List of top Mathematics Questions

The set of all real values of $x$ for which $\frac{x^2-1}{(x-4)(x-3)} \ge 1$ is
If $\alpha$, $\beta$, and $\gamma$ are the roots of the equation $2x^3 + 3x^2 - 5x - 7 = 0$, then $\frac{1}{\alpha^2} + \frac{1}{\beta^2} + \frac{1}{\gamma^2} =$
If the order and degree of the differential equation \(x \frac{d^2 y}{dx^2} = \left(1 + \left(\frac{d^2 y}{dx^2}\right)^2\right)^{-1/2}\) are \(k\) and \(l\) respectively, then \(k, l\) are the roots of
The equation of the curve passing through the point \( (0, \pi) \) and satisfying the differential equation \( ydx = (x + y^3 \cos y)dy \) is
Evaluate the integral \( \displaystyle \int_{1/5}^{1/2} \frac{\sqrt{x - x^2}}{x^3} \, dx \):
If \(\int \frac{1}{((x+4)^3 (x+1)^5)^{1/4}} \, dx = A \cdot \left(\frac{x+4}{x+1}\right)^n + c\), then
If \( \int e^{\sin x}(1 + \sec x \tan x)\, dx = e^{\sin x}f(x) + c \), then in \( 0 \leq x \leq 2\pi \), the number of solutions of \( f(x) = 1 \) is
Evaluate: \[ \int \frac{dx}{(x+1)\sqrt{x^2+1}} \]
If \( m \) and \( M \) are the absolute minimum and absolute maximum values of the function \( f(x) = 2\sqrt{2 \sin x - \tan x} \) in the interval \( \left[0, \frac{\pi}{3} \right] \), then \( m + M = \)
The function \( f(x) = xe^{-x} \) for all \( x \in \mathbb{R} \) attains a maximum value at \( x = k \), then \( k = \)
The slope of a tangent drawn at the point \( P(\alpha, \beta) \) lying on the curve \( y = \frac{1}{2x - 5} \) is \( -2 \). If \( P \) lies in the fourth quadrant, then \( \alpha - \beta = \)
The interval in which the function \( f(x) = \tan^{-1}(\sin x + \cos x) \) is an increasing function, is:
If \( y = (\log x)^{1/x} + x^{\log x} \), then at \( x = e \), \( \frac{dy}{dx} \) equals:
Evaluate the limit: \[ \lim_{x \to 0} \frac{(\csc x - \cot x)(e^x - e^{-x})}{\sqrt{3} - \sqrt{2 + \cos x}} \]
If a real valued function \( f(x) = \begin{cases} (1 + \sin x)^{\csc x} & , -\frac{\pi}{2} < x < 0 \\ a & , x = 0 \\ \frac{e^{2/x} + e^{3/x}}{ae^{2/x} + be^{3/x}} & , 0 < x < \frac{\pi}{2} \end{cases} \) is continuous at \(x = 0\), then \(ab = \)
If the direction cosines of two lines satisfy the equations $ l - 2m + n = 0 $ and $ lm + 10mn - 2nl = 0 $, and $ \theta $ is the angle between the lines, then $ \cos \theta = $
If \(3x+2\sqrt{2}y+k=0\) is a normal to the hyperbola \(4x^2-9y^2-36=0\) making positive intercepts on both the axes, then \(k=\) Options :
If (1, a), (b, 2) are conjugate points with respect to the circle \(x^2 + y^2 = 25\), then \(4a + 2b =\)
If the combined equation of the lines joining the origin to the points of intersection of the curve $ x^2 + y^2 - 2x - 4y + 2 = 0 $ and the line $ x + y - 2 = 0 $ is $ (l_1x + m_1y)(l_2x + m_2y) = 0 $, then $ l_1 + l_2 + m_1 + m_2 = $
If the equation of the pair of lines passing through (1, 1) and perpendicular to the pair of lines \(2x^2 + xy - y^2 - x + 2y - 1 = 0\) is \(ax^2 + 2hxy + by^2 + 2gx + 3y = 0\). then \(\frac{b}{a} =\)
After the coordinate axes are rotated through an angle \(\frac{\pi}{4}\) in the anticlockwise direction without shifting the origin, if the equation \(x^2 + y^2 - 2x - 4y - 20 = 0\) transforms to \(ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0\) in the new coordinate system, then
\[ \begin{vmatrix} a & h & g \\ h & b & f \\ g & f & c \end{vmatrix} \]
The mean and variance of a binomial distribution are \(x\) and \(5\) respectively. If \(x\) is an integer, then the possible values for \(x\) are
A bag contains 5 balls of unknown colors. There are equal chances that out of these five balls, there may be 0 or 1 or 2 or 3 or 4 or 5 red balls. A ball is taken out from the bag at random and is found to be red. The probability that it is the only red ball in the bag is:
A four member committee is to be formed from a group containing 9 men and 5 women. If a committee is formed randomly, then the probability that it contains atleast one woman is
There are 8 boys and 7 girls in a class room. If the names of all those children are written on paper slips and 3 slips are drawn at random from them, then the probability of getting the names of one boy and two girls or one girl and two boys is