List of top Mathematics Questions

Which one of the following functions is one-to-one?
If $A = \begin{pmatrix}1&5\\ 0&2\end{pmatrix}$ , then
$\int\frac{1}{\sin x\, \cos x}$ dx is equal to
Find the projection of the vector \(\hat{i}+3\hat{j}+7\hat{k}\) on the vector \(7\hat{i}-\hat{j}+8\hat{k}.\)
If $|z + 1| < |z - 1|$ , then $z$ lies
$\tan ( 2 \sin^{-1} ( \frac{5}{13} )) = $
If $a$ is positive and if $A$ and $G$ are the arithmetic mean and the geometric mean of the roots of $ {{x}^{2}}-2ax+{{a}^{2}}=0 $ respectively, then
If a$_1$ = 4 and $a_{n+1}=a_{n}+4n\quad for\quad n\ge1. $ then the value of a$_{100}$ is
If $a_1, a_2 , a_3 , a_4$ are in A.P., then $\frac{1}{\sqrt{a_{1}}+\sqrt{a_{2}}}+\frac{1}{\sqrt{a_{2}}+\sqrt{a_{3}}}+\frac{1}{\sqrt{a_{3}}+\sqrt{a_{4}}}=$
A die has four blank faces and two faces marked $3$. The chance of getting a total of $12$ in $5$ throws is
If $ \alpha $ and $ \beta $ are the roots of the equation $ a{{x}^{2}}+ $ $ bx+c=0,\text{ }\alpha \beta =3 $ and $a, b, c$ are in $A.P.$, then $ \alpha +\beta $ is equal to
The value of $ \displaystyle\lim _{x \rightarrow 0} \frac{\cot 4 x}{\text{cosec} 3 x}$ is equal to
The period of the function $f\left(x\right)= cos 4x+$ tan $3x$ is
The solution set of inequality $\frac{2x}{x^2 - 9} \leq \frac{1}{x + 2 }$ is
The perpendicular distance (d) of a line Ax + By + C = 0 from a point $(x_1, y_1)$ is given by :
A random variable X has the following probability distribution:
\(X\)012
\(P(X)\)\(\frac{25}{36}\)k\(\frac{1}{36}\)
If the mean of the random variable X is \(\frac{1}{3}\), then the variance is
$\displaystyle\lim_{x\to0}\frac{e^{x^2} -cos x}{x^{2}}=$
$\int\left(\frac{x-a}{x}-\frac{x}{x+a}\right) dx$ is equal to
If the 21st and 22nd terms in the expansion of $(1 + x)^{44}$, are equal, then x =
Three numbers $x, y$ and $z $ are in arithmetic progression. If $x + y + z = - 3$ and $xyz= 8$, then $x^2 + y^2 + z^2$ is equal to
Solve the following equations: 
(a) 10p = 100
(b) 10p + 10 = 100
(c)\(\frac{p}{4}\)=5
(d) \(\frac{-p}{3}\)=5
(e)\(\frac{3p}{4}\)=6
(f)3s=-9
(g)3s+12=0
(h)3s=0
(i)2q=6
(j)2q-6=0
(k)2q+6=0
(l)2q+6=12

In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.

  1. f : R→R defined by f(x)=3−4x
  2. f : R→R defined by f(x)=1+x2
Which factors are not included in the prime factorisation of a composite number?
Let $ z=\frac{11-3i}{1+i}. $ If a is a real number such that $ z-i\alpha $ is real, then the value of $ \alpha $ is
Let $S_{n}$ denote the sum of first $n$ terms of an $A.P$. and $S_{2n} = 3S_{n}$. If $S_{3n} =k S_{n}$, then the value of $k$ is equal to