm, then QR is equal to
1. 7 cm
2. 8 cm
3. 9 cm
4. 10 cm
Q.8 Two poles AB = 6 m and CD = 11 m stand on a ground as shown in the figure. If
BC = 12 m, then AD is equal to
1. 13 m
2. 15 m
3. 17 m
4. 18 m
NAS-X_Cycle 2 : : 2017-18 MATHEMATICS Test Form-23
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Q.9 In the given figure, DE � BC. If AD = 2 cm, AB = 5 cm and DE = 3 cm, then BC is
equal to
1. 5 cm
2. 6 cm
3. 6.5 cm
4. 7.5 cm
Q.10 ABCD is a cyclic quadrilateral. If ∠ABC = 70°, then ∠ADC is equal to
1. 20°
2. 70°
3. 110°
4. 140°
Q.11 P is a point at a distance of 10 cm from the centre O of a circle and PQ and PR are
tangents to the circle. If radius of the circle is 6 cm, then the area of quadrilateral PQOR
is equal to
1. 24 cm2
2. 36 cm2
3. 48 cm2
4. 96 cm2
Q.12 One diagonal of a rhombus is 24 cm and its side is 13 cm. The length of the second
diagonal is
1. 5 cm
2. 10 cm
3. 12 cm
4. 15 cm
NAS-X_Cycle 2 : : 2017-18 MATHEMATICS Test Form-23
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Q.13 ∆ABC ~ ∆DEF, ar (∆ABC) = 64 cm2 and ar (∆DEF) = 144 cm
2. If EF = 6 cm, then BC is
equal to
1. 2 cm
2. 3 cm
3. 4 cm
4. 6 cm
Q.14 The two tangents drawn from an external point P to a circle with centre O are
perpendicular to each other. If length of each tangent is 6 cm, then radius of the circle is
1. 3 cm
2. 6 cm
3. 9 cm
4. 12 cm
Q.15 In ∆ABC and ∆DEF if ∠ B = ∠ E, ∠ F = ∠ C and AB = 2DE, then two triangles are
1. congruent but not similar
2. similar but not congruent
3. neither congruent nor similar
4. congruent as well as similar
Q.16 In the given figure, DE � BC. If AC = 20 cm, EC = 5 cm and DE = 12 cm, then BC is
equal to
1. 15 cm
2. 16 cm
3. 18 cm
4. 24 cm
NAS-X_Cycle 2 : : 2017-18 MATHEMATICS Test Form-23
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Q.17 If ∆ ABC ≅ ∆ PQR , then which of the following is true?
1. B ↔ R
2. C ↔ Q
3. A ↔ R
4. A ↔ P
Q.18 If a1, a2, a3 , ... upto a21 are in A.P. with common difference d ,
then a1 , a5 , a9 , a13
1. must be in A.P. with common difference 16 d
2. must be in A.P. with common difference d
3. must be in A.P. with common difference 4 d
4. may not be in A.P.
