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

If y = `sin^-1 (xsqrt(1 - x) + sqrt(x) sqrt(1 - x^2))`, then `("d"y)/("d"x)` = ______.

The line passing through (– 2, 0) and (1, 3) makes an angle of ______ with X-axis.

If y = `cos^-1 ((x + 1)/(x - 1)) + "cosec"^-1 ((x - 1)/(x + 1))`, then `("d"y)/("d"x)` is ______.

If b², a², c² are in A.P., then `1/(a + b), 1/(b + c), 1/(c + a)` will be in ______

The gradient of the curve passing through (4, 0) is given by `"dy"/("d"x) - "y"/x + (5x)/((x + 2)(x - 3))` = 0 if the point (5, a) lies on the curve, then the value of a is ______.

The line which passes through the origin and intersect the two lines `(x - 1)/2 = (y + 3)/4 = (z - 5)/3, (x - 4)/2 = (y + 3)/3 = (z - 14)/4`, is ______.

A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and then passes through the point (5, 3). The co-ordinates of the point A is ______.

`int 1/(x^2 + 1)^2 dx` = ______.

If `int dx/sqrt(16 - 9x^2)` = A sin^–1 (Bx) + C then A + B = ______.

If planes `vecr.(phati - hatj + 2hatk) + 3` = 0 and `vecr.(2hati - phatj - hatk) - 5` = 0 include angle `π/3` then the value of p is ______.

If `int 1/((x^2 + 4)(x^2 + 9))dx = A tan^-1  x/2 + B tan^-1(x/3) + C`, then A – B = ______.

If `intsqrt((x - 5)/(x - 7))dx = Asqrt(x^2 - 12x + 35) + log|x| - 6 + sqrt(x^2 - 12x + 35) + C|`, then A = ______.

lf Rolle's theorem for f(x) = e^x (sin x – cos x) is verified on `[π/4, (5π)/4]`, then the value of c is ______.

The internal angles of a convex polygon are in A.P. The smallest angle is 120° and the common difference is 5°. The number to sides of the polygon is ______.

The fourth term of an A.P. is three times of the first term and the seventh term exceeds the twice of the third term by one, then the common difference of the progression is ______.

The number of permutations by taking all letters and keeping the vowels of the word ‘COMBINE’ in the odd places is ______.

The three straight lines ax + by = c, bx + cy = a and cx + ay = b are collinear, if ______.

If the line joining two points A (2, 0) and B (3, 1) is rotated about A in anticlockwise direction through an angle of 15°, then the equation of the line in new position is ______.

Given two independent events A and B such that P (A) = 0.3, P (B) = 0.6. Find 

1. P (A and B)
2. P(A and not B)
3. P(A or B)
4. P(neither A nor B)

The inverse of the function y = `(16^x - 16^-x)/(16^x + 16^-x)` is