bits matematics mock

7/26/2019 Bits Matematics Mock

http://slidepdf.com/reader/full/bits-matematics-mock 1/5

MATHEMATICS (Mock Test-2)

81. If x = at

2

, y = 2at, then

dy

dx is equal to :Mock Test–2 (Mathematics)

(a) 1 ⁄ t (b) t(c) 2at (d) 2a

82. If α, β are the roots of the equation

3x2 − 6x + 5 = 0, then the equation whose

roots are α + β and2

α + β

is :

(a) x2 − 3x − 2 = 0 (b) x2 − 3x + 2 = 0

(c) x2 + 3x + 2 = 0 (d) x2 + 3x − 1 = 0

83. The A.M. of two number is 34 and G.M.is 16, the numbers are :(a) 64 and 3 (b) 64 and 4

(c) 2 and 64 (d) none of these84. The value of the determinant

111

x y z

y + z z + xx + y

is equal to :

(a) 1 + x + y + z (b) (x − y) ( y − z) ( z − x)(c) x + y + z (d) 0

85. If A and B are skew symmetric matricesof order n, then :(a) A + B is a zero matrix(b) A + B is a diagonal matrix(c) A + B is symmetric(d) A + B is skew symmetric

86. Let A and B be two sets such thatn ( A) = 70, n (B) = 60 and n ( A ∪ B) = 110.

Then n ( A ∩ B) is equal to :(a) 120 (b) 100(c) 20 (d) 240

87. In ∆ ABC, a = 4, b = 12 and ∠B = 60˚, then

the value of sin A is :(a)

2√ 3

(b)√ 32

(c)1

2√ 3 (d)

13√ 2

88. If sin (120˚ − α) = sin (120˚ − β) and0 < α, β < π, then all value of α, β are

given by :

(a) α + β = π3

(b) α = β or α + β = π3

(c) α = β (d) α + β = 0

89. The number of 4 digits can be formed

out of the digits 3, 4, 5, 6, 7, 8, 0, if no

digit is repeated, then their number isequal to :(a) 270 (b) 720

(c) 6C4 (d) 7P2



90. Maximum value of f (x) = sin x + cos x is :(a) 2 (b) 1

(c) √ 2 (d) 1

⁄ √ 2

91. Let A =

12

00, B =

01

0

12, then :

(a) AB ≠ 0, BA ≠ 0(b) AB ≠ BA = 0(c) AB = 0, BA ≠ 0(d) AB = 0, BA = 0

92. If |a → | = |b →

|, then (a → + b →

) . (a → − b →

) is :(a) positive(b) negative

(c) zero(d) none of these

93. The value of the integral

∫ α

β dx√ (x − α) (β − x)

is equal to :

(a)π2

(b) π

(c) 0 (d) none of these

94. If Q.D. = 16, the most likely value of S.D.

will be :(a) 42 (b) 24(c) 10 (d) none of these

95. The vectors λ i → + j

→ + 2k

→, i → + λ j

→ − k

→ and

2i → + j

→ − λ k

→ are coplanar if :

(a) λ = −1 (b) λ = 1(c) λ = 0 (d) λ = −2

96. Area of parallelogram whose diagonals

are a → and b →

is :

(a) a →

+ b →

(b) a →

. b →

(c)

1

2 |a

→

× b

→

| (d) |a

→

× b

→

|

97. 1 + 1

2 ! +

13 !

+ 14 !

+ … is :

(a) 2e (b) e(c) e − 1 (d) none of these

98.If the difference of two unit vectors isagain a unit vector, then angle betweenthem is :(a) 90˚ (b) 60˚(c) 45˚ (d) 30˚

Mock Test–2 (Mathematics)



99. The curves y = x2 and 6 y = 7 − x3 intersectat the point (1, 1) at an angle :

(a) π6 (b) π3

(c)π2

(d)π4

100.

If xn = cos

π2n

+ i sin

π2n

, then the vaue

of x1, x

2, x

3 … ∞ is :

(a) −i (b) −1(c) i (d) 1

101. cos3 θ − cos 3θ

cos θ +

sin3 θ + sin 3θsin θ

is equal

to :(a) 0 (b) 5

(c) 3 (d) 1

102.limx → 3

x − 3√ x − 2 − √ 4 − x

equals :

(a) 1 (b) 0(c) 2 (d) none of these

103. ∫ ex

( f (x) + f ′ (x)) dx is equal to :(a) ex f (x) (b) ex f ′ (x)(c) ex ( f (x) − f ′ (x)) (d) none of these

