List of top Mathematics Questions

\(\displaystyle\int e^{x}\left(\log x+\frac{1}{x^{2}}\right)dx\) is equal to
(consider \(\log_e x = \log x\))
If \(y = \sqrt{\dfrac{1-x}{1+x}}\), then the value of \((1 - x^2)\dfrac{dy}{dx} + y\) is
If \(2f(x)+f\left(\frac{1}{x}\right)=\frac{1}{x}-5,\ x\neq 0\), then \(\displaystyle\int_{1}^{2}f(x)dx\) is equal to:
(consider \(\log_e x = \log x\))
If \(A\) is a square matrix of order \(3 \times 3\), and \(|\text{adj } A| = 25\), then the value of \(|2A|\) is
If \(AB = A\) and \(BA = B\), where \(A\) and \(B\) are square matrices of same order, then
If \(\Delta = \begin{vmatrix} 1 & x & x^2 \\ x^2 & 1 & x \\ x & x^2 & 1 \end{vmatrix} = (1 + ax^3)^b\), then which of the following statements are TRUE?
A. \(a = -1\) and \(b = 2\)
B. \(x = 1\) is a multiple root of \(\Delta = 0\)
C. \(x = 1\) is a simple root of \(\Delta = 0\)
D. \(x = 3\) is a simple root of \(\Delta = 0\)
Choose the correct answer from the options given below:
\(A\) is any matrix, defined by \(A = [a_{ij}]_{3\times 3}\), where \(a_{ij} = |i - j|\), then which of the following statements are true ?
A. \(A\) is symmetric matrix.
B. \(A\) is skew-symmetric matrix.
C. \(A\) is diagonal matrix.
D. \(A\) is non singular matrix.
Choose the correct answer from the options given below:
If \( \sin x \cos x = \frac{1}{4} \), then the general solution is:
The centers for disease control have determined that when a person is given a vaccine, the probability that the person will develop immunity to a virus is \(0.8\). If \(8\) people are given this vaccine, then the probability that exactly \(4\) will develop immunity is...
The Variance of the following probability distribution of X is
X\(0\)\(1\)\(2\)\(3\)
P(X)\(q^3\)\(3q^2p\)\(3qp^2\)\(p^3\)
where \(0 < p < 1,q = 1-p\)
The minimum value of \(Z = 3x+y\), subject to the constraints \(2x+3y\leq 6,x+y\geq 1,x\geq 0,y\geq 0\) is....
If A and B are two events such that \(P(A) = \frac{2}{3}\), \(P(B) = \frac{1}{2}\) and \(P(A|B) = \frac{2}{3}\), then \(P(A^'\cup B)+P(A\cup B^') =\)
Let \((\overset{̄}{p}∧\overset{̄}{q})\) denote the angle between \(\overset{̄}{p}\) and \(\overset{̄}{q}\). If \(\overset{̄}{a}+\overset{̄}{b}+\overset{̄}{c} = \overset{̄}{0},|\overset{̄}{a}| = 7,|\overset{̄}{b}| = 5\) and \(|\overset{̄}{c}| = 3\) then (take \(π = \frac{22}{7}\))
The equation of the plane containing the lines \(\frac{x-1}{2} = \frac{y+1}{λ} = \frac{z}{2}\) and \(\frac{x+1}{5} = \frac{y+1}{2} = \frac{z}{λ}\) is
If a unit vector makes angles \(\frac{π}{4}\) with \(\hat{i}\), \(\frac{π}{3}\) with \(\hat{j}\) and \(θ\in (0,π)\) with \(\hat{k}\), then a value of \(θ\) is equal to...
If the lines \(\frac{x-5}{5m+2} = \frac{2-y}{5} = \frac{1-z}{-1}\) and \(x = \frac{2y+1}{4m} = \frac{1-z}{-3}\) are perpendicular to each other, then the value of m is ...
The direction cosines of a line which is perpendicular to the lines \(\frac{x-7}{2} = \frac{y+17}{-3} = \frac{z-6}{1}\) and \(\frac{x+5}{1} = \frac{y+3}{2} = \frac{z-6}{-2}\) are...
For the line \(\frac{x+1}{1} = \frac{y-2}{2} = \frac{z+3}{3}\), identify the incorrect statement among the following.
If \(\overset{̄}{a}\) and \(\overset{̄}{b}\) are unit vectors and \(θ\) (\(0 < θ < π\)) is the angle between them, then the value of \(\frac{|\overset{̄}{a}+\overset{̄}{b}|}{|\overset{̄}{a}-\overset{̄}{b}|}\) is equal to...
If the differential equation \(\begin{array}{cc}f(x) & f^'(x) \\ f^'(x) & f^{''}(x)\end{array} = 0\) for all \(x\) and \(f(0) = 1,f^'(0) = 2\), then...
If ABCDEF is a regular hexagon and \(\overline{AB}+\overline{AC}+\overline{AD}+\overline{AE}+\overline{AF} = p\overline{AD} = q\overline{AO}\), where O is the center of the hexagon, then the values of \(p\) and \(q\) respectively are
The vector \(\overset{̄}{r}\) whose magnitude is \(3\sqrt{2}\) units and which makes angles of \(\frac{π}{4}\) and \(\frac{π}{2}\) with the positive y- and z-axes respectively is....
The solution of the differential equation \(\frac{dy}{dx} = e^{x-y}+x^2e^{-y}\) is...
The solution of the differential equation \(x^2\frac{dy}{dx}-xy = 1\) is...
The area of the smaller region bounded by the circle \(x^2+y^2 = 4\) and the line \(x = 1\) is...