Q.19 The median of the numbers 4, 15, 19, 21, 6 is
1. 19
2. 15
3. 15.5
4. 17
Q.20 The product of a non-zero rational and an irrational number is
1. always irrational
2. always rational
3. rational or irrational
4. one
Q.21 AOB is a sector of a circle of radius 4 cm subtending an angle of 45o at the centre ‘O’ of
the circle. Area of the sector, in cm2, is
1. π 2. 2 π
3. 3 π
4. 4 π
NAS-X_Cycle 2 : : 2017-18 MATHEMATICS Test Form-23
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Q.22 In the given figure, AB is a diameter of the circle with centre O. If OD = BD = OB and
CD⊥ΑΒ, then C A B∠ is equal to
1. 30°
2. 45°
3. 50°
4. 60°
Q.23 In the given figure, if AC and BD intersect at P, then ∠ PBA is equal to
1. 30°
2. 70°
3. 80°
4. 100°
Q.24 The distance between the points A (5, – 8) and B (– 2, 3) is
1. 170
2. 34
3. 18
4. 10
Q.25 If ,
1
5θcos = then θtan is equal to
1. 6
2. 3 6
3. 6 2
4. 2 6
NAS-X_Cycle 2 : : 2017-18 MATHEMATICS Test Form-23
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Q.26 If A = 60° and B = 30°, then sin A cos B – cos A sin B is equal to
1. 1
2
2. 1
2
3. 3
2
4. 3
Q.27 If tan A = cot B, then A + B is equal to
1. 90°
2. 60°
3. 45°
4. 30°
Q.28 If the area of an equilateral triangle is 216 3 cm , then the perimeter of the triangle is
1. 8 cm
2. 16 cm
3. 24 cm
4. 32 cm
Q.29 A cone and a cylinder stand on equal bases and have the same height. The ratio of
their volumes is
1. 1 : 3
2. 1 : 2
3. 2 : 3
4. 2 : 1
Q.30 If the surface area of a sphere is 324 π cm2, then its volume is
1. 972 π cm3
2. 960 π cm3
3. 729 π cm3
4. 546.75 π cm3
NAS-X_Cycle 2 : : 2017-18 MATHEMATICS Test Form-23
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Q.31 The curved surface area of a right circular cone, with slant height 16 cm and base
diameter 14 cm, is (Take π 22=7
)
1. 112 cm2
2. 224 cm2
3. 352 cm2
4. 704 cm2
Q.32 If the radius and height of a solid cylinder are 7 cm and 30 cm respectively, then the
volume of the cylinder is (Take π 22=7
)
1. 660 cm3
2. 1320 cm3
3. 2310 cm3
4. 4620 cm3
Q.33 A bag contains 5 white balls, 7 red balls and 2 blue balls. One ball is drawn at random
from the bag. What is the probability that the ball drawn is 'not white'?
1. 5
14
2. 1
2
3. 1
7
4. 9
14
Q.34 If angle between two radii of a circle is 140°, then the angle between tangents at the
ends of the radii is
1. 40°
2. 70°
3. 90°
4. 140°
NAS-X_Cycle 2 : : 2017-18 MATHEMATICS Test Form-23
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Q.35 Mean of 100 numbers was found to be 50. But later on, it was observed that one of the
number 150 was wrongly taken as 50 at one place. The correct mean is
1. 49
2. 50
3. 51
4. 52
Q.36 The vertices of a triangle are (4, 5), (1, 3) and (6, 7). The area of the triangle is
1. 9 sq units
2. 2 sq units
3. 1 sq unit
4. 12 sq units
Q.37 There is a cylinder of height 30 cm and its radius is 14 cm. It is melted to form a new
cylinder of radius 7 cm. The height of the new cylinder is
1. 100 cm
2. 120 cm
3. 140 cm
4. 150 cm
Q.38 If sinθ 1
= ,2
then θ2cosec is equal to
1. 1
4
2. 2
3. 1
4. 4
Q.39 For the frequency distribution :
Class 10-20 20-30 30-40 40-50 50-60
Frequency 43 34 65 71 56
The class mark of the modal class is
1. 25
2. 30
3. 45
4. 55
NAS-X_Cycle 2 : : 2017-18 MATHEMATICS Test Form-23
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Q.40 A card is drawn at random from a pack of cards numbered from 1 to 52, one number
on one card. The probability that the number on the card drawn bears a perfect
square is
1. 3
26
2. 7
52
3. 2
13
4. 9
52
Q.41 The mean of eight numbers is 42. If one number is 63, then the mean of the remaining
numbers is
1. 36
2. 37
3. 38
4. 39
Q.42 The following table gives the marks obtained by 80 students in a test :
Marks No. of students
0 – 10
10 – 20
20 – 30
30 – 40
40 – 50
50 – 60
3
9
15
30
18
5
The median class is
1. 10-20
2. 20-30
3. 30-40
4. 40-50
NAS-X_Cycle 2 : : 2017-18 MATHEMATICS Test Form-23
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Q.43 The quadratic polynomial, whose zeroes are 3 and 4, is
1.
