WBJEE Mathematics Sample Paper III - JEE MCQ

The line y = 2t² intersects the ellipse   in real points if

General solution of sin x + cosx = 

If A and B square matrices of the same order and AB = 3I, then A^–1 is equal to

The co-ordinates of the focus of the parabola described parametrically by x = 5t² + 2, y = 10t + 4 are

For any two sets A and B, A – (A – B) equals

If a = 2√2 , b = 6, A = 45º, then

A Mapping from IN to IN is defined as follows :
f : IN o IN
f(n) = (n + 5)² , n ∈ IN
(IN is the set of natural numbers). Then

In a triangle ABC if sin A sin   then the triangle is

The value of

A positive acute angle is divided into two parts whose tangents are and . Then the angle is

If 

The value of 

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The second order derivative of a sin³t with respect to a cos³t at 

The smallest value of 5 cos θ + 12 is

The general solution of the differential equation 

Product of any r consecutive natural numbers is always divisible by

The integrating factor of the differential equation  is given by

If x² + y² = 1 then

If c₀ , c₁ , c₂ , ..................., c_n denote the co-efficients in the expansion of (1 + x)ⁿ then the value of c₁ + 2c₂ + 3c₃ + ..... + nc_n is

A polygon has 44 diagonals. The number of its sides is

If α,β be the roots of x² – a(x – 1) + b = 0, then the value of  

The angle between the lines joining the foci of an ellipse to one particular extremity of the minor axis is 90º. The eccentricity of the ellipse is

The order of the differential equation 

The sum of all real roots of the equation |x – 2|² + |x – 2| – 2 = 0