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

If the tangent at (1, 7) to the curve x² = y – 6 touches the circle x² + y² + 16x + 12y + c = 0 then the value of c is ______.

The normal to the hyperbola `x^2/a^2 - y^2/9` = 1 at the point `(8, 3sqrt(3))` on it passes through the point ______.

The value of `lim_(x rightarrow 0) (sqrt((1 + x^2)) - sqrt(1 - x^2))/x^2` is ______.

The value of `d/(dx)[tan^-1((a - x)/(1 + ax))]` is ______.

Which of the following linear inequalities satisfy the shaded region of the given figure?

A curve is represented by the equation x = sec²t and y = cot t, where t is a parameter. If the tangent at the point P on the curve where t = `π/4` meets 4 the curve again at the point Q, then |PQ| is equal to ______.

The general solution of x(1 + y²)^1/2 dx + y(1 + x²)^1/2 dy = 0 is ______.

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?

The line 5x + y – 1 = 0 coincides with one of the lines given by 5x² + xy – kx – 2y + 2 = 0 then the value of k is ______.

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 ______.