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

Principal solutions at the equation sin 2x + cos 2x = 0, where π < x < 2 π are ______.

The general solution of the equation tan² x = 1 is ______.

If A_ij denotes the cofactor of the element a_ij of the determinant `|(2, -3, 5),(6, 0, 4),(1, 5, -7)|`, then value of a₁₁A₃₁ + a₁₂A₃₂ + a₁₃A₃₃ is ______.

If the tangent to the curve, y = x³ + ax – b at the point (1, –5) is perpendicular to the line –x + y + 4 = 0, then which of the following point lies on the curve?

Let T_n denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If T_{n + 1} – T_n = 21, then n is equal to ______.

If a = sin θ + cos θ, b = sin³ θ + cos³ θ, then ______.

The general solution of sin x – 3 sin 2x + sin 3x = cos x – 3 cos 2x + cos 3x is ______.

Let f(x) be a polynomial function of the second degree. If f(1) = f(–1) and a₁, a₂, a₃ are in AP, then f’(a₁), f’(a₂), f’(a₃) are in ______.

The value of `lim_(x rightarrow 0) 1/x^3 int_0^x (t log (1 + t))/(t^4 + 4) dt` is ______.

With usual notations, in any ΔABC, if a cos B = b cos A, then the triangle is ______.

The mean and variance of n observations x₁ ,x₂, x₃, ..., x_n are 5 and 0, respectively. If `sum_(x = 1)^n x_i^2` = 400, then the value of n is equal to ______.

`lim_(x rightarrow 0) (1 - cos x)/x^2` is equal to ______.

The value of x obtained from the equation `|(x + a, b, c),(c, x + b, a),(a, b, x + c)|` = 0 will be ______.

The value of determinant `|((α^x + a^-x)^2, (α^x - α^-x)^2, 1),((β^x + β^-x)^2, (β^x - β^-x)^2, 1),((γ^x + γ^-x)^2, (γ^x - γ^-x)^2, 1)|`

In ΔABC, a(cos²B + cos²C) + cos A(c cos C + b cos B) = ?

In ΔABC, if (a+ b - c)(a + b + c) = 3ab, then ______.

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 ______.

Degree of the given differential equation

`(("d"^3"y")/"dx"^2)^2 = (1 + "dy"/"dx")^(1/3)` is

The probability distribution of a r.v. X is

Then F (-1) = ?

In a ΔABC, cot `(("A - B")/2)* tan (("A + B")/2)` is equal to