List of top Mathematics Questions

The differential equation of all parabolas, whose axes are parallel to Y-axis, is

If $Z_{1}=4i^{40}-5i^{35}+6i^{17}+2$, $Z_{2}=-1+i$ where $i=\sqrt{-1}$, then $|Z_{1}+Z_{2}|=$

Let two non-collinear vectors $\hat{a}$ and $\hat{b}$ form an acute angle. A point P moves, so that at any time t the position vector $\overline{OP}$, where O is origin, is given by $\hat{a}\sin t+\hat{b}\cos t.$ when P is farthest from origin O, let M be the length of OP and $\hat{u}$ be the unit vector along $\overline{OP,}$ then

The number of solutions in $[0,2\pi]$ of the equation $16^{\sin^{2}x}+16^{\cos^{2}x}=10$ is

If two vertices of a triangle are $A(3,1,4)$ and $B(-4,5,-3)$ and the centroid of the triangle is $G(-1,2,1),$ then the third vertex C of the triangle is

In a Binomial distribution with $n=4$ if $2P(X=3)=3P(X=2)$, then the variance is

If $I = \int \frac{dx}{\sin(x-a) \sin(x-b)}$, then $I$ is given by}

The length of the perpendicular drawn from the point $(1, 2, 3)$ to the line $\frac{x-6}{3} = \frac{y-7}{2} = \frac{z-7}{-2}$ is

Let $f(x) = 5 - |x-2|$ and $g(x) = |x + 1|$, $x \in \mathbb{R}$. If $f(x)$ attains maximum value at $\alpha$ and $g(x)$ attains minimum value at $\beta$, then $\lim_{x \to \alpha\beta} \frac{(x-1)(x^2-5x+6)}{x^2-6x+8}$ is equal to}

Let $P(x)$ be a polynomial of degree 2, with $P(2) = -1$, $P'(2) = 0$, $P''(2) = 2$, then $P(1.001)$ is

Given a polynomial $P(x) = ax^2 + bx + c$ such that $P''(2)=2$, $P'(2)=0$, and $P(2)=-1$. Find the approximate value of $P(1.001)$ using linear approximation.

A lot of 100 bulbs contains 10 defective bulbs. Five bulbs are selected at random from the lot and are sent to retail store. Then the probability that the store will receive at most one defective bulb is

If $a \cos 2\theta + b \sin 2\theta = c$ has $\alpha$ and $\beta$ as its roots, then the value of $\tan \alpha + \tan \beta$ is

A vector parallel to the line of intersection of the planes $\vec{r} \cdot (3\hat{i} - \hat{j} + \hat{k}) = 1$ and $\vec{r} \cdot (\hat{i} + 4\hat{j} - 2\hat{k}) = 2$ is

$\int \frac{dx}{\cot^2 x - 1} = \frac{1}{A} \log |\sec 2x + \tan 2x| - \frac{x}{B} + c$, (where $c$ is constant of integration), then $A + B =$}

If $f'(x) = \sin(\log x)$ and $y = f\left(\frac{2x+3}{3-2x}\right)$, then $\frac{dy}{dx}$ at $x=1$ is

There are 6 positive and 8 negative numbers. From these four numbers are chosen at random and multiplied. Then the probability, that the product is a negative number, is

If $f(x) = \frac{2x-3}{3x-4}, x \neq \frac{4}{3}$, then the value of $f^{-1}(x)$ is

The area bounded by the curve $y = |x - 2|$, $x = 1$, $x = 3$ and X-axis is

The centroid of the triangle formed by the lines $x + 3y = 10$ and $6x^2 + xy - y^2 = 0$ is

If $|\vec{a}| = \sqrt{3}$; $|\vec{b}| = 5$; $\vec{b} \cdot \vec{c} = 10$, angle between $\vec{b}$ and $\vec{c}$ is $\frac{\pi}{3}$, $\vec{a}$ is perpendicular to $\vec{b} \times \vec{c}$. Then the value of $|\vec{a} \times (\vec{b} \times \vec{c})|$ is

If the lines $\frac{x-k}{2} = \frac{y+1}{3} = \frac{z-1}{4}$ and $\frac{x-3}{1} = \frac{y-\frac{9}{2{2} = \frac{z}{1}$ intersect, then the value of k is

The statement $[p \land (q \lor r)] \lor [\sim r \land \sim q \land p]$ is equivalent to}

The differential equation representing the family of curves $y^2 = 2c(x + \sqrt{c})$, where $c$ is a positive parameter, is of}

If $f(a) = 2$, $f'(a) = 1$, $g(a) = -1$, $g'(a) = 2$, then as $x$ approaches $a$, $\frac{g(x)f(a)-g(a)f(x)}{(x-a)}$ approaches}