List of top Mathematics Questions

If $ y = sec(tan^{-1}x) $ , then $ \frac{dy}{dx} $ at $ x = 1 $ is

If $ f(x) = \frac{x}{2} -1 $ then on the interval $ [0,\pi] $

A polygon has $44$ diagonals. The number of its sides are

If origin is the centroid of a $ \Delta PQR $ with vertices $ P(2a,2,6),Q(-4,3b,- 10) $ and $ (8,14,2c) $ , then the value of $ a,b $ and $ c $ are respectively.

Given that the points $ P(3,2, - 4) $ , $ Q(5,4, - 6) $ and $ R(9,8,-10) $ are collinear, the ratio in which $ Q $ divides $ PR $ externally is

If $ A $ and $ B $ are two square matrices such that $ AB $ = $ A $ and $ BA $ = $ B $ , then

The function $ f(x) = cos^2x $ is strictly decreasing on

Consider the following propositions : p : I take medicine q : I can sleep Then, the compound statement $ \sim p \rightarrow \sim q $ means

If $ \begin{bmatrix}\alpha&\beta\\ \gamma&-\alpha\end{bmatrix} $ is to be square root of the two rowed unit matrix, then $ \alpha $ , $ \beta $ and $ \gamma $ should statisfy the relation

The sum of two numbers is $10$. Their product will be maximum when they are

The maximum value of $ \frac{log x}{x} $ is

The value of the integral $ \int_{-2}^{0}\frac{dx}{\sqrt{12-x^{2}-4x}} $ is

The integral $ \int \sqrt{16-9x^2} $ $dx$ equals

The value of the integral $ \int_{0}^{1} $ $ \frac{e^{5log_{e}x}-e^{4log_{e}x}}{e^{log_{e}x^3}-e^{log_{e}x^2}}dx $ is

$ \int \frac{x^3dx}{1+x^4} $ equals

A line perpendicular to the line segment joining the points $ (1,0) $ and $ (2,3) $ divides it in the ratio $ 1 : n $ . The equation of the line is

If the straight lines $2x + 3y - 3 = 0$ and $x + ky + 7 = 0$ are perpendicular, then the value of $k$ is

If $a = 3, b = 4, c = 5$ each one of $a ,b$ & $c$ is perpendicular to the sum of the remaining then $| a + b + c | $ is equal to

If A = $ \begin {bmatrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b \end {bmatrix}$ is a matrix satisfying the equation $AA^T =9 I,$ where, $I$ is $3 \times 3$ identity matrix, then the ordered pair $(a, b)$ is equal to

The solution set of the inequation $\frac {x^2+6x-7}{|x+4|}<0$ is

If $ f(x) = 2-2x^2,$ find $\frac {f(3,8)-f(4)} {3.8-4} $,

The sum of coefficients of integral powers of $x$ in the binomial expansion $(1-2\sqrt x)^{50}$ is

The value of $ \tan( 1^\circ) +\, tan(89^\circ)$ is

The arithmetic mean of the data $0,1,2, \ldots \ldots, n$ with frequencies $1,{ }^{n} C_{1},{ }^{n} C_{2}, \ldots,{ }^{n} C_{n}$ is

In a certain town, $25\%$ of the families own a phone and $15\%$ own a car $65\%$ families own neither a phone nor a car and $2,000$ families own both a car and a phone. Consider the following three statements : (a) $5\%$ families own both a car and a phone. (b) $35\%$ families own either a car or a phone. (c) $40,000$ families live in the town. Then,