104. Maximum value of 5 + 4x − 4x2 is :(a) 7 (b) 6 (c) 3 (d) 2

105. If a, b, c, d, e are in G.P., then ec equals :

(a)db

(b)cb

(c)ba

(d)dc

106. In order that bigger sphere (centre C1,

radius R) may fully contain a smallersphere (centre C2, radius r), then correct

relationship is :

(a) C1C2 < 2 (R − r) (b) C1C2 < 12

(R + r)

(c) C1C2 < r + R (d) C1C2 < R − r

107. Given ddx f (x) = f (x) implies

ff (x) dx = f (x) + e. The function f (x) could

be :

(a) f (x) = ex (b) f (x) = log x

(c) f (x) = 1x

(d) f (x) = x




108. If f (x) = x + 2 when x ≤ 1 and f (x) = 4x − 1 when x > 1, then :

(a) f (x) is discontinuous at x = 0(b) f (x) is continuous at x = 1(c) Lim

x → 1 f (x) = 4

(d) none of these

109. If A and B are two 3 × 3 matrices suchthat det A = det B, then :

(a) A ′ = B (b) A ′ = B ′(c) A = B (d) none of these

110. Area bounded by lines y = 2 + x, y = 2 − x and x = 2 is :(a) 16 (b) 8(c) 3 (d) 4

111. All letters of the word ‘‘AGAIN’’ arepermuted in all possible ways and thewords so formed (with or withoutmeaning) are written as in dictionary

then the 50th word is :(a) INAGA (b) IAANG(c) NAAGI (d) NAAIG

112. The complex number z satisfying the

condition arg z − 1 z + 1

= π3

is :

(a) a parabola (b) a circle

(c) a straight line (d) none of these

113. The projections of a line segment on

x, y, z axes are 12, 4, 3. The length andthe direction cosines of the line segmentare :

(a) 11, < 1211

,1411

,311

>

(b) 19, < 1219

,419

,319

>

(c) 13, < 1213, 413, 313 >

(d) 15, < 1215

,415

,315

>

114. If ∫ 0

100π√ 1 − cos 2x dx = 200k , then k is

equal to :

(a) √ 3 (b) √ 2(c) 2√ 2 (d) π

115. If n is a positive integer, then n3 + 2n isdivisible by :(a) 2 (b) 3

(c) 5 (d) 6




116.1

1 . 2 −

12 . 3

+ 1

3 . 4 −

14 . 5

+ … is equal to :

(a) 4 log 2 − 1 (b) 3 log 2(c) 2 log 2 − 1 (d) none of these

117. If f (x) = 1 + α x, α ≠ 0 is the inverse of itself, then the value of α is :(a) 2 (b) −1(c) −2 (d) 0

118. The values of x which satisfies both theequations x2 − 1 ≤ 0 and x2 − x − 2 ≥ 0 liein :(a) (1, 2) (b) (−1)(c) (−1, 2) (d) (−1, 1)

119. The normal to the curvex = a (cos θ + θ sin θ), y = a (sin θ − θ cos θ)at any point θ is such that :(a) it is at a constant distance from the

origin(b) it makes a constant angle with x-axis(c) it passes through the origin(d) none of these

120. Given the four lines with equationsx + 2 y − 3 = 0, 3x + 4 y − 7 = 0,2x + 3 y − 4 = 0, 4x + 5 y − 6 = 0. Then :(a) they are all parallel(b) they are all concurrent(c) they are the sides of a quadrilateral(d) none of these

121. The range of the function f (x) = [x] − xdenotes the greatest integer ≤ x(a) [0, 1) (b) (−1, 0](c) (−1, 0) (d) none of these

122. √ 6 + 8i + √ 6 − 8i is equal to :(a) 3√ 2 i (b) 2√ 2 i(c) 4√ 2 i (d) none of these

123. If y = 4x − 5 is tangent to the curve

y2 = px3 + q at (2, 3), then :

(a) p = 2, q = 7 (b) p = −2, q = −7(c) p = −2, q = 7 (d) p = 2, q = −7

124. If the co-efficient of (r + 1)th term in the

expansion of (1 + x)2n

be euqal to that of (r + 3)th term, then :(a) n + r + 1 = 0 (b) n − r − 1 = 0(c) n − r + 1 = 0 (d) none of these

125. The centres of the circles

x2 + y2 = 1, x2 + y2 + 6x − 2 y = 1

and x2

+ y2

− 12x + 4 y = 1 lie on :(a) a straight line (b) a circle

(c) x2 = 9 y (d) none of these


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