List of top Mathematics Questions

If the p. d. f. of a continuous random variable X is given by \(f(x) = \{\begin{array}{cc}k(9+8x-x^2), & \text{for }-1\leq x\leq 4 \\ 0, & \text{otherwise}\end{array}\) then the value of \(k\) is \(\ldots\)

A fair die is thrown 4 times. If getting a prime number on the die is considered as a success, then the probability of getting no success at all is \(\ldots\)

In an entrance test, there are multiple choice questions. There are four possible answers to each question, only one of which is correct. The probability that a student knows the answer to a question is 90%. If he gets the correct answer to a question, then the probability that he was guessing is

The maximum value of \(z = 4x+y\) subject to the constraints \(x+y\leq 5,2x+y\leq 7,3x+2y\leq 11,x\geq 0,y\geq 0\) is \(\ldots\)

The acute angle between the lines \(2x = 3y = -z\) and \(6x = -y = -4z\) is \(\ldots\)

The angle between the line \(\overset{̄}{r} = (\hat{i}+2\hat{j}+\hat{k})+λ(\hat{i}+\hat{j}+\hat{k})\) and the plane \(\overset{̄}{r}\cdot (2\hat{i}-\hat{j}+\hat{k}) = 8\) is \(\ldots\)

If \(\overset{̄}{a}\cdot \overset{̄}{b} = β\) and \(\overset{̄}{a}\times \overset{̄}{b} = \overset{̄}{c}\) then \(\overset{̄}{a} =\)

If the equation of a plane passing through \(A(1,p,2)\), \(B(3,2,4)\) and parallel to the z axis, is \(3x-2y-q = 0\), then \(\ldots\)

The value of \(θ\in (0,\frac{π}{2})\) for which vectors \(\overset{̄}{a} = (sinθ)\hat{i}+(cosθ)\hat{j}\) and \(\overset{̄}{b} = \hat{i}-\sqrt{3}\hat{j}+2\hat{k}\) are perpendicular is

If \(|\overset{̄}{a}| = |\overset{̄}{b}| = 1,|\overset{̄}{c}| = 2\) and \(\overset{̄}{a}\times (\overset{̄}{a}\times \overset{̄}{c})+\overset{̄}{b} = \overset{̄}{0}\), then the acute angle between \(\overset{̄}{a}\) and \(\overset{̄}{c}\) is \(\ldots\)

The value of \(|\overset{̄}{a}\cdot \overset{̄}{b}|^2+|\overset{̄}{a}\times \overset{̄}{b}|\cdot |\overset{̄}{a}\times \overset{̄}{b}|\) is \(\ldots\)

The equation of the plane passing through the points having position vectors \((\overset{̄}{a}+\overset{̄}{b}),(\overset{̄}{b}+\overset{̄}{c})\) and \((\overset{̄}{a}+\overset{̄}{c})\) is \(\ldots\)

If the volume of the tetrahedron whose coterminous edges are given by the vectors \(\overset{̄}{a} = -2\hat{i}+3\hat{j}-3\hat{k}\), \(\overset{̄}{b} = 4\hat{i}+5\hat{j}+(λ-10)\hat{k}\), \(\overset{̄}{c} = 6\hat{i}+2\hat{j}-3\hat{k}\) is 11 cubic units, then the sum of the possible values of \(λ\) is \(\ldots\)

A spherical raindrop evaporates at a rate proportional to its surface area. The differential equation involving the rate of change of its radius \(r\) with time '\(t\)' is \(\ldots\) (where \(k\) is a positive constant)

The integrating factor of the differential equation \(x\frac{dy}{dx}+2y = x^2logx\) is

The differential equation of the family of all parabolas whose axis is the \(y\)-axis is \(\ldots\)

The order and degree of the differential equation \(\sqrt{⎷1+\frac{1}{(\frac{dy}{dx})^2}} = (\frac{d^2y}{dx^2})^{\frac{3}{2}}\) are \(\ldots\)

If the area bounded by \(y = x^3+ax\) (where \(a > 0\)), the \(x\)-axis and the lines \(x = -2\) and \(x = 1\) is \(\frac{37}{4}\) square units, then \(\ldots\)

If \(\int _0^2x(2-x)^b\,dx = \frac{32}{7}\), where \(b\in N\) then \(b =\)

\(\int _0^2|4x-5|\,dx = \ldots\)

The rate of disintegration of a radioactive element at any time is proportional to its mass at that time, where \(k\) \((k > 0)\) is the constant of proportionality. The time during which an original mass of 1.5 gm will disintegrate to a mass of 0.5 gm is \(\ldots\)

If \(\int e^{x+tan^{-1}x}(\frac{x^2+2}{sec^2(tan^{-1}x)})dx = e^{f(x)}+c\), then \(\ldots\)

Let \(f(x) = x\), \(f_1(x) = f(logx)\), \(f_2(x) = f_1(logx)\), \(f_3(x) = f_2(logx)\), \(\ldots\) and so on. Then \(\int \frac{1}{f(x)\,f_1(x)\,f_2(x)\,\ldots f_{2026}(x)}\,dx = \ldots\)

Let \(g(x) = f(x)+f(1-x)\) and \(f^{''}(x) < 0,0\leq x\leq 1\), then \(\ldots\)

If a particle moves such that the displacement (s) is proportional to the square of the velocity (v), then its acceleration (a) is