List of top Mathematics Questions

If \(p\) is the shortest distance between the lines \(\frac{x+1}{7} = \frac{y+1}{-6} = z+1\) and \(\overset{⃗}{r} = (3\hat{i}+5\hat{j}+7\hat{k})+μ(\hat{i}-2\hat{j}+\hat{k})\) then \([p]\) is... ,(where \([\,.\,]\) denotes the greatest integer function.)

The symmetric form of the equation of the line \(x = ay+b\), \(z = cy+d\) is

From a point P \((a,b,c)\), perpendiculars PA and PB are drawn to XY plane and ZX plane respectively. If O is the origin, then the equation of plane OAB is

The plane \(\frac{x}{2}+\frac{y}{3}+\frac{z}{4} = 1\) cuts the axes at the points A, B, C then the area of triangle ABC is

If \(ABC\) is a right-angled triangle in which \(BC\) is the longest side and the position vector of \(B\) and \(C\) are respectively \(3\hat{i}-2\hat{j}+\hat{k}\) and \(5\hat{i}+\hat{j}-3\hat{k}\), then the value of \(\overline{AB}\cdot \overline{AC}+\overline{BA}\cdot \overline{BC}+\overline{CA}\cdot \overline{CB}\) is

If \(|\overset{⃗}{a}| = 3\), \(|\overset{⃗}{b}| = 4\), \(|\overset{⃗}{c}| = 5\) such that each vector is perpendicular to the sum of the other two, then \(|\overset{⃗}{a}+\overset{⃗}{b}+\overset{⃗}{c}|\) is equal to

The solution of the differential equation \(\frac{dy}{dx} = \frac{a+bx}{c+dy}\) represents a family of circles centered at the origin if...

The value of \(x\) so that the volume of the parallelopiped formed by the vectors \(\hat{i}+x\hat{j}+\hat{k}\), \(\hat{j}+x\hat{k}\) and \(x\hat{i}+\hat{k}\) is minimum, is

The solution of the differential equation \(\frac{dy}{dx} = \frac{x-y}{x+y}\), when \(x = 0\) and \(y = 0\) represents ....

The sum of all real values of \(λ\) for which the vectors \(\overset{⃗}{a} = λ\hat{i}+\hat{j}+\hat{k}\), \(\overset{⃗}{b} = \hat{i}+λ\hat{j}+2\hat{k}\), \(\overset{⃗}{c} = 2\hat{i}+3\hat{j}+λ\hat{k}\) are coplanar is...

If \(A(\overset{⃗}{a})\), \(B(\overset{⃗}{b})\) and \(C(\overset{⃗}{c})\) are vertices of \(△ABC\). Point D divides segment BC internally in the ratio \(2:1\). Point E divides segment AD internally in the ratio \(1:2\), then the position vector of E is ____

If \(f(x) = \frac{1}{logx}\) and \(g(x) = \frac{1}{(logx)^2}\), then the value of \(\int [f(x)-g(x)]\,dx\) is...

If \(\int \frac{dx}{x^{7/2}(x^4+1)^{3/8}} = m(\frac{x^4+1}{x^4})^n+c\), where \(c\) is a constant of integration, then the value of \(\frac{n}{m}\) is...

The value of \(\int _2^4(\{x\}+[x])\,dx =\)...(where \(\{x\}\) and \([x]\) are the fractional part function and the greatest integer function, respectively)

If \([x]\) is the greatest integer function not greater than \(x\), then the value of \(\int _0^2x[x^2]\,dx\) is...

If the area of the region bounded by the parabola \(y^2 = 4kx\) and the line \(x = k\), (where \(k > 0\)) is \(\frac{128}{3}\) sq. units, then the value of \(sin^{-1}(\frac{2}{k})\) is equal to...

The area (in sq. units) of the region enclosed by \(\{(x,y)|y\leq x^2,xy\leq 8,y\geq 1\}\) is...

A particle is fired straight up from the ground. Its height in feet after \(t\) second is given by \(s(t) = 128t-16t^2\). The velocity of the particle when it hits the ground is...

A tank with a rectangular base and rectangular sides, open at the top is made. Depth of the tank is \(4\) m and its volume is \(36\) cubic meters. For making a tank cost of base material used is Rs. \(100\) per sq. meter and that of sides is Rs. \(50\) per sq. meter. Then minimum cost of tank is ..............

The value of integral \(\int \frac{dx}{sin^2x+tan^2x}\) is...

The derivative of \(log_{10}x\) with respect to \(log_x10\) is

The value of integral \(\int \frac{\sqrt{x^2+1}\,[log(x^2+1)-2logx]}{x^4}\,dx\) is equal to...

The value of \(c\) satisfied by the Rolle's theorem for the function \(f(x) = x^2(1-x)^2\), \(x\in [0,1]\) is...

Let \(x = at^2-1\), where \(a > 0\) and \(y = t^3+1\). If at \(t = 1\), \(\frac{d^2y}{dx^2} = \frac{3}{16}\), then the value of \(a\) is...

\(\sum _{k = 1}^{2026}sin^{-1}(cos\frac{kπ}{4}) =\)