List of top Mathematics Questions

If a discrete random variable \(X\) takes the values \(1,2,3,4\) such that \(2P(X = 1) = 3P(X = 2) = P(X = 3) = 5P(X = 4)\), then \(P(X = 4) = \ldots\)

On average, one out of 10 persons is busy. If six persons are selected at random, then the probability that at least 5 of them will be busy is...

Three numbers are chosen from 1 to 30. The probability that minimum is 10 and maximum is 26 is _______

If the distance of point \(B(2,1,-3)\) from the line passing through the point \(A(4,-2,2)\), and parallel to the vector \(\overset{⃗}{c} = -4\hat{i}-6\hat{j}-2\hat{k}\) is \(x\), then \(x^4+x^2+541 =\)

The equation of the perpendicular line from the point \((2,-3,1)\) to the line \(\frac{x+1}{2} = \frac{y-3}{3} = \frac{z+2}{-1}\) is

The sum of the coordinates of one of the points on the line \(\frac{x-2}{1} = \frac{y+3}{-2} = \frac{z+5}{2}\) which is at a distance of 3 units from the point \((2,-3,-5)\) is ...

In the following figure, the shaded region represents the system of constraints:

If A and B are the feet of the perpendiculars drawn from \((1,2,3)\) to planes \(YZ\) and \(ZX\), then the equation of the plane passing through the points A, B and the origin is

The angle between the line \(x-1 = 2-y = \frac{2z-6}{4}\) and the plane \(\overset{⃗}{r}\cdot (2\hat{i}+\hat{j}+\hat{k}) = 10\) is

If \(|\overset{⃗}{a}\cdot \overset{⃗}{b}| = |\overset{⃗}{a}\times \overset{⃗}{b}|\), \(\overset{⃗}{a}\cdot \overset{⃗}{b} < 0\) and \(θ\) is the angle between \(\overset{⃗}{a}\) and \(\overset{⃗}{b}\), then the value of \(sinθ+tanθ\) is...

The general solution of the differential equation \(secy+(x-e^{siny})\frac{dy}{dx} = 0\) is...

The general solution of the differential equations \(\frac{dy}{dx} = (9x+y+5)^2\) is...

Let \(\overset{⃗}{a}\) and \(\overset{⃗}{b}\) be linearly independent vectors such that
\(|\overset{⃗}{a}| = \sqrt{3},|\overset{⃗}{b}| = 3\) and \(|\overset{⃗}{a}-\overset{⃗}{b}| = 4\).
If \(\overset{⃗}{a}\times (2\hat{i}+2\hat{j}-\hat{k}) = (2\hat{i}+2\hat{j}-\hat{k})\times \overset{⃗}{b}\) and \(|(\overset{⃗}{a}+\overset{⃗}{b})\cdot (3\hat{i}+4\hat{j}+2\hat{k})| = \sqrt{λ}\), then \(λ = \ldots\)

Let \(\overset{⃗}{a} = λ\hat{i}+\hat{j}+\hat{k},\overset{⃗}{b} = 2\hat{i}+4\hat{j}+4\hat{k},\overset{⃗}{c} = \hat{i}+μ\hat{j}+\hat{k}\)
If \(\overset{⃗}{a}\) is parallel to \(\overset{⃗}{b}\) and \(\overset{⃗}{b}\) is perpendicular to \(\overset{⃗}{c}\) then \(λ-μ = \ldots\)

The value of \(b\) such that the scalar product of the vector \(\hat{i}+\hat{j}+\hat{k}\) with the unit vector parallel to the sum of the vectors \(2\hat{i}+4\hat{j}-5\hat{k}\) and \(b\hat{i}+2\hat{j}+3\hat{k}\) is one, is...

The area of the region bounded by curves \(y = sinx,y = cosx\) and the lines \(x = 0\), \(x = \frac{π}{4}\) is

The function \(f(x) = \int _0^x\frac{dt}{1+cost}\) satisfies which of the following differential equations?

If \(\int _a^b(x^2-x)\,dx = 18,\int _a^bx^3\,dx = 0\), then \(a+b\) is equal to

Let \(f(x) = x-[x]\) for every real number \(x\), where \([x]\) is integral part of \(x\). then \(\int _{-1}^1f(x)\,dx\) is

If \(f(x) = \frac{sin^{-1}x}{\sqrt{1-x^2}}\) and \(g(x) = e^{sin^{-1}x}\), then the value of \(\int f(x)g(x)\,dx = \ldots\)

The value of the definite integral \(\int _0^π\frac{1}{5+4cosx}\,dx\) is equal to ...

If \(\int f(x)\,dx = g(x)\) then \(\int x^3f(x^2)\,dx\) is equal to

The equation of the tangent to the curve \(y = \sqrt{9-3x^2}\) at the point where the ordinate and abscissa equal is...

The coordinates of the points on the curve \(4y = x^2\) that are nearest to the point \((0,5)\) are ...

If \(\int \frac{sinx}{sin4x}\,dx = αlog\frac{1+sinx}{1-sinx}+βlog\frac{1+\sqrt{2}sinx}{1-\sqrt{2}sinx}+c\), then the value of \(32(α+β^2) =\)