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

If x = f(t) and y = g (t) are differentiable functions of t, then `(d^2y)/(dx^2)` is ______.

If α and β are roots of the equation x² + 5|x| – 6 = 0, then the value of |tan^–1α – tan^–1 β| is ______.

Symbolic form of the given switching circuit is equivalent to:

If M is the arithmetic mean of two distinct real number l and n (I, n > 1) and G₁, G₂ and G₃ are three geometric means between l and n, then `G_1^4 + 2G_2^4 + G_3^4` is equal to ______.

If log₂ x + log₂ y ≥ 6, then the least value of x + y is ______.

If θ lies in the first quadrant and 5 tan θ = 4, then `(5 sin θ - 3 cos θ)/(sin θ + 2 cos θ)` is equal to ______.

The means of two samples of sizes 60 and 120 respectively are 35.4 and 30.9 and the standard deviations are 4 and 5. Obtain the standard deviation of the sample of size 180 obtained by combining the two samples.

For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4 respectively. The variance of the combined data set is ______ 

If the vectors `"a"hat"i" + "a"hat"j" + "c"hat"k", hat"i" + hat"k", "c"hat"i" + "c"hat"j" + "b"hat"k"` are coplanar, then c is ______.

The sum of n terms of the series 2² + 4² + 6² + ........ is ______.

`(x + 1/x)^2 + (x^2 + 1/x^2)^2 + (x^3 + 1/x^3)^2` ....upto n terms is ______.

If A(1, 3, 2), B(a, b, - 4) and C(5, 1, c) are the vertices of triangle ABC and G(3, b, c) is its centroid, then

If the plane 2x + 3y + 5z = 1 intersects the co-ordinate axes at the points A, B, C, then the centroid of Δ ABC is ______.

Let G be the centroid of a Δ ABC and O be any other point in that plane, then OA + OB + OC + CG = ?

In a quadrilateral ABCD, M and N are the mid-points of the sides AB and CD respectively. If AD + BC = tMN, then t = ____________.

In a triangle ABC, if `1/(a + c) + 1/(b + c) = 3/(a + b + c)` then angle C is equal to ______

If G(3, -5, r) is centroid of triangle ABC where A(7, - 8, 1), B(p, q, 5) and C(q + 1, 5p, 0) are vertices of a triangle then values of p, q, rare respectively.

P is the point of intersection of the diagonals of the parallelogram ABCD. If O is any point, then `overline"OA" + overline"OB" + overline"OC" + overline"OD"` = ______ 

If P(2, 2), Q(- 2, 4) and R(3, 4) are the vertices of Δ PQR then the equation of the median through vertex R is ______.

If the position vectors of points A and B are `hati + 8hatj + 4hatk` and `7hati + 2hatj - 8hatk`, then what will be the position vector of the midpoint of AB?