2 –7 12x x+
2. 2 7 12x x+ +
3. 2 – 7 –12x x
4. 2 7 –12x x+
Q.44 If the nth
term of an A.P. is 6n – 4, then its common difference is
1. –6
2. 6
3. 8
4. –8
Q.45 If ax bx c+ + =20 has equal roots, then c is equal to
1. –
2
b
a
2. 2
b
a
3.
2–
4
b
a
4.
2
4
b
a
Q.46 Product of the roots of the equation ( ) ( ) ( )a b x b c x c a20− + − + − = is
1. –
–
c a
b a
2. –
–
b c
a b
3. –
–
c a
a b
4. –
–
b c
b a
NAS-X_Cycle 2 : : 2017-18 MATHEMATICS Test Form-23
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Q.47 The sum of first 10 terms of the A.P. : – 5, – 2, 1, … is
1. 85
2. 82
3. 79
4. 76
Q.48 The zeroes of the quadratic polynomial 3x2 + 15x + 12 are
1. both positive
2. both negative
3. one positive and one negative
4. equal in magnitude, but opposite in signs
Q.49 The graphs of the equations 2x + y = 7 and x – 2y = 1 are
1. parallel lines
2. coincident lines
3. intersecting at the point (1, 3)
4. intersecting at the point (3, 1 )
Q.50 Given that one of the zeroes of the cubic polynomial ax bx cx d3 2+ + + is zero, the
product of the other two zeroes is
1. –c
a
2. c
a
3. 0
4. –b
a
Q.51 The sum and the product of the equation x2+ px + q = 0 are 4 and – 3 respectively.
The values of p and q are respectively
1. 4 and 3
2. – 4 and – 3
3. – 4 and 3
4. 4 and – 3
NAS-X_Cycle 2 : : 2017-18 MATHEMATICS Test Form-23
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Q.52 If the sum of first 20 even natural numbers is equal to k times the sum of first 20 odd
natural numbers, then k is equal to
1. 1
20
2. 19
20
3. 21
40
4. 21
20
Q.53 Arcs of two congruent circles subtend angles of 60° and 20° at their respective centres.
The ratio of lengths of corresponding arcs is
1. 2 : 1
2. 1 : 3
3. 3 : 1
4. 1 : 2
Q.54 In the given figure, O is the centre of a circle of diameter AD = 34 cm.
If AB = 30 cm and OC AB,⊥ then OC =
1. 4 cm
2. 8 cm
3. 15 cm
4. 17 cm
NAS-X_Cycle 2 : : 2017-18 MATHEMATICS Test Form-23
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Q.55 In the given figure, O is the centre of the circle. If ∠AOB= 90° and ∠ABC= 30°,
then ∠CAB is equal to
1. 90°
2. 105°
3. 120°
4. 130°
Q.56 In the given figure, AB and CD are towers of heights h1 and h2 respectively. O is the
mid-point of AC. If AB and CD subtend angles 30° and 60° at O, then h1 : h2 =
1. 2 : 1
2. 2 : 3
3. 3 : 2
4. 1 : 3
Q.57 The value of ( )...
23 1 2 3n n
n− + + + + , where n is a positive integer, is
1. 2n + 1
2. 3n
3. 2n – 1
4. – 3n
NAS-X_Cycle 2 : : 2017-18 MATHEMATICS Test Form-23
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Q.58 The roots of the equation 2
– 2 – 35 0x x = are
1. –5, 7
2. 7, –5
3. –7, –5
4. 7, 5
Q.59 The sum of the roots of the equation 2
2 – 3 6 0+ =x x is
1. 3
2. 3
2
3. – 3
4. 2
3
Q.60 If the quadratic equation 2
– 2 0x x k+ = has equal roots, then the value of k is
1. 0
2. 2
3. – 1
4. 1
