List of top Mathematics Questions

A fair die is thrown at random. Let A be the event that the number obtained on the die is a non-even prime number and B be the event that the number obtained on the die is an odd number.
Let \(p:P(A) = \frac{1}{3}\), \(q\) : A and B are independent events.
Then the truth values of statements \(p\) and \(q\) respectively are.....

The feasible region represented by the constraints \(y-2x\leq 4,x+y\geq 5,x\leq 4,y\geq 2,x,y\geq 0\) is ...........

The vector equation of the line whose cartesian equations are \(x = 2,2y-3z+7 = 0\)

The probability distribution of a random variable X is given by

\(X = x\)	\(1\)	\(2\)	\(3\)	\(4\)
\(P(X = x)\)	\(k\)	\(2k\)	\(3k\)	\(4k\)

Then the c.d.f. of X is given by

The lines \(\frac{x-2}{1} = \frac{y-3}{1} = \frac{z-4}{-k}\) and \(\frac{x-1}{k} = \frac{y-4}{2} = \frac{z-5}{1}\) are coplanar if

The direction ratios of the normal to the plane passing through (1, 0, 0), (0, 1, 0) which makes an angle of measure \(45^{\circ}\) with the plane \(2x+3y = 7\) are....

The lines \(\frac{x-1}{-1} = \frac{y+2}{1} = \frac{z-3}{-2}\) and \(\frac{x-1}{1} = \frac{y+2}{1} = \frac{z+1}{-2}\) are

If the product of the distances of the point (1, 2, 3) from the origin and the plane \(2x-3y+z+k = 0\) is 7, then the value of k is

A parallelogram is constructed on \(5\overset{̄}{a}+2\overset{̄}{b}\) and \(\overset{̄}{a}-3\overset{̄}{b}\) as its adjacent sides, with \(|\overset{̄}{a}| = 2\sqrt{2},|\overset{̄}{b}| = 3\) . The angle between \(\overset{̄}{a}\) and \(\overset{̄}{b}\) is \(\frac{π}{4}\) . Then the length of the diagonals of the parallelogram are

The acute angle between the vector \(2\hat{i}+\hat{j}-3\hat{k}\) and the plane containing the vectors \(2\hat{i}+3\hat{j}-\hat{k}\) and \(\hat{i}-\hat{j}+2\hat{k}\) is

The rate of reduction is proportional to the square root of a persons existing assets at that moment. If his assets at the beginning are 10000 and they dwindle down to 5625 in 2 years, then the person will be bankrupt in

If a vector \(3\hat{i}+4\hat{j}-5\hat{k}\) is rotated through a certain angle about the origin in the anti-clockwise direction, then the components of the new vector are \(a+1,-3,5\) . The possible values of \(a\) is

Let A, B, C, D be the points in the plane with position vectors \(-2\hat{i}-\hat{j}\), \(4\hat{i}\), \(3\hat{i}+3\hat{j}\) and \(-3\hat{i}+2\hat{j}\) respectively, then \(◻\)ABCD is

The degree of the differential equation obtained from the equation \((y-a)^2 = 4(x-b)\) [where \(a\) and b are arbitrary constants] is

Let \(\overset{̄}{a} = \hat{i}+\hat{j}\), \(\overset{̄}{c} = \hat{i}-\hat{j}\) and a vector \(\overset{̄}{b}\) be such that \(\overset{̄}{a}\times \overset{̄}{b} = \overset{̄}{c}\) and \(\overset{̄}{a}\cdot \overset{̄}{b} = 3\) then \(|\overset{̄}{b}| =\)

The solution of the differential equation \((x+2y^3)\frac{dy}{dx}-y = 0\) is

\(\int cot^4x\,dx\) is equal to

\(\int \frac{(x+1)(x+logx)^2}{x}\,dx =\)

The integrating factor of the differential equation \((1+t^2)+(x-e^{tan^{-1}t})\frac{dt}{dx} = 0\) is

\(\int \frac{cos^3x}{sin^2x+sinx}\,dx =\)

\(\int _{π/6}^{π/3}\frac{sinx-cosx}{1+sinxcosx}\,dx =\)

\(\int _0^{log5}\frac{e^x\sqrt{e^x-1}}{e^x+3}\,dx =\)

A triangle has two fixed vertices A \((a,0)\) and B\((0,b)\) . Let its third vertex C is moving along the line \(x = y\). If \(s\) is the area of triangle ABC, then \(\frac{ds}{dx} =\)

The minimum value of \(\frac{logx}{x}\) in the interval \((2,\infty )\) is

If \(y^{\frac{1}{m}}+y^{\frac{-1}{m}} = 2x\) , then \((x^2-1)y_1^2 =\)