List of top Mathematics Questions

If $a$ and $b$ are positive numbers such that $ a>b, $ then the minimum value of $ a\sec \theta -b\tan \theta \left( 0

The chord joining the points $(5, 5)$ and $(11, 227)$ on the curve $y =3x^{2}-11x-15$ is parallel to tangent at a point on the curve. Then the abscissa of the point is

If $ {{c}_{1}},{{c}_{2}},{{c}_{3}},{{c}_{4}},{{c}_{5}} $ and $ {{c}_{6}} $ are constants, then the order of the differential equation whose general solution is given by $ y={{c}_{1}}cos $ $ (x+{{c}_{2}})+{{c}_{3}}\sin (x+{{c}_{4}})+{{c}_{5}}{{e}^{x}}+{{c}_{6}} $

If $a = e^{i \theta}$ , then $\frac{1 + a}{1-a}$ is equal to

A man of $2\,m$ height walks at a uniform speed of $6 \,km/h$ away from a lamp post of $6 \,m$ height. The rate at which the length of his shadow increases is

If $A = \begin{pmatrix}1&0\\ 1&1\end{pmatrix}$ , then $A^n + nI$ is equal to

If tan $\frac{\theta}{2}=\frac{1}{2}$,then the value of sin $\theta$ is

A complete cycle of a traffic light takes $60\, seconds$. During each cycle the light is green for $25\, seconds$, yellow for $5 \,seconds$ and red for $30\, seconds$. At a randomly chosen time, the probability that the light will not be green, is

If $ y={{\sin }^{-1}}\sqrt{1-x}, $ then $ \frac{dy}{dx} $ is equal to

Solution of diff. equation $(6x + 2y - 10)\frac{dy}{dx}=2x+9y-20$ is

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

If a$_1$ = 4 and $a_{n+1}=a_{n}+4n\quad for\quad n\ge1. $ then the value of a$_{100}$ is

If $a$ 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 $a_1, a_2 , a_3 , a_4$ 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 period of the function $f\left(x\right)= cos 4x+$ tan $3x$ is

The value of $ \displaystyle\lim _{x \rightarrow 0} \frac{\cot 4 x}{\text{cosec} 3 x}$ is equal to

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 :