List of top Mathematics Questions asked in MHT CET

For three simple statements p, q, and r, p → (q ˅ r) is logically equivalent to

If a and b are two vectors such that I$\vec {a}$I + I$\vec {b}$I = $\sqrt 2$ with $\vec {a}$.$\vec {b}$ = –1, then the angle between $\vec {a}$ and $\vec {b}$ is

Give that f(x) =$\frac {1-cos4x}{x^2}$ if x < 0 ,f(x) = a if x = 0 , f(x) =$\frac {\sqrt {x}}{\sqrt {16 + \sqrt {x} }- 4}$ if x > 0, is continuous at x = 0, then a will be

$\int_{-π/2}^{π/2} f(x) \,dx$ =?
Where f(x) = sin |x| + cos |x|, x ∈ $(-\frac {π}{2}, \frac {π}{2})$

$y = tan^{-1} (\frac{4 sin 2x}{cos 2x - 6sin^2x})$ then $\frac{dy}{dx}$ at $x=0$.

In a triangle ABC, with usual notations ∠A = 60°, then (1 + $\frac {a}{c}$ + $\frac {b}{c}$)(1 + $\frac {c}{b}$ - $\frac {a}{b}$) = ?

The area of the region bounded by the y-axis, y = cos x, y = sin x, when 0 ≤ x ≤$\frac {π}{4}$, is

The general solution of the differential equation x² + y² – 2xy $\frac {dy}{dx}$ = 0 is (where C is a constant of integration.)

The function f(x) = 2x³ – 9x² + 12x +29 is monotonically increasing in the interval.

Argument of $\frac {1-i√3}{1+i√3}$ is

The equation of the line perpendicular to 2x – 3y + 5 = 0 and making an intercept 3 with positive Y-axis is

Probability of getting odd numbers in first 100 numbers.

$\int \cos^3 x \cdot e^{\log(\sin x)} , dx = $

If \[ \lim_{x \to 5} \frac{x^k - 5^k}{x - 5} = 500 \], then the value of $ k $, where $ k \in \mathbb{N} $ is

In a triangle ABC, with usual notations $a = 2$, $b = 3$, $c = 5$, then $\frac{\cos A}{a} + \frac{\cos B}{b} + \frac{\cos C}{c} =$

The area of the triangle ABC is $10\sqrt{3}\ \text{cm}^2$, angle B is $60^\circ$ and its perimeter is $20\ \text{cm}$, then $\ell(\text{AC}) =$

If $a = \lim_{n \rightarrow \infty} \frac{1+2+3+\ldots+n}{n^2}$ and $b = \lim_{n \rightarrow \infty} \frac{1^2+2^2+3^2+\ldots+n^2}{n^3}$, then

If lines represented by the equation $px^2 - qy^2 = 0$ are distinct, then

If $A = \begin{bmatrix} 1 & 0 & 2 \\ -1 & 1 & -2 \\ 0 & 2 & 1 \end{bmatrix}$ and $\text{adj } A = \begin{bmatrix} 5 & x & -2 \\ 1 & 1 & 0 \\ -2 & -2 & y \end{bmatrix}$, then the value of $x + y$ is

A polygon has 44 diagonals. Then the number of sides of the polygon are

If $x = 1 + 2i$, then the value of $x^3 + 7x^2 - x + 16$ is

If $\vec{a}$, $\vec{b}$, $\vec{c}$ are mutually perpendicular vectors having magnitudes $1$, $2$, $3$ respectively, then $[\vec{a} + \vec{b} + \vec{c} \quad \vec{b} - \vec{a} \quad \vec{c}] =$

If the variance of the data $2, 4, 5, 6, 8, 17$ is $23.33$, then the variance of $4, 8, 10, 12, 16, 34$ will be

The shortest distance between lines $\vec{r} = (2\hat{i} - \hat{j}) + \lambda(2\hat{i} + \hat{j} - 3\hat{k})$ and $\vec{r} = (\hat{i} - \hat{j} + 2\hat{k}) + \mu(2\hat{i} + \hat{j} - 5\hat{k})$ is

A random variable $X \sim B(n, p)$. If the values of the mean and variance of $X$ are $18$ and $12$ respectively, then $n =$