WBJEE  MATHEMATICS
 Number of Questions : 40
 Time : 60 Minutes
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Question 1 
The eccentricity of the hyperbola 4x^{2} – 9y^{2} = 36 is
A  √11/3 
B  √15/3 
C  √13/3 
D  √14/3 
Question 2 
The length of the latus rectum of the ellipse 16x^{2} + 25y^{2} = 400 is
A  5/16 unit 
B  5/32 unit 
C  32/5 unit 
D  16/5 unit 
Question 3 
The vertex of the parabola y^{2} + 6x – 2y + 13 = 0 is
A  (–2, 1) 
B  (7/2,1) 
C  (1, –1) 
D  (3/2,1) 
Question 4 
The coordinates of a moving point p are (2t^{2} + 4, 4t + 6). Then its locus will be a
A  parabola 
B  circle 
C  straight line 
D  ellipse 
Question 5 
The equation 8x^{2} + 12y^{2} – 4x + 4y – 1 = 0 represents
A  a parabola 
B  a hyperbola 
C  a circle 
D  an ellipse 
Question 6 
If the straight line y = mx lies outside of the circle x^{2} + y^{2} – 20y + 90 = 0, then the value of m will satisfy
A  m < 3 
B  m > 3 
C  m < 3 
D  m > 3 
Question 7 
The locus of the centre of a circle which passes through two variable points (a, 0), (–a, 0) is
A  x + y = a 
B  x = 1 
C  x + y = 2a 
D  x = 0 
Question 8 
The coordinates of the two points lying on x + y = 4 and at a unit distance from the straight line 4x + 3y = 10 are
A  (3, 1), (–7, 11) 
B  (–3, 1), (7, 11) 
C  (3, 1), (7, 11) 
D  (5, 3), (–1, 2) 
Question 9 
The intercept on the line y = x by the circle x^{2} + y^{2} – 2x = 0 is AB. Equation of the circle with AB as diameter is
A  x(x – 1) +y(y – 1) = 0 
B  (x –1)(x–2)+(y–1)+(y–2)= 0 
C  x^{2} + y^{2} = 2 
D  x^{2} + y^{2} = 1 
Question 10 
If the coordinates of one end of a diameter of the circle x^{2}+y^{2}+4x–8y+5=0, is (2,1), the coordinates of the other end is
A  (–6, 7) 
B  (7, –6) 
C  (6, 7) 
D  (–6, –7) 
Question 11 
If the three points A(1,6), B(3, –4) and C(x, y) are collinear then the equation satisfying by x and y is
A  5x –13y + 5 = 0 
B  5x + 13y + 5 = 0 
C  13x –5y +5 = 0 
D  5x + y – 11= 0 
Question 12 
If sin θ= 2t/1+t^{2} and θ lies in the second quadrant, then cos θ is equal to
A  1+t^{2}/1t^{2} 
B  t^{2}1/1+t^{2} 
C  1t^{2}/1+t^{2} 
D  1t^{2}/1+t^{2} 
Question 13 
The solutions set of inequation cos^{–1}x < sin^{–1}x is
A  [1/√2,1] 
B  (1/√2,1] 
C  [–1, 1] 
D  [0, 1] 
Question 14 
The number of solutions of 2sinx + cos x = 3 is
A  1 
B  2 
C  infinite 
D  No solution 
Question 15 
Let tan α = a/a+1 and tan β = 1/2a+1 then α + β is
A  π 
B  π/3 
C  π/2 
D  π/4 
Question 16 
If θ + φ = π/4, , then (1+ tan θ)(1+ tan φ) is equal to
A  1/3 
B  1 
C  5/2 
D  2 
Question 17 
If sin θ and cos θ are the roots of the equation ax^{2} – bx + c = 0, then a, b and c satisfy the relation
A  a^{2} + c^{2} + 2ab = 0 
B  a^{2}  b^{2} + 2ac = 0 
C  a^{2}  b^{2}  2ac = 0 
D  a^{2} + b^{2} + 2ac = 0 
Question 18 
If A and B are two matrices such that A+B and AB are both defined, then
A  A and B can be any matrices 
B  A, B are square matrices not necessarily of the same order 
C  Number of columns of A = number of rows of B 
D  A, B are square matrices of the same order 
Question 20 
A  z is purely real 
B  (z  ‾ z ) i is purely imaginary 
C  z is purely imaginary 
D  z + ‾ z = 0 
Question 21 
The equation of the locus of the point of intersection of the straight lines x sin θ + (1 – cos θ) y = a sin θ and x sin θ – (1 + cos θ) y + a sin θ = 0 is
A  y^{2} = 4x 
B  x^{2} + y^{2} = a^{2} 
C  x = ± ay 
D  y ± ax 
Question 22 
If sinθ + cosθ = 0 and 0 < θ < π, then θ
A  π/4 
B  3π/4 
C  π/2 
D  0 
Question 23 
The value of cos 15°  sin 15° is
A  1/2√2 
B  1/√2 
C  1/√2 
D  0 
Question 24 
The period of the function f(x) = cos 4x + tan 3x is
A  π/4 
B  π/3 
C  π 
D  π/2 
Question 25 
If y = 2x^{3} – 2x^{2} + 3x – 5, then for x = 2 and Δ x = 0.1 value of Δ y is
A  0 
B  1.9 
C  0.9 
D  2.002 
Question 26 
The approximate value of ^{5}√33 correct to 4 decimal places is
A  2.1001 
B  2.0125 
C  2.0500 
D  2.0000 
Question 28 
For the function f(x)=e^{cosx} , Rolle’s theorem is
A  applicable when π/4 ≤ x ≤ π/2 
B  applicable when 0 ≤ x ≤ π 
C  applicable when 0 ≤ x ≤ π/2 
D  applicable when π/2 ≤ x ≤ 3π/2 
Question 29 
A  (A + Bx^{4})e^{4x} 
B  (A + B x)e^{5x} 
C  (A + Bx)e^{–4x} 
D  (A + Bx^{2})e^{4x} 
Question 31 
A  4 tan^{–1} x^{3} + c

B  x^{2} + 1/4 tan ^{–1} x^{4} + c 
C  1/4 tan ^{–1} x^{4} + c 
D  x + 4 tan^{–1} x^{4} + c 
Question 34 
A  Strictly increasing at x = 0 
B  strictly increasing when x > 0 
C  increasing when x ≥ 0

D  not continuous at x = 0 and so it is not increasing when x > 0 
Question 35 
The function f(x) = ax + b is strictly increasing for all real x if
A  a < 0 
B  a ≤ 0 
C  a > 0 
D  a = 0 
Question 36 
A  2 sin x + log  sec x + tan x  + C 
B  2 sin x – log sec x – tan x + c 
C  2 sin x – log sec x + tan x + C 
D  2 sin x + log sec x – tan x + C 
Question 38 
The general solution of the differential equation log_{e} (dy/dx) =x + y is
A  e^{x} + e^{–y} = C 
B  e^{–x} + e^{–y} = C 
C  e^{x} + e^{y = C } 
D  e^{y} + e^{–x} = C 
Question 39 
If y = A/x + Bx^{ 2} , then x ^{2} d ^{2} y/d x ^{2}
A  2y 
B  y^{3} 
C  y^{4} 
D  y^{2} 
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