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

`int ("e"^x(1 + x))/(cos^2 ("e"^x x))"d"x` is equals to ______.

The constraints –x₁ + x₂ ≤ 1, –x₁ + 3x₂ ≤ 9, x₁x₂ ≥ 0 define on ______.

The inverse of f(x) = `2/3 (10^x - 10^-x)/(10^x + 10^-x)` is ______.

The foot of the perpendicular drawn from the origin to a plane is the point (1, –3, 1). What is the intercept cut on the x-axis by the plane?

Three vertices of a parallelogram ABCD are A ( 3, –1, 2), B (1, 2, –4) and C (–1, 1, 2). The coordinates of fourth vertex D are ______.

The equation of the plane containing the line `(x + 1)/(-3) = (y - 3)/2 = (z + 2)/1` and the point (0, 7, –7), is ______.

The co-ordinates of the foot of perpendicular from the point A (1, 1, 1) on the line joining the points B (1, 4, 6) and C (5, 4, 4) are ______.

The distance of the point (1, –2, 3) from the plane x – y + z = 5 measured parallel to the line `x/2 = y/3 = (z - 1)/(-6)` is ______.

The maximum value of z = 5x + 2y, subject to the constraints x + y ≤ 7, x + 2y ≤ 10, x, y ≥ 0 is ______.

A fair coin is tossed 99 times. If X is the number of times head occurs, P(X = r) is maximum when r is ______.

The maximum value of 2x + y subject to 3x + 5y ≤ 26 and 5x + 3y ≤ 30, x ≥ 0, y ≥ 0 is ______.

If g(x) is the inverse function of f(x) and f'(x) = `1/(1 + x^4)`, then g'(x) is ______.

If lines `(x - 1)/2 = (y + 1)/3 = (z - 1)/4` and x – 3 = `(y - k)/2` = z intersect then the value of k is ______.

If the origin and the points P(2, 3, 4), Q(1, 2, 3) and R(x, y, z) are coplanar, then ______.

A box contains 6 pens, 12 of which are defective. Two pens are taken randomly from the box. If r.v. X : number of defective pens obtained, then standard deviation of X = ______.

`int_0^3 [x]dx` = ______, where [x] is greatest integer function.

If the distance of points `2hati + 3hatj + λhatk` from the plane `r.(3hati + 2hatj + 6hatk)` = 13 is 5 units, then λ = ______.

The shaded part of given figure indicates in feasible region, then the constraints are:

If random variable `x ∼ b (n = 5, P = 1/3)`, then P(2 < X < 4) is equal to ______.

The objective function Z = x₁ + x₂, subject to the constraints are x₁ + x₂ ≤ 10, – 2x₁ + 3x₂ ≤ 15, x₁ ≤ 6, x₁, x₂ ≥ 0, has maximum value ______ of the feasible region.