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

If f(x) = `(sin^2x)/(1 + cotx) + (cos^2x)/(1 + tan x)`, then `"f'"(pi/4)` is ______.

The only statement among the following i.e., a tautology is ______.

The equation of tangent to the curve `(x/"a")^"n" + (y/"b")^"n"` = 2 at the point (a, b) is ______.

`int_0^(pi/2) 1/(1 + cos^3x) "d"x` = ______.

The area of the curve xy² =  4(2 – x) bounded by Y-axis is ______.

The equation of the plane passing through the points (1, –2, 1), (2, –1, –3) and (0, 1, 5) is ______.

If `(cos(x - y))/(cos(x + y)) = ("a" + "b")/("a" - "b")`, then cot x × cot y is equal to ______.

The equation of the plane passing through a point having position vector`-2hat"i" + 7hat"j" + 5hat"k"` and parallel to the vectors `4hat"i" - hat"j" + 3hat"k"` and `hat"i" + hat"j" + hat"k"` is ______.

If m and n are respectively the order and degree of the differential equation of the family of parabolas with focus at the origin and X-axis as its axis, then mn - m + n = ______.

If x = a cos³θ, y = a sin³θ, then `1 + (("d"y)/("d"x))^2` is ______.

`int_0^1 "e"^(5logx) "d"x` = ______.

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 ______.