List of top Mathematics Questions

The value of $\cos^2 \, 48^{\circ} - \sin^2 12^{\circ}$ is
The value of $\cos \frac{2\pi}{7} + \cos \frac{4 \pi}{7} + \cos \frac{6\pi}{7} $ is equal to
The value of $\cos\left( 2 \cos^{-1} x + \sin^{-1} x\right) $ at $x = \frac{1}{5} $ is
The value of $\cos \, 1^{\circ} \, \cos \, 2^{\circ} \, \cos \, 3^{\circ} ... \cos \, 179^{\circ}$ is
The value of $\cos \, 12^{\circ} + \cos \, 84^{\circ} + \cos \, 156^{\circ} + \cos \, 132^{\circ}$ is
The value of $\cos^{-1} \left(\cos \frac{7\pi}{6}\right) $ is
The value of $c$ in Rolle's theorem for the function $f(x) = x^3 - 3x$ in the interval $\left[0, \sqrt{3}\right]$ is
The value of $\binom{30}{0}\binom{30}{10}-\binom{30}{1}\binom{30}{11}+\binom{30}{2}\binom{30}{12} .....+ \binom{30}{20}\binom{30}{30}$ is where $\binom{n}{r} = ^{n}C_{r}$
The value of $2^{1/4}.4^{1/8}. 8^{1/6}....\infty $ is
The value of $\left(1+i\right)^{4} \left(1+\frac{1}{i}\right)^{4}$ is
The value of 1.2.3 + 2.3.4 +3.4.5 + ... + n terms is
The value of $\frac{1}{81^n}-\frac{10}{81^n}\,^{2n}C_1+\frac{10^2}{81^n}\,^{2n}C_2-\frac{10^3}{81^n}\,^{2n}C_3+.....+\frac{10^{2n}}{81^n}is$
The value of $1^2.C_1 + 3^2.C_3 + 5^2.C_5 + ...$ is :
The value o $\frac{3+cot\,76^\circ cot\,16^\circ}{cot\,76^\circ + cot\,16^\circ} is $
The two vertices of a triangle are $(4,2,1)$ and $(5,1,4)$. If the centroid is $(5,2,3)$, then the third vertex is
The triplet $(x, y, z)$ is chosen from the set $\{1,2,3,... n\}$, such that $x \le y < z$. The number of such triplets is
The transformation 'orthogonal projection on X- axis' is given by matrix
The three concurrent edges of a parallelepiped represents the vectors $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ such that $[\overrightarrow{a}\,\overrightarrow{b}\,\overrightarrow{c}]= \lambda$. Then the volume of the parallelopiped whose three concurrent edges are the three concurrent diagonals of three faces of the given parallelopiped is
The term independent of $x$ in the expansion of $(x- \frac {3} {x^2})^{18}$
The symbolic form of "(either p) or (not p )" is
The symbolic form of "p and q" is
The sum of two unit vectors is a unit vector. The magnitude of their difference is
The sum of the infinite series $\sin^{-1}\frac{1}{\sqrt2}+\sin^{-1}\left(\frac{\sqrt2-1}{\sqrt6}\right)+\sin^{-1}\left(\frac{\sqrt3-\sqrt2}{\sqrt{12}}\right)+...+\sin^{-1}\left(\frac{\sqrt n-\sqrt{n-1}}{\sqrt{n(n+1)}}\right)$ is
The sum of the numbers $436.32$, $227.2$ and $0.301$ in appropriate significant figures is
The sum of two positive integers is at most 5. The difference between two times of second number and first number is at most 4. If the first number is x and second number y, then for maximizing the product of these two numbers, the mathematical formulation is