List of top Mathematics Questions

The equation of the tangent to the ellipse \[ \frac{x^2}{16}+\frac{y^2}{9}=1 \] which is parallel to the line \[ 3x+4y+5=0 \] is

The eccentricity of the hyperbola \[ 16x^2-9y^2=144 \] is

If \[ X\sim B\!\left(n,\frac14\right), \] \[ P(X=2)=P(X=3) \] and \[ \sum_{k=0}^{2}P(X=k)=\frac{39}{411}, \] then \(n=\)

If the probability function of a random variable \(X\) is \[ P(X=x)=ak^x,\qquad x=0,1,2,\ldots, \] then the value of \(k\) is

A bag \(P\) contains \(5\) white and \(4\) blue balls. Another bag \(Q\) contains \(4\) white and \(5\) blue balls. One ball is drawn at random from bag \(P\) and transferred to another bag. Then one ball is drawn from bag \(Q\). Find the probability that the ball drawn from bag \(Q\) has the same colour as the ball transferred from bag \(P\).

If it is known that a woman has two children and she has at least one girl child, then the probability that both children are girls is

In a sample space, \(E\) is an event associated with the events \(A\) and \(B\). If \[ P(A|E)=l \] and \[ P(E|B)=m, \] then \(P(B|E)\) is

From the set of numbers \[ \{1,2,3,4,5,6,7,8,9,10,11,12\}, \] two numbers are selected at random. The probability that the two numbers selected differ by a prime number is

The shortest distance between the lines \[ \vec r=\vec a+t\vec b \] and \[ \vec r=\vec c+s\vec d \] where \[ \vec a=\hat i-2\hat j+2\hat k, \quad \vec b=3\hat i-2\hat j-2\hat k, \] \[ \vec c=6\hat i+2\hat j+2\hat k, \quad \vec d=-4\hat i-\hat k, \] is

Given that \[ \vec a=2\hat i-\hat j+2\hat k,\qquad \vec b=\hat i-2\hat j+2\hat k,\qquad \vec c=2\hat i-2\hat j-\hat k, \] if \(\vec d\) is a vector perpendicular to the plane containing \(\vec a,\vec b,\vec c\) and \[ |\vec d-\vec c|=2, \] then \[ |(\vec d-\vec c)\times(\vec a\times\vec b)|= \]

If \[ |\vec a|=2k, \qquad |\vec b|=k \] and \[ |\vec a-\vec b|^2=20k^2-|2\vec a+\vec b|^2, \] then \[ |\vec a\times\vec b| = \ ? \]

The variance of the following frequency distribution is

The ratio in which the point \[ (3,4) \] divides the line segment joining \[ (1,2) \] and \[ (5,6) \] is:

If \[ \vec a=2\hat i+\hat j-\hat k \] and \[ \vec b=\hat i-2\hat j+3\hat k, \] then the value of \[ \vec a+\vec b \] is:

Let \(\vec a,\vec b\) be two non-collinear vectors. If \[ \vec r=(x+2y-3)\vec a+(2x-y+1)\vec b \] and \[ \vec R=(3x-y-2)\vec a+(x+3y+2)\vec b \] are vectors such that \[ 2\vec r=m\vec R, \] then \(x+5y=\)

If \[ x+\frac1x=3, \] then the value of \[ x^2+\frac1{x^2} \] is:

If \[ \log_a 2+\log_a 5=1, \] then the value of \(a\) is:

If \[ A= \begin{bmatrix} 1&2\\ 3&4 \end{bmatrix}, \] then \(\det(A)\) is equal to:

If \[ z=\cos\theta+i\sin\theta, \] then \(|z|\) is equal to:

The distance between the points \[ (1,2) \quad \text{and} \quad (4,6) \] is:

If the arithmetic mean of the numbers \[ 2,4,6,\ldots,2n \] is \(\frac{7}{4}\), then \(n\) is equal to:

If the coefficients of the first, second, and third terms in the expansion of \( (1+x)^n \) are in the ratio \(1:20:190\), then \(n\) is equal to:

If \[ \sin\theta+\cos\theta=1, \] then the value of \[ \sin\theta\cos\theta \] is:

If \[ \log_2(x-1)+\log_2(x+1)=3, \] then \(x\) is equal to:

If \[ f(x)=|x-2|+|x+1|, \] then the minimum value of \(f(x)\) is: