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WBJEE Previous Year - 2011 - Question 1

The eccentricity of the hyperbola 4x^{2} – 9y^{2} = 36 is

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WBJEE Previous Year - 2011 - Question 2

The length of the latus rectum of the ellipse 16x^{2} + 25y^{2} = 400 is

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WBJEE Previous Year - 2011 - Question 3

The vertex of the parabola y^{2} + 6x – 2y + 13 = 0 is

( y −1)^{2}= −6x − 12

( y −1)^{2}= −6(x +12) = 4(-6/4)(x+2)

Vertex →(−2, 1)

WBJEE Previous Year - 2011 - Question 4

The coordinates of a moving point p are (2t^{2} + 4, 4t + 6). Then its locus will be a

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WBJEE Previous Year - 2011 - Question 5

The equation 8x^{2} + 12y^{2} – 4x + 4y – 1 = 0 represents

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WBJEE Previous Year - 2011 - 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

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WBJEE Previous Year - 2011 - Question 7

The locus of the centre of a circle which passes through two variable points (a, 0), (–a, 0) is

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WBJEE Previous Year - 2011 - 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

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WBJEE Previous Year - 2011 - 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

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WBJEE Previous Year - 2011 - Question 10

If the coordinates of one end of a diameter of the circle x2+y2+4x–8y+5=0, is (2,1), the coordinates of the other end is

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WBJEE Previous Year - 2011 - 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

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WBJEE Previous Year - 2011 - Question 12

and θ lies in the second quadrant, then cosθ is equal to

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WBJEE Previous Year - 2011 - Question 13

The solutions set of inequation cos^{–1}x < sin^{–1}x is

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WBJEE Previous Year - 2011 - Question 17

If sinθ and cosθ are the roots of the equation ax^{2} – bx + c = 0, then a, b and c satisfy the relation

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WBJEE Previous Year - 2011 - Question 18

If A and B are two matrices such that A+B and AB are both defined, then

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WBJEE Previous Year - 2011 - 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

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WBJEE Previous Year - 2011 - Question 25

If y = 2x^{3 }– 2x^{2} + 3x – 5, then for x = 2 and Δ x = 0.1 value of Δ y is

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WBJEE Previous Year - 2011 - Question 26

The approximate value of 5√33 correct to 4 decimal places is

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WBJEE Previous Year - 2011 - Question 28

For the function f(x) = e^{cos x }, Rolle’s theorem is

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WBJEE Previous Year - 2011 - Question 33

The degree and order of the differential equation are repectively

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WBJEE Previous Year - 2011 - Question 35

The function f(x) = ax + b is strictly increasing for all real x if

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WBJEE Previous Year - 2011 - Question 41

4 boys and 2 girls occupy seats in a row at random. Then the probability that the two girls occupy seats side by side is

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WBJEE Previous Year - 2011 - Question 42

A coin is tossed again and again. If tail appears on first three tosses, then the chance that head appears on fourth toss is

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WBJEE Previous Year - 2011 - Question 46

If A and B are coefficients of xn in the expansions of (1+ x)^{2n} and (1+x)^{2n – 1} respectively, then A/B is equal to

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WBJEE Previous Year - 2011 - Question 47

If n > 1 is an integer and x ≠0, then (1 + x)^{n} – nx – 1is divisible by

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WBJEE Previous Year - 2011 - Question 48

If ^{n}C_{4}, ^{n}C_{5} and ^{n}C_{6} are in A.P., then n is

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WBJEE Previous Year - 2011 - Question 49

The number of diagonals in a polygon is 20. The number of sides of the polygon is

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WBJEE Previous Year - 2011 - Question 51

Let a , b, c be three real numbers such that a + 2b + 4c = 0. Then the equation ax^{2} + bx + c = 0

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WBJEE Previous Year - 2011 - Question 52

If the ratio of the roots of the equation px^{2} + qx + r = 0 is a : b, then ab/(a + b)^{2 }is

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WBJEE Previous Year - 2011 - Question 53

If α and β are the roots of the equation x^{2 }+ x + 1 = 0, then the equation whose roots are α^{19} and β^{7} is

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WBJEE Previous Year - 2011 - Question 54

For the real parameter t, the locus of the complex number z = (1 – t²) + i√(1 + t^{2}) in the complex plane is

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WBJEE Previous Year - 2011 - Question 55

if x + 1/x = 2cosθ, then for any integer n , x^{n} + 1/x_{n}

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WBJEE Previous Year - 2011 - Question 56

If ω ≠ 1 is a cube root of unity, then the sum of the series S = 1 + 2ω + 3ω ² + .......... + 3nω^{ 3n – 1} is

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WBJEE Previous Year - 2011 - Question 57

If log_{3}x + log_{3}y = 2 + log_{3}2 and log_{3}(x + y) = 2, then

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WBJEE Previous Year - 2011 - Question 59

The sequence log a, log a^{2}/b, loga^{3}/b^{2}, ....... is

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WBJEE Previous Year - 2011 - Question 60

If in a triangle ABC, sin A, sin B, sin C are in A.P., then

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