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

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 ______.

The negation of the statement 7 is greater than 4 or 6 is less than 7.

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

If y = `(sin x)^sin x` , then `"dy"/"dx"` = ?

The odds in favour of drawing a king from a pack of 52 playing cards is ______.

The rate at which the metal cools in moving air is proportional to the difference of temperatures between the metal and air. If the air temperature is 290 K and the metal temperature drops from 370 K to 330 K in 1 O min, then the time required to drop the temperature upto 295 K.

For every value of x, the function f(x) = `1/"a"^x`, a > 0 is ______.

The equations of planes parallel to the plane x + 2y + 2z + 8 = 0, which are at a distance of 2 units from the point (1, 1, 2) are ________.

`int "dx"/(x^2 + 4x + 13)` = ?

The area of the square increases at the rate of 0.5 cm²/sec. The rate at which its perimeter is increasing when the side of the square is 10 cm long is ______.