List of top Mathematics Questions

If the variance of four numbers \(w,x,y,z\) is \(9\), then the variance of \[ 5w,5x,5y,5z \] is

An unbiased coin is tossed \(3\) times. If the third toss gets head, then the probability of getting at least one more head is

Let \(P\) be a real number and \(|P|\geq 2\). If \(A\), \(B\), \(C\) are variable angles such that \[ \sqrt{P^2-4}\tan A+P\tan B+\sqrt{P^2+4}\tan C=6P, \] then the minimum value of \[ \tan^2 A+\tan^2 B+\tan^2 C \] is

If \[ \vec{a}=\hat{i}+\hat{j}+\hat{k},\quad \vec{c}=\hat{j}-\hat{k}, \] \[ \vec{a}\times \vec{b}=\vec{c} \] and \[ \vec{a}\cdot \vec{b}=3, \] then \(\vec{b}=\)

In a trapezium \(ABCD\), \[ \overrightarrow{BC}=\lambda \overrightarrow{AD} \] and \[ \vec{x}=\overrightarrow{AC}+\overrightarrow{BD}. \] If \[ \vec{x}=p\overrightarrow{AD}, \] then \(p=\)

The vectors \[ \vec{a}=2\hat{i}+3\hat{j}+6\hat{k} \] and \(\vec{b}\) are collinear and \[ |\vec{b}|=21, \] then \(\vec{b}=\)

In a triangle \(ABC\), if \[ a\cos A=b\cos B \] where \(a\neq b\), then \(\triangle ABC\) is

In a triangle \(ABC\), if \(\angle A=60^\circ\), then \[ \frac{b}{c+a}+\frac{c}{a+b}= \]

In a \(\triangle ABC\), \[ |\overrightarrow{CB}|=a,\quad |\overrightarrow{CA}|=b,\quad |\overrightarrow{AB}|=c \] and \(CD\) is the median through the vertex \(C\). Then \[ \overrightarrow{CA}\cdot \overrightarrow{CD}= \]

Evaluate: \[ \cos^2 45^\circ+\cos^2 135^\circ+\cos^2 225^\circ+\cos^2 315^\circ= \]

In a triangle \(ABC\), \[ \frac{a-b}{a+b}= \]

Let \(\theta\in \mathbb{R}\) such that \[ 3\sinh(2\theta)=13-3e^{2\theta}, \] then \(\theta=\)

Simplify: \[ \frac{1}{1+\sin\theta}+\frac{1}{1-\sin\theta}= \]

Simplify: \[ \frac{\cos x}{1+\sin x}+\tan x= \]

The number of numbers between \(2000\) and \(5000\) that can be formed with the digits \(0,1,2,3,4\), repetition of digits not allowed, and are multiples of \(3\), is

If the equivalent partial fraction of \[ \frac{x^3}{(2x-1)(x+2)(x-3)} \] is given by \[ A+\frac{B}{2x-1}+\frac{C}{x+2}+\frac{D}{x-3}, \] then the value of \(C\) is

Let \(T_n\) be the number of all possible triangles formed by joining vertices of an \(n\)-sided regular polygon. If \[ T_{n+1}-T_n=10, \] then the value of \(n\) is

How many numbers between \(10\) and \(10,000\) can be formed by using the digits \(1,2,3,4,5\), if no digit is repeated in any number?

If \(\theta\) is any angle, then \[ \sin^2\theta \cos^2\theta= \]

Evaluate: \[ (4\cos^2 9^\circ-3)(4\cos^2 27^\circ-3)= \]

If \(a\), \(b\), \(c\) are distinct positive real numbers and \[ a^2+b^2+c^2=1, \] then the value of \(ab+bc+ca\) is

If \(a\), \(b\), \(c\), \(d\) are real numbers such that \[ a\lt b\lt c\lt d, \] then the roots of the equation \[ (x-a)(x-c)+2(x-b)(x-d)=0 \] are

If one root of the quadratic equation \[ ax^2+bx+c=0 \] is equal to the \(n^{th}\) power of the other, then \[ (ac^n)^{\frac{1}{n+1}}+(a^nc)^{\frac{1}{n+1}}= \]

In how many ways can the letters of the word ``ASSASSINATION'' be arranged so that all \(S\)'s are together?

Evaluate: \[ (-1+\sqrt{3})^{60}= \]