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

If x = `sqrt("a"^(sin^-1 "t")), "y" = sqrt("a"^(cos^-1 "t")), "then" "dy"/"dx"` = ______

If the point (x₁, y₁) satisfies px - qy < 13, then the solution set represented by the inequation is ______ 

If `t = v^2/3`, then `(-v/2 (df)/dt)` is equal to, (where f is acceleration) ______ 

The statement ∼(p ↔ ∼q) is ______

Derivative of (tanx)⁴ is ______ 

The angle between the tangents to the curve y = `x^2 - 5x + 6` at the points (2, 0) and (3, 0) is ______ 

Equation of Z-axis is ______

Slope of normal to the curve y = x⁴ - 7x² at x = 2 is ______ 

A die is thrown 4 times. Getting an even number is considered a success. Then the variance of the distribution of success is ______

y = {x(x - 3)}² increases for all values of x lying in the interval.

If `sum_("r" - 1)^"n" (2"r" + 1) = 440,` then n = _____.

The number of solutions of cos 2θ = sin θ in (0, 2π) is ______

If function

f(x) = `x - |x|/x, x < 0`
      = `x + |x|/x, x > 0`
      = 1, x = 0, then

If y = `1 + x + x^2/(2!) + x^3/(3!) + x^4/(4!) + .....,` then `(d^2y)/(dx^2)` = ______

For the constraint of a linear optimizing function z = 3x₁ + 11x₂, given by 2x₁ + x₂ ≤ 2, 4x₁ + x₂ ≥ 4 and x₁, x₂ ≥ 0 

A particle moves so that x = 2 + 27t - t³. The direction of motion reverses after moving a distance of ______ units.

The value of sin 18° is ______.

If 4 sin^-1x + 6 cos^-1 x = 3π then x = ______.

If y = `(3x^2 - 4x + 7.5)^4, "then"  dy/dx` is ______ 

The shortest distance between A (1, 0, 2) and the line `(x + 1)/3 = (y - 2)/(-2) = (z + 1)/(-1)` is given by line joining A and B, then B in the line is ______