List of practice Questions

The probability that a certain kind of component will survive a given shock test is \(\frac{3}{4}\). The probability that exactly 2 of the next 4 components tested survive is
Mean and standard deviation of marks obtained in some particular subject by four classes are given below. Report the class with the best performance
A random variable \(X\) follows binomial distribution with mean \(\alpha\) and variance \(\beta\). Then
Area enclosed by the curve \(\pi\left[4(x-\sqrt{2})^2+y^2\right]=8\) is
The value of \(\int_{0}^{a}\sqrt{\frac{a-x}{x}}\,dx\) is
Let \(y\) be the number of people in a village at time \(t\). Assume that the rate of change of the population is proportional to the number of people in the village at any time and further assume that the population never increases in time. Then the population of the village at any fixed time \(t\) is given by
The differential equation of all straight lines touching the circle \(x^2+y^2=a^2\) is
The differential equation \(\left|\frac{dy}{dx}\right|+|y|+3=0\) admits
Solution of the differential equation \(xdy-ydx-\sqrt{x^2+y^2}\,dx=0\) is
Let P, Q, R and S be statements and suppose that \(P\to Q \to R \to P\); if \(\sim S \to R\), then
The directrix of the parabola \(y^2 + 4x + 3 = 0\) is
If \(g(x)\) is a polynomial satisfying \(g(x)g(y)=g(x)+g(y)+g(xy)-2\) for all real \(x\) and \(y\) and \(g(2)=5\), then \(\lim_{x\to 3} g(x)\) is
The value of \(f(0)\) so that \(\frac{-e^x+2^x}{x}\) may be continuous at \(x=0\) is
Let \([\,]\) denote the greatest integer function and \(f(x)=[\tan^2 x]\). Then
A spherical balloon is expanding. If the radius is increasing at the rate of 2 centimeters per minute, the rate at which the volume increases (in cubic centimeters per minute) when the radius is 5 centimeters is
The length of the parabola \(y^2=12x\) cut off by the latus-rectum is
If \(I=\int \frac{x^5}{\sqrt{1+x^3}}\,dx\), then \(I\) is equal to
If \(\left|\frac{z-25}{z-1}\right|=5\), the value of \(|z|\)
Argument of the complex number \(\left(\frac{-1-3i}{2+i}\right)\) is
In a triangle ABC, the sides \(b\) and \(c\) are the roots of the equation \(x^2-61x+820=0\) and \(A=\tan^{-1}\left(\frac{4}{3}\right)\), then \(a^2\) is equal to
The shortest distance between the straight lines through the points \(A_1=(6,2,2)\) and \(A_2=(-4,0,-1)\), in the directions of \((1,-2,2)\) and \((3,-2,-2)\) is
The center and radius of the sphere \(x^2+y^2+z^2-3x-4z+1=0\) are
Let A and B are two fixed points in a plane then locus of another point C on the same plane then CA+CB = constant, \(>AB\) is
Identify the reactant
Maleic acid and Fumaric acid are