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

If ax² + 2xy – 3y² + 4x + c = 0 represents a pair of perpendicular lines, then ______.

If plane x + ay + z = 4 has equal intercepts on axes, then 'a' is equal to ______.

If equation tan θ + tan 2θ + tan θ tan 2θ = 1, θ = ______.

`int_(-1)^1 (x + x^3)/(9 - x^2)  "d"x` = ______.

If the line `(x + 1)/2 = (y - 5)/3 = (z - "p")/6` lies in the plane 3x – 14y + 6z + 49 = 0, then the value of p is ______.

The equation of the 1 plane passing through the points (1, –1, 1), (3, 2, 4) and parallel to Y-axis is ______.

The differential equation for all the straight lines which are at the distance of 2 units from the origin is ______.

The differential equation whose solution is (x – h)² + (y – k)² = a² is (where a is a constant) ______.

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 ______.