List of top Mathematics Questions

In a $\Delta ABC$, the lengths of the two larger sides are $10$ and $9$ units, respectively. If the angles are in AP, then the length of the third side can be

A bag contains $3$ red and $3$ white balls. Two balls are drawn one by one. The probability that they are of different colours is.

The position of a projectile launched from the origin at $t=0$ is given by $\hat{r}=\left(40 \hat{i}+50\hat{ j}\right) m$ at $t=2 s$. If the projectile was launched at an angle $\theta$ from the horizontal, then $\theta$ is $\left(\right.$ take $\left. g=10\, ms ^{-2}\right)$

The total number of $4$-digit numbers in which the digits are in descending order, is

Let $M$ be a $3 \times 3$ non-singular matrix with $det(M)=\alpha$. If $\left[M^{-1} adj(adj(M)]=K I\right.$, then the value of $K$ is

The value of $ \tan( 1^\circ) +\, tan(89^\circ)$ is

Let $O$ be the vertex and $Q$ be any point on the parabola, $x^2$ = 8y. If the point $P$ divides the line segment $OQ$ internally in the ratio $1 : 3$, then the locus of $P$ is

Let $PQ$ be a double ordinate of the parabola, $y^2= - 4x$, where P lies in the second quadrant. If R divides $PQ$ in the ratio $2 : 1$, then the locus of R is :

The equation of the plane containing the lines $2x - 5y + z = 3, x + y + \, z = 5$ and parallel to the plane $x + 3 y+ 6 z = 1$ is

If in a regular polygon the number of diagonals is $54$, then the number of sides of this polygon is :

If the mean and the variance of a binomial variate $X$ are $2$ and $1$ respectively, then the probability that $X$ takes a value greater than or equal to one is :

If $\log _{0.2}(x-1)>\log _{0.04}(x+5)$, then

A box contains $6$ red marbles numbers from $1$ through $6$ and $4$ white marbles $12$ through $15$. Find the probability that a marble drawn 'at random' is white and odd numbered.

If $\alpha$ and $\beta$ are the roots of $x^2 - ax + b^2 = 0$, then $\alpha^2 + \beta^2$ is equal to

Write the set builder form $A = {-1, 1}$

A bag contains $(2 n+1)$ 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 quadratic expression $\left(2x+1\right)^{2}-px+q\ne0$ for any real $x$ if

The area (in s units) of the quadrilateral formed by the tangents at the end points of the latera recta to the ellipse $\frac{x^{2}}{9}+\frac{y^{2}}{5}=1$, is:

If $\quad \tan \theta \cdot \tan \left(120^{\circ}-\theta\right) \tan \left(120^{\circ}+\theta\right)=\frac{1}{\sqrt{3}}$, then $\theta$ is equal to

If $f: R \rightarrow R, g: R \rightarrow R$ are defined by $f(x)=5\, x-3, g(x)=x^{2}+3$, then $g o f^{-1}(3)$ is equal to

The system $2\,x+3 y+z=5,3\,x+y+5\,z=7$ and $x+4\,y-2\,z=3$ has

The value of the sum $1 \cdot 2 \cdot 3+2 \cdot 3 \cdot 4+3 \cdot 4 \cdot 5+\ldots$ upto $n$ terms is equal to

The common roots of the equations $z^{3}+2 z^{2}+2 z+1=0, z^{2014}+z^{2015}+1=0$ are

If $\omega$ is a complex cube root of unity, then $\omega^{\left(\frac{1}{3}+\frac{2}{9}+\frac{4}{27}+\ldots \infty\right)}+\omega^{\left(\frac{1}{2}+\frac{3}{8}+\frac{9}{32}+\ldots \infty\right) \text { is equal to }}$

If $A=\left\{x \in R / \frac{\pi}{4} \leq x \leq \frac{\pi}{3}\right\}$ and $f(x)=\sin x-x$, then $f(A)$ is equal to