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

The solution of the equation `1 + ("d"x)/("d"y) = (2y)/x` is ______.

The solution for the differential equation `("d"y)/y +("d"x)/x` = 0 is ______.

The value of (2 + i)³ × (2 – i)³ is ______.

`lim_(n→∞)tan{sum_(r = 1)^n tan^-1(1/(1 + r + r^2))}` is equal to ______. 

If `veca + vecb = vecc ((λx)hati + yhatj + 4zhatk) + (yhati + xhatj + 3yhatk) = -zhati - 2zhatj - (λ + 1)xhatk` are sides of triangle as shown is figure then value of λ is ______.

(where x, y, z are not all zero)

If α and β are the roots of the equation x² + 2x + 4 = 0, then `1/α^3 + 1/β^3` is equal to ______.

The term independent of x in the expansion of `(root(6)(x) - 1/root(3)(x))^9` is ______.

The equation of a circle with centre at (1, 0) and circumference 10π units is ______.

If A and B are two events, such that P(A ∪ B) = `3/4`, P(A ∩ B) = `1/4`, P(A^c) = `2/3` where A^c stands for the complementary event of A, then P(B) is given by ______.

The area bounded by y – 1 = |x|, y = 0 and |x| = `1/2` will be ______.

The area bounded by the curves x + 2y² = 0 and x + 3y² = 1 is ______.

Number of values of x which lie in [0, 2π] and satisfy the equation

`(cos  x/4 - 2sinx) sinx + (1 + sin  x/4 - 2cosx)cosx` = 0

If α, β, γ and a, b, c are complex numbers such that `α/a +  β/b + γ/c` = 1 + i and `a/α +  b/β + c/γ` = 0, then the value of `α^2/a^2 +  β^2/b^2 + γ^2/c^2` is equal to ______.

Let p, q and r be any three logical statements. Which of the following is true?

If sin^–1a + sin^–1b + sin^–1c = π, then find the value of `asqrt(1 - a^2) + bsqrt(1 - b^2) + csqrt(1 - c^2)`.

If ax + b (sec (tan^–1 x)) = c and ay + b (sec.(tan^–1 y)) = c, then `(x + y)/(1 - xy)` = ______.

The cost of running a bus from A to B, is ₹`(av + b/v)`, where v km/h is the average speed of the bus. When the bus travels at 30 km/h, the cost comes out to be ₹ 75 while at 40 km/h, it is ₹ 65. Then the most economical speed (in km/h) of the bus is ______.

In a binomial distribution `B(n, p = 1/4)`, if the probability of at least one success is greater than or equal to `9/10`, then n is greater than ______.

The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.

`int (x + sinx)/(1 + cosx)dx` is equal to ______.