List of top Mathematics Questions

Given the probability density function (p.d.f.) of the random variable X, \(f(x) = \frac{1}{2a}\), \(0 < x < 2a\), \(a > 0\)
\(= 0\), otherwise, then which of the following is correct ?
If in \(6\) trials, X is a binomial random variable which follows the relation \(9P(x = 4) = P(x = 2)\), then the probability of failure is...
Consider a game of tossing a six sided fair die. If the face that comes up is \(6\), the player wins Rs. \(36\) and he loses Rs. \(k^2\), where \(k\) is the face that comes up \(k = \{1,2,3,4,5\}\), then the expected winning amount in this game in Rs. 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
The symmetric form of the equation of the line \(x = ay+b\), \(z = cy+d\) is
The shaded region in the provided graph represents the solution set for which of the following systems of linear inequalities?
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 \(p\) 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.)
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 solution of the differential equation \(\frac{dy}{dx} = \frac{a+bx}{c+dy}\) represents a family of circles centered at the origin if...
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 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...
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 ....
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 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...
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...
If \([x]\) is the greatest integer function not greater than \(x\), then the value of \(\int _0^2x[x^2]\,dx\) 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...
The value of \(\int _2^4(\{x\}+[x])\,dx =\)...(where \(\{x\}\) and \([x]\) are the fractional part function and the greatest integer function, respectively)
The value of integral \(\int \frac{\sqrt{x^2+1}\,[log(x^2+1)-2logx]}{x^4}\,dx\) is equal to...
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...