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

If the points `P(overlinea+2overlineb+overlinec)`, `Q(2overlinea+3overlineb), R(overlineb+ t overlinec)` are collinear, where `overlinea, overlineb, overlinec` are three non-coplanar vectors, the value of t is ______ 

Which of the following is true?

If the plane x - 3y + 5z = d passes through the point (1, 2, 4), then the lengths of intercepts cut by it on the axes of X, Y, Z are respectively ______ 

Area of the ellipse `x^2/9 + y^2/4` = 1 is ______.

Let L be the line joining the origin to the point of intersection of the lines represented by 2x² – 3xy – 2y² + 10x + 5y = 0. lf L is perpendicular to the line kx + y + 3 = 0, then k = ______.

`int_(-pi/4)^(pi/4) 1/(1 - sinx) "d"x` = ______.

How many numbers greater than 200 and divisible by 2 can be made from the digits 4, 5, 6, and 7 if no digit is repeated. 

The d.r.s of normal to the plane through (1, 0, 0), (0, 1, 0) which makes an angle `pi/4` with plane x + y = 3, are ______.

The differential equation representing the family of parabolas having vertex at origin and axis along positive direction of X-axis is ______.

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` = ______.