List of top Mathematics Questions

\((1+\tan A+\sec A)(1+\sec A-\tan A)-2\sec A=\)

If \(\triangle ABC\) and \(\triangle PQR\) are similar triangles in which \(\angle A=47^\circ\) and \(\angle Q=83^\circ\), then \(\angle C\) is

Rewrite the expression as single function of an angle, if \[ \frac{2\tan31^\circ}{1-\tan^2 31^\circ}=? \]

Two adjacent angles are said to form a linear pair of angles, if their non-common arms are two

If \(\sin\theta=\frac{24}{25}\) and \(0^\circ<\theta<90^\circ\), then what is the value of \(\cos\theta\)?

\(\left|\begin{matrix}x_1 & y_1\\ x_2 & y_2\end{matrix}\right|\) represents the area of

The diameter of an electric cable \(X\) is a continuous random variable with probability density function \[ f(x)=kx(1-x),\quad 0\leq x\leq 1. \] Find \[ P\left(X<\frac{1}{2}\ \middle|\ \frac{1}{3}<X<\frac{2}{3}\right) \]

A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed \(3\) times, what is the probability of getting \(2\) tails and \(1\) head.

A random variable \(X\) has the following probability mass function as follows:

Then the value of \(a\) is

The mean of a binomial distribution is \(5\) and its standard deviation is \(2\). Then the value of \(n\) and \(p\) are

The point of intersection of the lines \[ \frac{x-6}{-6}=\frac{y+4}{4}=\frac{z-4}{-8} \] and \[ \frac{x+1}{2}=\frac{y+2}{4}=\frac{z+3}{-2} \] is

If \(I=\displaystyle\int_0^1 \frac{x^2}{1+x^6}\,dx\), then \(I=\)

If \(|\vec{a}+\vec{b}|=|\vec{a}-\vec{b}|\), then

The lines \(2x-3y=5\) and \(3x-4y=7\) are the diameters of a circle of area \(154\) sq.unit. The equation of this circle is

The distance between the circumcenter and orthocenter of the triangle whose vertices are \((0,0)\), \((6,8)\) and \((-4,3)\) is

If \(\vec{a}=2\hat{i}+\hat{j}-8\hat{k}\) and \(\vec{b}=\hat{i}+3\hat{j}-4\hat{k}\), then the magnitude of \(\vec{a}+\vec{b}\) is

If \(\alpha,\beta\) are the roots of \(x^2-3x+a=0\), and \(\gamma,\delta\) are the roots of \(x^2-12x+b=0\), and the numbers \(\alpha,\beta,\gamma,\delta\) in order form an increasing G.P., then:

The value of \(c\) satisfied by Rolle's theorem for the function \(f(x)=\log\left(\frac{x^2+6}{5x}\right)\) in the interval \([2,3]\) is

If \(x^2+y^2=t-\frac{1}{t}\) and \(x^4+y^4=t^2+\frac{1}{t^2}\), then \(\frac{x}{y}\frac{dy}{dx}\) is equal to

Find the solution of \((x^2-3y^2)dx+2xydy=0\)

If the product of three positive real numbers say \(a,b,c\) be \(27\), then the minimum value of \(ab+bc+ca\) is equal to

Rajdhani express going from Bombay to Delhi stops at five intermediate stations ten passengers enter the train during the journey with ten different tickets of two classes. The number of different sets of tickets they may have is

In a class tournament when the participants were to play one game with another, two class players fell ill, having played three games each. If the total number of games played is \(84\), the number of participants at the beginning was

\(N\) different objects can be arranged taken all at a time in

A locker in bank has 3 digit lock. Mahesh forgot his password and was trying all possible combinations. He took 6 seconds for each try. The problem was that each digit can be from 0 to 9. How much time will be needed by Mahesh to try all the combinations?