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

`int_-1^1 (17x^5 - x^4 + 29x^3 - 31x + 1)/(x^2 + 1) dx` is equal to ______.

What will be the equation of plane passing through a point (1, 4, – 2) and parallel to the given plane – 2x + y – 3z = 9?

Find k, if the slope of one of the lines given by kx² + 8xy + y² = 0 exceeds the slope of the other by 6.

Let g(x) be the inverse of the function f(x) and f'(x) = `2/(x^2 + 3)`, then 2g'(x) is equal to 

The maximum value of P = 7x + 6y subject to constraints x + 2y ≤ 24, 2x + y ≤ 30 and x ≥ 0, y ≥ 0 is ______.

If m₁ and m₂ are slopes of lines represented by 6x² - 5xy + y² = 0, then (m₁)³ + (m₂)³ = ?

The angle between the tangents to the circle x² + y² = 25 from the point (7, -1) is ______.

The number of arrangements of the letters of the word BANANA in which two N's do not appear adjacently is ______.

The angle between the lines `("x - 1")/4 = ("y - 3")/1 = "z"/8` and `("x - 2")/2 = ("y + 1")/2 = "z - 4"/1` is ______.

If the slopes of the lines given by the equation ax² + 2hxy + by² = 0 are in the ratio 5 : 3, then the ratio h² : ab = ______.

The equation of a line passing through the point (7, - 4) and perpendicular to the line passing through the points (2, 3) and (1 , - 2 ) is ______.

The probability that bomb will miss the target is 0.2. Then, the probability that out of 10 bombs dropped exactly 2 will hit the target is ____________.

The letters of the word 'LOGARITHM' are arranged at random. The probability that arrangement starts with vowel and end with consonant is ____________.

If for an arithmetic progression, 9 times nineth term is equal to 13 times thirteenth term, then value of twenty second term is ____________.

If the angle between the lines given by the equation x² - 3xy + λy² + 3x - 5y + 2 = 0, λ ≥ 0, is `tan^-1 (1/3)`, then λ = ______.

The angle between the line r = `(hat"i" + hat"j" - hat"k") + λ (3hat"i" + hat"j")` and the plane `"r". (hat"i" + 2hat"j" + 3hat"k")` = 8 is ____________.

If `int(sin2x)/(sin5x  sin3x)dx = 1/3log|sin 3x| - 1/5log|f(x)| + c`, then f(x) = ______

Differential coefficient of `tan^-1(x/(1 + sqrt(1 - x^2)))` w.r.t. sin^-1 x is ______ 

If 2y = `(cot^-1((sqrt3cosx + sinx)/(cosx - sqrt3 sinx)))^2`, x ∈ `(0, pi/2)` then `dy/dx` is equal to ______

In tossing 8 coins, the probability of getting exactly 3 tails is ______