MA THEMATICS (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, βare the roots of the equation 3x 2 −6x+5 =0, then the equation whose roots are α+βand 2 α+β is : (a) x 2 −3x−2 =0 (b) x 2 −3x+2 =0 (c) x 2 +3x+2 =0 (d) x 2 +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 these 84. The value of the determinant 1 1 1 x y z y+z z+x x+y is equal to : (a) 1 +x+y+z(b) ( x−y)( y−z)( z−x) (c) x+y+z(d) 0 85. If Aand Bare skew symmetric matrices of order n, then : (a) A+Bis a zero matrix (b) A+Bis a diagonal matrix (c) A+Bis symmetric (d) A+Bis skew symmetric 86. Let Aand Bbe two sets such that n( 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
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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
(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