MAH-MHT CET (PCM/PCB) entrance exam Question Bank Solutions

Eccentricity of ellipse `x^2/a^2 + y^2/b^2` = 1, if it passes through point (9, 5) and (12, 4) is ______.

Equation of the ellipse whose axes are along the coordinate axes, vertices are (± 5, 0) and foci at (± 4, 0) is ______.

If (2, 3, 9), (5, 2, 1), (1, λ, 8) and (λ, 2, 3) are coplanar, then the product of all possible values of λ is ______.

Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is transferred from Bag I to Bag II and then a ball is draw from Bag II. The ball so drawn is found to be black in colour. Then the probability, that the transferred ball is red, is ______.

Evaluate: `int_0^π 1/(5 + 4 cos x)dx`

What is `int_0^(π/2)` sin 2x ℓ n (cot x) dx equal to ?

For a biased dice, the probability for the different faces to turn up are

The dice is tossed and it is told that either the face 1 or face 2 has shown up, then the probability that it is face 1, is ______.

If `π/2` < x < π, then `intxsqrt((1 + cos2x)/2)dx` = ______.

With the usual notation `int_1^2 ([x^2] - [x]^2)dx` is equal to ______.

(p ∧∼ q) ∧ (∼ p ∧ q) is ______.

`int_(π/3)^(π/2) x sin(π[x] - x)dx` is equal to ______.

The equation of the plane through the line x + y + z + 3 = 0 = 2x – y + 3z + 1 and parallel to the line `x/1 = y/2 = z/3`, is ______.

Let A, B be two events such that the probability of A is `3/10` and conditional probability of A given B is `1/2`. The probability that exactly one of the events A or B happen equals.

If `vecp, vecq` and `vecr` are nonzero, noncoplanar vectors then `[(vecp + vecq - vecr, vecp - vecq, vecq - vecr)]` = ______.

If `int_0^K dx/(2 + 18x^2) = π/24`, then the value of K is ______.

If y = (tan^–1 x)² then `(x^2 + 1)^2 (d^2y)/(dx^2) + 2x(x^2 + 1) (dy)/(dx)` = ______.

`int e^x [(2 + sin 2x)/(1 + cos 2x)]dx` = ______.

If `2sin(θ + π/3) = cos(θ - π/6)`, then tan θ, = ______.

The point of intersection of line represented by x² – y² + 3y – 2 = 0 is ______.

`int_0^(π/4) x. sec^2 x  dx` = ______.