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

If x = p sin θ, y = q cos θ, then `dy/dx` = ______ 

If S₁ and S₂ are respectively the sets of local minimum and local maximum points of the function, f(x) = 9x⁴ + 12x³ - 36x² + 25, x ∈ R, then ______ 

`lim_(x -> 5) |x - 5|/(x - 5)` = ______.

Determine the system of linear equation for which the solution set is the shaded region in the following figure ______.

The number of solutions of sin x + sin 3x + sin 5x = 0 in the interval `[pi/2, (3pi)/2]` is ______.

3. 9. 15. 21 ...... upto 50 factors is equal to ______.

`lim_(x -> 0) (sin 4x + sin 2x)/(sin5x - sin3x)` = ______.

Find out which of the following statements have the same meaning: 
i. If Meena makes a software then she is happy.

ii. If Meena does not make a software then she is not happy.

iii. If Meena is not happy then she hasn't made a software.

iv. If Meena is happy then she has made a software.

Solution set of the inequality y ≥ 0 is ______.

The normal of the curve x = a(cos θ + θ sin θ) and y = a(sin θ – θ cos θ), at any point θ, is such that ______.

If y = `(2sinα)/(1 + cosα + sinα)`, then value of `(1 - cos α + sin α)/(1 + sin α)` is ______.

By using principle of mathematical induction for every natural number, (ab)ⁿ = ______.

The set of real x satisfying the inequality `(5 - 2x)/3 ≤ x/6 - 5` is [a, ∞). The value of ‘a’ is ______.

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 ______.