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

In a series of observations, coefficient of variation is 25 and mean is 20, then the variance is ______.

Which of the following is the third root of `(1 + i)/sqrt2`? 

If (1 + ω²)^m = (1 + ω⁴)^m and ω is an imaginary cube root of unity, then least positive integral value of m is ______.

If α, β, γ are the cube roots of p (p < 0), then for any x, y and z, `(xalpha + "y"beta + "z"gamma)/(xbeta + "y"gamma + "z"alpha)` = ______.

Find the mean deviation about the mean for the data.

If the mean deviation of number 1, 1 + d, 1 + 2d, ..., 1 + 100d from their mean is 255, then d is equal to ______.

If the cube roots of the unity are 1, ω and ω², then the roots of the equation (x – 1)³ + 8 = 0, are ______.

The direction ratio of the line 2x - 1 = 3y + 2 = z - 2 are ______.

The length of the perpendicular from (0, 2, 3) to the line `(x + 3)/5 = (y - 1)/2 = (z + 4)/3` is

The equation of the line passing through (1, 2, 3) and perpendicular to the lines `x - 1 = (y + 2)/2 = (z + 4)/4` and `(x - 1)/2 = (y - 2)/2` = z + 3 is ______.

If A = {x, y, z}, B = {1, 2}, then the total number of relations from set A to set B are ______.

If the foot of the perpendicular drawn from the point (0, 0, 0) to the plane is ( 4, - 2, -5) then the equation of the plane is ______.

The direction ratios of the normal to the plane passing through origin and the line of intersection of the planes x + 2y + 3z = 4 and 4x + 3y + 2z = 1 are ______.

The direction ratios of a line perpendicular to the lines with direction ratios 1, 3, 2, and -1, 1, 2 are ______ 

The direction ratios of the line which is perpendicular to the two lines `(x - 1)/2 = ("y" - 1)/(-2) = ("z + 1")/1 and (x - 2)/1 = ("y - 1")/(- 2) = ("z + 3")/2` are ______.

The volume of tetrahedron whose vertices are A(3, 7, 4), B(5, -2, 3), C(-4, 5, 6), D(1, 2, 3) is ______.

If the volume of the tetrahedron formed by the coterminous edges `bar"a", bar"b" and bar"c"` is 5, then the volume of the parallelopiped formed by the coterminous edges `bar"a" xx bar"b", bar"b" xx bar"c" and bar"c" xx bar"a"` is

If the scalar triple product of the vectors `-3hat"i" + 7hat"j" - 3hat"k", 3hat"i" - 7hat"j" + lambdahat"k" and 7hat"i" - 5hat"j" - 5hat"j"` is 272 then λ = ______.

If the volume of tetrahedron whose vertices are A(0, 1, 2), B(2, -3, 0), C(1, 0, 2) and D(-2,-3,lambda) is `7/3` cu.units, then the value of λ is ______.

If the points having the position vectors `2hat"i" + hat"j" - hat"k", -hat"j", 4hat"i" + 4hat"k"` and `lambdahat"i" + hat"k"` lie on the same plane, then λ is equal to ______.