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

If z₁ = 2 – 4i and z₂ = 1 + 2i, then `bar"z"_1 + bar"z"_2` = ______.

The acute angle between the curve x = 2y² and y = 2x² at `(1/2, 1/2)` is ______.

If `3tan^-1x +cot^-1x = pi`, then xis equal to ______.

Let f(x) be a non-negative continuous function such that the area bounded by the curve y = f(x), X-axis and the ordinates x = `pi/4` and x = `beta > pi/4` is `(beta sin beta + pi/4 cos beta + sqrt(2)beta)`. Then `"f"(pi/2)` is ______.

The general solution of the differential equation `y  "d"x - (1 + x^2) cot^-1 x  "d"y` = 0 is ______.

The solution of the differential equation `("d"y)/("d"x) + 2y tan x = 2x cos^2x` is ______.

The value of `sin^-1[cos(pi/3)] + sin^-1[tan((5pi)/4)]` is ______.

If `int x^3"e"^(x^2) "d"x = "e"^(x^2)/2 "f"(x) + "c"`, then f(x) = ______.

Circle x² + y² – 4x = 0 touches ______.

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 ______.