List of top Mathematics Questions

If $\theta + \phi = \frac{\pi}{4}$, then $\left(1+ \tan\,?\right)\left(1+ \tan\,\phi\right)$ is equal to
Let $f(x) = \tan^{-1}x$. Then $f'(x) + f''(x)$ is = $0$, when $x$ is equal to
The number $(101)^{100} - 1$ is divisible by
Define a relation $R$ on $A =\{1, 2, 3, 4\}$ as $_xR_y$ if $x$ divides $y$. $R$ is
If $\frac {Log\,x}{b-c} = \frac {Log\,y}{c-a}=\frac {Log \,z}{a-b}$ then the value of $ x^{b+c} . y^{c+a}.z^{a+b} $ is
If rth and (r + 1)th terms in the expansion of $(p + q)^n$ are equal, then $\frac {(n+1)q} {r(p+q)} $ is
The sum of the reciprocals of focal distances of a focal chord $PQ$ of $y^2 = 4ax$ is
If $\vec{a}, \vec{b}$ and $\vec{c}$ are unit vectors such that $\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}$ then angle between $\vec{a \text { and }} \vec{b}$ is
A value of $ \theta$ satisfying $\sin 5 \theta - \sin 3 \theta + \sin \; \theta=0$ such that $0
The domain of $ f(x) = sin^{-1} [Log_2 (\frac {x} {2})] $ is
If lines represented by $x + 3y - 6 = 0, 2x+y-4=0$ and $kx - 3y + 1 = 0$ are concurrent, then the value of $k$ is
The negation of $p \to (\sim p \vee q) $ is
In any triangle $ABC$, the simplified form of $\frac {Cos 2A}{a^2}-\frac{Cos2B}{b^2}$ is
The value of $\sin 10^{\circ} \cdot \sin 30^{\circ} \cdot \sin 50^{\circ}-\sin 70^{\circ}$ is
There are 10 points in a plane, out of these 6 are collinear. If N is the number of triangles formed by joining these points. then :
For each natural number $n, (n + 1)^7 - n^7 -1$ is divisible by 7. For each natural number $n, n^7 - n$ is divisible by 7.
In Argand's plane, the point corresponding to $\frac {(1-i\sqrt {3})(1+i)} {(\sqrt {3}+i)}$ lies in
If $ I_{1}=\int_{0}^{\frac{\pi}{2}} f (sin \,2x)sin \,xdx $ and $ I_2 = \int^{\pi/4}_{0}\,f(cos2x) cosx \,dx\,then\, I_1/I_2 $ =
$ \int\limits_0^{\pi /8} \tan^2 (2x) dx = $
A value of $b$ for which the equations $x^2+bx-1=0,x^2+x+b=0$ have one root in common is
A line is drawn through the point $ P(3,11) $ to cut the circle $ x^2+ y^2 = 9 $ at point $ A $ and $ B $ . Then, $ PA \cdot PB $ is equal to
Total number of solutions of $ sin^4x +cos^4x = sin x cos x $ is $ [0,2\pi] $ is equal to
The locus of the point of intersection of the tangents at the extremeties of a chord of the circle $ x^2+y^2 = a^2 $ which touches the circle $ x^2 + y^2 - 2ax = 0 $ passes through the point
The projections of a directed lines segment on the coordinate axes are $ 12, 4, 3 $ . The direction cosines of the line are
Sachin and Rahul attempted to solve a quadratic equaiton. Sachin made a mistake in writing down the constant term and ended up in roots (4, 3). Rahul made a mistake in writing down coefficient of x to get roots (3, 2). The correct roots of equation are :