List of top Mathematics Questions

If $\lim_{n\rightarrow5}(\frac{[n]}{2})^{3}-(\frac{[n]^{3}}{2^{4}})=k$, then $\lim_{n\rightarrow k^{+}}(\frac{[n]}{2})^{3}-(\frac{[n]^{3}}{2^{4}})=$

The equation of the conjugate hyperbola of the hyperbola $x^{2}-4y^{2}-2x-8y-19=0$ is

If the equation of a circle passing through the point (2, 1) and the points of intersection of the circles $x^{2}+y^{2}+4x-6y-3=0$ and $x^{2}+y^{2}-2x+2y-2=0$ is $x^{2}+y^{2}+2gx+2fy+c=0$, then $2g+f=$

If the major axis of an ellipse subtends an angle of $120^{\circ}$ at one end of its minor axis and the length of its semi latus rectum is $\frac{4}{\sqrt{3}}$, then the sum of the lengths of its axes is

Through the focus of the parabola $x^{2}-4x-8y+44=0$, if tangents are drawn to another parabola $y^{2}=20x$, then the sum of the Y - coordinates of the points of contact of these tangents is

If $(h, k)$ is the pole of the line $2x-3y+4=0$ with respect to the circle $x^{2}+y^{2}-4x+6y-3=0$, then $10h+k=$

If $y=mx+c$, $m>0$ is a common tangent to the parabolas $y^{2}=8x$ and $y^{2}=1+4x$, then $m+c=$

If a circle passing through the points $(1, 5)$ and $(4,0)$ makes equal intercepts on coordinate axes and if its centre lies in the first quadrant, then $\sqrt{4g^{2}-c^{2}}=$

The product of the lengths of the perpendiculars drawn from the point $(1, 2)$ to the pair of lines $2x^{2}-3xy-2y^{2}=0$ is

If a tangent drawn to the circle $x^{2}+y^{2}-6x-8y-11=0$ is perpendicular to the line $3x + 4y + k = 0$, then the distance from the origin to this tangent is

If the equation $ax^{2}+2hxy+by^{2}+2gx+2fy+c=0$ represents a pair of parallel lines, then $g^{2}h^{2}=$

If $L$ represents a normal drawn at the point $P\left(\frac{\pi}{4}\right)$ on the circle $x^{2}+y^{2}+6x-6y-14=0$, then the equation of the diameter of this circle which is perpendicular to $L$ is

Consider the random experiment of throwing a die and tossing a coin. Let \[ \{(a,b)\mid a\in\{H,T\},\ b\in\{1,2,\ldots,6\}\} \] denote the outcomes of the experiment. If $X$ is a random variable defined by \[ X(a,b)=b, \] then the variance of $X$ is

The equation of a line $L_{1}$ passing through the point $(2, 4)$ and making an angle $\tan^{-1}(2)$ with another line $x+2y=4$ is $ax+by+c=0$. If this line $L_{1}$ is neither horizontal nor vertical, then $\frac{b+c}{a}=$

Let $A(1,2)$ and $C(3,4)$ be the end points of one of the diagonals of a square $ABCD$. If $B(\alpha,\beta)$ and $D(\gamma,\delta)$ are the end points of another diagonal of this square, then $\alpha+\beta-\gamma+\delta=$

If the distance of a variable point $P$ from the fixed line \[ 2x-y+1=0 \] is twice the distance of $P$ from another fixed line \[ 2x+y-2=0, \] then a point on the locus of $P$ is

When the origin is shifted to the point \[ \left(\frac74,-\frac14\right) \] by translation of axes, the transformed equation of \[ x^2-2xy+3y^2+2gx+2fy-6=0 \] is \[ 8X^2-16XY+24Y^2+k=0. \] Then \[ -27(2f+g)= \]

If $X\sim B(n,p)$ is a binomial variate, $8p^2+15p-2=0$ and the product of the mean and variance of $X$ is $\dfrac78$, then $P(X=4)=$

Out of the first $20$ consecutive natural numbers, $3$ numbers are chosen at random. If these $3$ numbers are in arithmetic progression with common difference $d\in\mathbb N$, then the probability of getting those $3$ numbers whose common difference is a prime number is

Let $A$ and $B$ be two non-empty sets with $n(A)=4$ and $n(B)=5$. If a mapping is selected at random from the set of all mappings from $A$ to $B$, then the probability of getting a many-one mapping is

If $\vec a,\vec b,\vec c$ are $3$ vectors such that \[ \vec b=2\hat i-\hat j,\qquad \vec c=\hat j+2\hat k, \] \[ |\vec a+\vec b|=3,\qquad |\vec a\times(\vec b\times\vec c)|=3\sqrt2 \] and \[ (\vec a,\vec b\times\vec c)=\frac{\pi}{3}, \] then $\vec a\cdot\vec b=$

If five unit squares are selected at random from a chess board, then the probability that they all lie on a diagonal is

Bag $A$ contains $3$ white and $4$ black balls. Bag $B$ contains $4$ white and $3$ black balls. Bag $C$ contains $2$ white and $5$ black balls. A bag is randomly selected and then a ball is randomly drawn from that bag. If the ball drawn was found to be white, then the probability that the ball is drawn from bag $C$ is

The mean deviation about the mean for the following data is \[ \begin{array}{c|cccc} x_i & 1 & 2 & 4 & 7\\ \hline f_i & 3 & 2 & 4 & 1 \end{array} \]

Let $\vec a,\vec b$ and $\vec c$ be three non-zero vectors such that no two of them are collinear. If the vector $\vec a+\vec b$ is collinear with $\vec c$ and $\vec b+\vec c$ is collinear with $\vec a$, then \[ \vec a+\vec b+\vec c= \]