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

`cos  (2π)/7 + cos  (4π)/7 + cos  (6π)/7`

The value of `tan  π/5 + 2 tan  (2π)/5 + 4 cot  (4π)/5` is ______.

If x and y are acute angles, such that cos x + cos y = `3/2` and sin x + sin y = `3/4`, then sin (x + y) equals:

The value of cos 52° + cos 68° + cos 172° is ______.

If sin θ + sin 2θ + sin 3θ = sin α and cos θ + cos 2θ + cos 3θ = cos α, then θ is equal to ______.

tan 20° tan 40° tan 60° tan 80° is equal to ______.

`lim_(x rightarrow ∞) sum_(x = 1)^20 cos^(2n) (x - 10)` is equal to ______.

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 ______.

`lim_(x rightarrow π/2) ([1 - tan (x/2)] (1 - sin x))/([1 + tan (x/2)] (π - 2x)^3` is ______.

The value of `int ((x^2 - 1)dx)/(x^3 sqrt(2x^4 - 2x^2 + 1)` is ______.

The mean of the number a, b, 5, 8, 10 is 6 and variance is 6.80. Then, which one of the following gives possible values of a and b?

If log (x + y) = log (xy) + 3, then `dy/dx` = ______. 

If xy = tan^–1 (xy) + cot^–1 (xy), then `(dy/dx)_((4","  2))` = ______.

where (x, y) ∈ R

A plane passes through (1, - 2, 1) and is perpendicular to two planes 2x - 2y + z = 0 and x - y + 2z = 4. The distance of the plane from the point (1, 2, 2) is ______.

If f(x) = px⁵ + qx⁴ + 5x³ - 10 has local maximum and minimum at x = 1 and x = 3 respectively then (p, q) = ______.

The shortest distance between the lines

`bar"r" = (hat"i" + 2hat"j" + hat"k") + lambda (hat"i" - hat"j" + hat"k")` and

`bar"r" = (2hat"i" - hat"j" - hat"k") + mu(2hat"i" + hat"j" + 2hat"k")` is

If the tangent to the curve y = 3x² - 2x + 1 at a point Pis parallel toy = 4x + 3, the co-ordinates of P are

The maximum volume of a right circular cylinder if the sum of its radius and height is 6 m is ______.

The area of the Δ ABC is `10sqrt3` cm², angle B is 60° and its perimeter is 20 cm , then l(AC) = ______.

If A and Bare supplementary angles, then `sin^2  "A"/2 + sin^2  "B"/2` = ______.