List of top Mathematics Questions

In a △ ABC, the lengths of the two larger sides are 10 and 9 units, respectively. If the angles are in A.P., then the length of the third side can be
The mean square deviation of a set of n observations about points -2 and 2 are 18 and 10 respectively. The standard deviation of the set is
Let a, b, c be three vectors satisfying a × b = ( a × c), | a|=| c|=1, | b|=4 and | b × c|=√(15). If a · b = ?, then λ equals
If fraceˣ+e⁵xe³x=a₀+a₁x+a₂x²+a₃x³+⋯ then the value of 2a₁+2³a₃+2⁵a₅+⋯ is
A bag contains (2n+1) coins. It is known that n of these coins have a head on both sides, whereas the remaining (n+1) coins are fair. A coin is picked up at random from the bag and tossed. If the probability that the toss results in a head is (31)/(42), then n is equal to
The period of tan 3θ is
The value of
\( \dfrac{3}{4} + \dfrac{15}{16} + \dfrac{63}{64} + \cdots \)
up to \( n \) terms is
If φ(x) is a differentiable function, then the solution of the differential equation dy+yφ'(x)-φ(x)φ'(x)dx=0 is
If g is the inverse of function f and f'(x)=sin x, then g'(x) is equal to
Evaluate limₓtₒᵢₙftyfracint₀²x x eˣ²dxe⁴x²
The average age of 8 men is increased by 2 years when one of them whose age is 20 yr is replaced by a new man. What is the age of the new man?
If \( \omega \) is the complex cube root of unity, then the value of
\( \omega + \omega \left( \dfrac{1}{2} + \dfrac{3}{8} + \dfrac{9}{32} + \dfrac{27}{128} + \cdots \right) \) is
The root of the equation 2(1+i)x²-4(2-i)x-5-3i=0 which has greater modulus is
$\cos ^{2} 5^{\circ}-\cos ^{2} 15^{\circ}-\sin ^{2} 15^{\circ}+\sin ^{2} 35^{\circ}$ $+\cos 15^{\circ} \sin 15^{\circ}-\cos 5^{\circ} \sin 35^{\circ}=$
If $\begin{vmatrix}a+b+2c&a&b\\ c&2a+b+c&b\\ c&a&a+2b+c\end{vmatrix} = 2 $, then $a^3 + b^3 + c^3 - 3abc$ =
If $\cos \theta \neq 0$ and $\sec \theta - 1 = ( \sqrt{2} - 1 ) \tan \theta $ then $\theta $ =
If $\sqrt{1-x^{6} }+ \sqrt{1-y^{6}} =a\left(x^{3} -y^{3}\right) , $ then $ y^{2} \frac{dy}{dx} = $
If $k$ is one of the roots of the equation $x^2 - 25x + 24 = 0 $ such that $A = \begin{bmatrix}1&2&1\\ 3&2&3\\ 1&1&k\end{bmatrix} $ is a non-singular matrix, then $A^{-1}$ =
If $y = \sin^2 (\cot^{-1} \sqrt{\frac{1+x}{1-x}} ) $, then $\frac{dy}{dx}$ =
If $\alpha$ and $\beta$ are the roots of $x^{2}+7 x+3=0$ and $\frac{2 \alpha}{3-4 \alpha}, \frac{2 \beta}{3-4 \beta}$ are the roots of $a x^{2}+b x+c=0$ and $GCD$ of $a, b, c$ is $1$ , then $a+b+c=$
If $\alpha , \beta , \gamma$ are the roots of $x^3 - 6x^2 + 11x - 6 = 0 $ , then the equation having the roots $\alpha^2 + \beta^2 + \gamma^2$ and $\gamma^2 + \alpha^2$ is
If $f(x)=(2k + 1)x - 3 - ke^{-x } + 2e^x$ is monotonically increasing for all $x \in R$, then the least value of $k$ is
If $x = \frac{3}{10} + \frac{3.7}{10.15} + \frac{3.7.9}{10.15.20} + $ ...., then $5x + 8$ =
If each line of a pair of lines passing through origin is at a perpendicular distance of $4$ units from the point $(3, 4)$, then the equation of the pair of lines is
If two unbiased six-faced dice are thrown simultaneously until a sum of either $7$ or $11$ occurs, then the probability that $7$ comes before $11$ is