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

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 ______

If y = `tan^-1((sqrtx + 1)/(sqrtx - 1)) + tan^-1((sqrtx - 1)/(sqrtx + 1))`, then the value of `dy/dx` = ______

A group of 5 men and 4 women are arranged at random, one after the other. The probability that women and men occupy alternate seats is ______

If `y = tan^-1((sqrtx - x)/(1 + x^{3/2}))`, then y'(1) is ______ 

If `y = cot^-1((6cotx - 5)/(5cotx + 6)), "then" dy/dx` = ______ 

The derivative of `cos^-1 (2x^2 - 1)` w.r.t `cos^-1 x` is ______

The angle between the lines represented by the equation ax² + xy + by² = 0 will be 45°, if ______ 

The plane 2x - 3y + 6z - 11 = 0 makes an angle sin^-1 (α) with X-axis. The value of α is equal to ______ 

The derivative of `sin^-1(2xsqrt(1 - x^2))` with respect to `sin^-1(3x - 4x^3)` is ______