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

Let `square`PQRS be a quadrilateral. If M and N are midpoints of the sides PQ and RS respectively then `bar"PS" + bar"OR"` = ______.

In ΔABC, P is the midpoint of BC, Q divides CA internally in the ratio 2:1 and R divides AB externally in the ratio 1:2, then ______.

In ΔABC the mid-point of the sides AB, BC and CA are respectively (l, 0, 0), (0, m, 0) and (0, 0, n). Then, `("AB"^2 + "BC"^2 + "CA"^2)/("l"^2 + "m"^2 + "n"^2)` is equal to ______.

ΔABC has vertices at A = (2, 3, 5), B = (–1, 3, 2) and C = (λ, 5, µ). If the median through A is equally inclined to the axes, then the values of λ and µ respectively are ______.

M and N are the mid-points of the diagonals AC and BD respectively of quadrilateral ABCD, then AB + AD + CB + CD is equal to ______.

If G(g), H(h) and (p) are centroid orthocentre and circumcentre of a triangle and xp + yh + zg = 0, then (x, y, z) is equal to ______.

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 ______.