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

The general solution of the equation tan θ + tan 4θ + tan 7θ = tan θ tan 4θ tan 7θ is ______.

General solution of the equation sin 2x – sin 4x + sin 6x = 0 is ______.

The equation of tangent to the curve y = `sin^-1  (2x)/(1 + x^2)` at x = `sqrt(3)` is ______.

If the curves ay + x² = 7 and x³ = y cut orthogonally at (1, 1), then the value of a is ______.

Which of the following equation has no solution?

If x = e^θ, (sin θ – cos θ), y = e^θ (sin θ + cos θ) then `dy/dx` at θ = `π/4` is ______.

If the line y = 4x – 5 touches to the curve y² = ax 3+ bat the point (2, 3) then 7a + 2b = ______.

The number of principal solutions of tan 2θ = 1 is ______.

The object function z = 4x₁ + 5x₂, subject to 2x₁ + x₂ ≥ 7, 2x₁ + 3x₂ ≤ 15, x₂ ≤ 3, x₁, x₂ ≥ 0 has minimum value at the point is ______.

The sides of a rectangle are given by x = ± a and y = ± b. The equation of the circle passing through the vertices of the rectangle is ______.

The point on the curve y = `sqrt(x - 1)`, where the tangent is perpendicular to the line 2x + y – 5 = 0 is ______.

The objective function of LPP defined over the convex set attains it optimum value at ______.

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 ______.