List of top Mathematics Questions

The least distance from origin to a point on the line \(y=x+3\) which lies at a distance of \(2\) units from \((0,3)\) is

If \(6\) is the mean of a Poisson distribution, then
\[ P(X\geq3)= \]

Suppose a triangle is formed by \(x+y=10\) and the coordinate axes. Then the number of points \((x,y)\), where \(x\) and \(y\) are natural numbers, lying inside the triangle is

Starting from the point \(A(-3,4)\), a moving object touches \(2x+y-7=0\) at \(B\) and reaches the point \(C(0,1)\). If the object travels along the shortest path, the distance between \(A\) and \(B\) is

If \(x\) is chosen at random from the set \(\{1,2,3,4\}\) and \(y\) is chosen at random from the set \(\{5,6,7\}\), then the probability that \(xy\) will be even is

In a lottery containing \(35\) tickets, exactly \(10\) tickets bear a prize. If a ticket is drawn at random, then the probability of not getting a prize is

A box contains \(100\) balls, numbered from \(1\) to \(100\). If \(3\) balls are selected one after the other at random with replacement from the box, then the probability that the sum of the three numbers on the balls selected from the box is an odd number, is

A bag contains \(7\) green and \(5\) black balls. \(3\) balls are drawn at random one after the other. If the balls are not replaced, then the probability of all three balls being green is

The discrete random variables \(X\) and \(Y\) are independent from one another and are defined as
\[ X\sim B(16,0.25) \] and
\[ Y\sim P(2). \] Then the sum of the variances of \(X\) and \(Y\) is

The mean deviation about the mean for the following data:
\[ 5,6,7,8,6,9,13,12,15 \] is

The point of intersection of the lines
\[ \vec r=2\vec b+t(6\vec c-\vec a) \] and
\[ \vec r=\vec a+s(\vec b-3\vec c) \] is

In quadrilateral \(ABCD\),
\[ \overrightarrow{AB}=\vec a, \qquad \overrightarrow{BC}=\vec b, \qquad \overrightarrow{DA}=\vec a-\vec b \] \(M\) is the midpoint of \(BC\) and \(X\) is a point on \(DM\) such that
\[ \overrightarrow{DX}=\frac45\overrightarrow{DM}. \] Then the points \(A,X,C\)

Let \(\vec a=x\hat i+y\hat j+z\hat k\) and \(x=2y\). If \(|\vec a|=5\sqrt2\) and \(\vec a\) makes an angle of \(135^\circ\) with the \(z\)-axis, then \(\vec a=\)

Let \(\vec a,\vec b,\vec c\) be the position vectors of the vertices of a triangle \(ABC\). Through the vertices, lines are drawn parallel to the sides to form the triangle \(A'B'C'\). Then the centroid of \(\triangle A'B'C'\) is

The vectors \(3\vec a-5\vec b\) and \(2\vec a+\vec b\) are mutually perpendicular and the vectors \(\vec a+4\vec b\) and \(-\vec a+\vec b\) are also mutually perpendicular. Then the acute angle between \(\vec a\) and \(\vec b\) is

In a triangle \(ABC\),
\[ r_1\cot\frac{A}{2}+r_2\cot\frac{B}{2}+r_3\cot\frac{C}{2}= \] where \(r_1,r_2,r_3\) are the exradii and \(s\) is the semi-perimeter.

If the angles of a triangle \(ABC\) are in the ratio \(1:2:3\), then the corresponding sides are in the ratio

If
\[ \cosech x=\frac45, \] then \(\sinh x=\)

The value of
\[ \frac{1+\tanh x}{1-\tanh x} \] is

In a triangle \(ABC\), if \(a\neq b\), then
\[ \frac{a\cos A-b\cos B}{a\cos B-b\cos A}+\cos C= \]

If in a triangle \(ABC\), \(a=2\), \(b=3\) and \(c=4\), then
\[ \tan\left(\frac{A}{2}\right)= \]

A person writes letters to \(6\) friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in the wrong envelopes?
\[ \text{Notation: } D_n=n!\left(\sum_{i=0}^{n}\frac{(-1)^i}{i!}\right) \]

If
\[ \frac{x^4+24x^2+28}{(x^2+1)^3} = \frac{Ax+B}{x^2+1} + \frac{Cx+D}{(x^2+1)^2} + \frac{Ex+F}{(x^2+1)^3}, \] then the value of \(A+B+C+D+E+F\) is

The value of
\[ \frac{\sin\theta+\sin3\theta}{\cos\theta+\cos3\theta} \] is

If
\[ (1+\tan1^\circ)(1+\tan2^\circ)\cdots(1+\tan45^\circ)=2^n, \] then \(n=\)