List of top Mathematics Questions

For real constants $a$ and $b$, let \[ f(x) = \begin{cases} \frac{a \sin x - 2x}{x}, & x < 0 \\ bx, & x \ge 0 \end{cases} \] 

If $f$ is a differentiable function, then the value of $a + b$ is 
 

If $\{x_n\}_{n \ge 1}$ is a sequence of real numbers such that $\lim_{n \to \infty} \frac{x_n}{n} = 0.001$, then
 

The maximum value of the function \[ y = \frac{x^2}{x^4 + 4}, x \in \mathbb{R}, \] is ............
Which one of the following series is convergent?
Which of the following is FALSE?
The solution to the limit \( \lim_{x \to 0} \frac{2 - \sqrt{4 - x}}{x} \) is ...........
A sum was put at simple interest at a certain rate for 3 years. Had it been put at 1% higher rate, it would have fetched ₹5,100 more. The sum is _______.
Shiva invested a certain sum of money in a simple interest bond whose value grew to ₹300 at the end of 3 years and to ₹400 at the end of another 5 years. What was the rate of interest at which he invested his sum?
If $L=\sin ^{2}\left(\frac{\pi}{16}\right)-\sin ^{2}\left(\frac{\pi}{8}\right)$ and $M=\cos ^{2}\left(\frac{\pi}{16}\right)-\sin ^{2}\left(\frac{\pi}{8}\right),$ then :
A die is thrown $10$ times, the probability that an odd number will come up at least one time is
$\displaystyle \lim_{x \to 1}$$\left\{log_{e}\left(e^{x\left(x-1\right)}-e^{x\left(1-x\right)}\right)-log_{e}\left(4x\left(x-1\right)\right)\right\}$ is equal to :
The value of $\,^{16}C_9 + \,^{16}C_{10} -\,^{16}C_6 -\,^{16}C_7$ is
The value of
16C9 + 16C10- 16C6 - 16C7 is
If \(\begin{pmatrix} 2 & 1 \\ 3 & 2 \\ \end{pmatrix}A=\begin{pmatrix} 1 & 0 \\ 0 & 1 \\ \end{pmatrix}\), then the matrix A is
Let f(x) be a quadratic polynomial such that f(–1) + f(2) = 0. If one of the roots of f(x) = 0 is 3, then its other root lies in :
If A = {1, 2, 3, 4, 5, 6}, then the number of subsets of A which contain atleast two elements is

The value of 

\[\int e^{\sin x}\sin 2x\ dx\]

 is

Let $f :(-1, \infty) \rightarrow R$ be defined by $f (0)=1$ and $f ( x )=\frac{1}{ x } \log _{ e }(1+ x ), x \neq 0 .$ Then the function $f$
If $|tan \,A + \cot \,A = 2$, then the value of $\tan^4 A + \cot^ 4 A = $
The value of the limit
$\displaystyle\lim _{x \rightarrow \frac{\pi}{2}} \frac{4 \sqrt{2}(\sin 3 x+\sin x)}{\left(2 \sin 2 x \sin \frac{3 x}{2}+\cos \frac{5 x}{2}\right)-\left(\sqrt{2}+\sqrt{2} \cos 2 x+\cos \frac{3 x}{2}\right)}$
is _______

If f(x) = \(\left\{ \begin{aligned}     & \frac{1-\cos Kx}{x\sin x} ,\ \ \text{if x}\neq0 \\     &\ \ \ \ \ \  \ \frac{1}{2}\ \ \ \ \ \ \ \ \  ,\ \ \  \text{if x=0} \end{aligned} \right.\) is continuous at x = 0, then the value of K is

Let $a$ and $b$ be positive real numbers. Suppose $\overrightarrow{P Q}=a \hat{i}+b \hat{j}$ and $\overrightarrow{P S}=a \hat{i}-b \hat{j}$ are adjacent sides of a parallelogram $PQRS$. Let $\vec{ u }$ and $\vec{ v }$ be the projection vectors of $\vec{ w }=\hat{ i }+\hat{ j }$ along $\overrightarrow{ PQ }$ and $\overrightarrow{ PS }$, respectively. If $|\vec{u}|+|\vec{v}|=|\vec{w}|$ and if the area of the parallelogram $PQRS$ is $8$, then which of the following statements is/are TRUE?
Let $f: R \rightarrow R$ be a differentiable function such that its derivative $f^{\prime}$ is continuous and $f(\pi)=-6$. If $F$ : $[0$, $\pi] \rightarrow R$ is defined by $F(x)=\int\limits_{0}^{x} f(t) d t$, and if
$\int\limits_{0}^{\pi}\left(f^{\prime}(x)+F(x)\right) \cos x d x=2$
then the value of $f (0)$ is _____
A fruit vendor purchases two varieties of oranges at the rates of 12 oranges for ₹ 18 and 18 oranges for ₹ 12. He mixes the two varieties in the ratio of 2: 3 and sells the mixed stock at a price of ₹ 144 for 10 dozens. What percentage of profit or loss does he make ?
The inverse function of $f\left(x\right) = \frac{8^{2x}-8^{-2x}}{8^{2x} + 8^{-2x}}, x\epsilon \left(-1, 1\right),$ is __________.