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

If x² + (2h - 1)xy + y² - 24x - 8y + k = 0 is the equation of the circle and 12 is the radius of the circle, then ______.

If 2tan^-1 (cos x) = tan^-1 (cosec² x), then x = ______.

`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.

The principal value of `sin^-1 (sin  (3pi)/4)` is ______.

The shortest distance between the skew lines `overliner= (6hati + 2hatj + 2hatk) + t(hati - 2hatj + 2hatk)` and `overliner = (-4hati - hatk) + s(3hati - 2hatj - 2hatk)` is ______.

If the value of `lim_(x -> 1) (1 - (1 - x))^"m"/x` is 99, then n = ______.

Which of the following pair of straight lines intersect at right angles?

The equation of the circle with centre (4, 5) which passes through (7, 3) is ______.

The equation of circle whose diameter is the line joining the points (–5, 3) and (13, –3) is ______.

If sin `(sin^-1  1/3 + cos^-1 x) = 1`, then the value of x is ______.

`tan[2tan^-1 (1/3) - pi/4]` = ______.

`int (cos x)/(1 - sin x) "dx" =` ______.

If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.

The value of cot (- 1110°) is equal to ______.

General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)

`int[ tan (log x) + sec^2 (log x)] dx= ` ______

If `overline (a) =10hat("i") + lambda hat("j") + 2hat("k")` is perpendicular to `overline (b)= hat ("i")+hat("j")-hat("k")`, then λ is equal to ______.

If the line `x/(3) = y/(4)` = z is perpendicular to the line `(x - 1)/k = (y + 2)/(3) = (z - 3)/(k - 1)`, then the value of k is ______.

In a triangle ABC, ∠C = 90°, then the value of `tan^-1 ("a"/("b + c")) + tan^-1("b"/("c + a"))` is ______.

`cos(2sin^-1  3/4+cos^-1  3/4)=` ______.