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

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 ______.

If slopes of lines represented by kx² + 5xy + y² = 0 differ by 1, then k = ______.

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 = ______.

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

A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is `1/2`. Then the length of the semi-major axis is ______.

lf f : [1, ∞) `rightarrow` [2, ∞) is given by f(x) = `x + 1/x`, then f^–1(x) is equal to ______.

If the straight lines `(x - 1)/2 = (y + 1)/k = z/2` and `(x + 1)/5 = (y + 1)/2 = z/k` are coplanar, then the plane(s) containing these two lines is/are ______.

If z ≠ 0, then `int_(x = 0)^100` [arg | z |] dx is ______.

(where [.] denotes the greatest integer function)

The value of `int_-1^3 (|x - 2| + [x])  dx` is equal to ______.

(where [.] denotes greatest integer function)

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then, the number of such arrangements is ______.

The differential equation y' = `y/(x + sqrt(xy))` has general solution given by:

(where C is a constant of integration)

The equation of the plane passing through the points (1, 2, 3), (–1, 4, 2) and (3, 1, 1) is ______.

A circular pIate is contracting at the uniform rate of 5cm/sec. The rate at which the perimeter is decreasing when the radius of the circle is 10 cm Jong is

A man of height 1.9 m walks directly away from a lamp of height 4.75m on a level road at 6m/s. The rate at which the length of his shadow is increasing is

The equation of the plane passing through (3, 1, 2) and making equal intercepts on the coordinate axes is _______.

The function f(x) = 9 - x⁵ - x⁷ is decreasing for

(q v r) v (~ p v ~ q) is a ______.