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Mathematics
List of top Mathematics Questions
The value of
$\left(\frac{\cos\left(\frac{\pi}{2} + x\right) + \sin\left(\frac{\pi}{2}+ x\right)}{\cos\left(\frac{\pi}{2} - x\right) - \sin\left(\frac{\pi}{2} - x\right)}\right)^{2} $
is
Mathematics
Trigonometric Functions
The value of
$\cos\left( 2 \cos^{-1} x + \sin^{-1} x\right) $
at
$x = \frac{1}{5} $
is
Mathematics
Properties of Inverse Trigonometric Functions
The value of
$cos \,12^{\circ} + cos84^{\circ} + cos \,156^{\circ} + cos \,132^{\circ}$
is
Mathematics
Trigonometric Functions
The value of
$\cos^2 \, 48^{\circ} - \sin^2 12^{\circ}$
is
Mathematics
Trigonometric Functions
The value of
$\cos \frac{2\pi}{7} + \cos \frac{4 \pi}{7} + \cos \frac{6\pi}{7} $
is equal to
Mathematics
Trigonometric Functions
The value of
$\cos^{-1} \left(\cos \frac{7\pi}{6}\right) $
is
Mathematics
Properties of Inverse Trigonometric Functions
The value of
$\cos \, 1^{\circ} \, \cos \, 2^{\circ} \, \cos \, 3^{\circ} ... \cos \, 179^{\circ}$
is
Mathematics
Trigonometric Functions
The value of
$\cos \, 12^{\circ} + \cos \, 84^{\circ} + \cos \, 156^{\circ} + \cos \, 132^{\circ}$
is
Mathematics
Trigonometric Functions
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
Mathematics
Application of derivatives
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
$\binom{n}{r} = ^{n}C_{r}$
Mathematics
Combinations
The value of
$2^{1/4}.4^{1/8}. 8^{1/6}....\infty $
is
Mathematics
Sequence and series
The value of
$\left(1+i\right)^{4} \left(1+\frac{1}{i}\right)^{4}$
is
Mathematics
Complex numbers
The value of 1.2.3 + 2.3.4 +3.4.5 + ... + n terms is
Mathematics
Sum of First n Terms of an AP
The value of
$\frac{1}{81^n}-\frac{10}{81^n}\,^{2n}C_1+\frac{10^2}{81^n}\,^{2n}C_2-\frac{10^3}{81^n}\,^{2n}C_3+.....+\frac{10^{2n}}{81^n}is$
Mathematics
Binomial theorem
The value of
$1^2.C_1 + 3^2.C_3 + 5^2.C_5 + ...$
is :
Mathematics
Combinations
The value o
$\frac{3+cot\,76^\circ cot\,16^\circ}{cot\,76^\circ + cot\,16^\circ} is $
Mathematics
Trigonometric Functions
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
Mathematics
Equation of a Line in Space
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
Mathematics
Sets
The transformation 'orthogonal projection on X- axis' is given by matrix
Mathematics
Matrices
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
Mathematics
Vectors
The term independent of
$x$
in the expansion of
$(x- \frac {3} {x^2})^{18}$
Mathematics
Binomial theorem
The symbolic form of "(either p) or (not p )" is
Mathematics
mathematical reasoning
The symbolic form of "p and q" is
Mathematics
mathematical reasoning
The sum of two unit vectors is a unit vector. The magnitude of their difference is
Mathematics
Vectors
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
Mathematics
Sum of First n Terms of an AP
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