List of top Mathematics Questions

If \( A = \begin{pmatrix} 1 & 2 & 2 \\ 2 & 1 & 1 \\ 1 & 2 & 1 \end{pmatrix} \), then \( |\text{Adj}(A^2)| = \)

$\int_{-2}^{4} |2-x^2| dx =$

The general solution of the differential equation $\frac{dy}{dx} + (\sec x \csc x)y = \cos^2 x$ is

$\int_{-1}^{1} \frac{\log 2 - \log(1+x)}{\sqrt{1-x^2}} dx =$

$\int \frac{3^x(x\log 3 - 1)}{x^2} dx =$

$\int_{0}^{\pi/4} \frac{\sec x}{3\cos x + 4\sin x} dx =$

If $\frac{5\pi}{4}<x<\frac{7\pi}{4}$, then $\int \sqrt{\frac{1-\sin 2x}{1+\sin 2x}} dx =$

For a real number 'a', if a real valued function $f(x) = 4x^3 + ax^2 + 3x - 2$ is monotonic in its domain, then the range of 'a' is

If the point P($x_1, y_1$) lying on the curve $y = x^2-x+1$ is the closest point to the line $y = x-3$ then the perpendicular distance from P to the line $3x+4y-2=0$ is

There is a possible error of 0.03 cm in a scale of length 1 foot with which the height of a closed right circular cylinder and the diameter of a sphere are measured as 3.5 feet each. If the radii of both cylinder and sphere are same, then the approximate error in the sum of the surface areas of both cylinder and sphere is (in square feet)

A man of 5 feet height is walking away from a light fixed at a height of 15 feet at the rate of K miles/hour. If the rate of increase of his shadow is $\frac{11}{5}$ feet/sec, then K = (Take 1 mile = 5280 feet)

If $y = \sqrt{\log(x^2+1)+\sqrt{\log(x^2+1)+\sqrt{\log(x^2+1)+...}}}$, $|x|<1$, then $\frac{dy}{dx} =$

If $y = \text{Sec}^{-1}x$, then $\frac{d^2y}{dx^2} =$

If $x = \sqrt{1-\tan y}$, then $\frac{dy}{dx} =$

If $[t]$ represents the greatest integer $\leq t$ then the value of $\lim_{x\to 3} \frac{11-[2-x]}{[x+10]}$ is

A line makes angles 60$^\circ$, 45$^\circ$, $\theta$ with positive X, Y, Z-axes respectively. If $\theta$ is an acute angle, then $\tan\theta =$

The number of values of 'k' for which the points (-4,9,k), (-1,6,k), (0,7,10) form a right-angled isosceles triangle is

If the perpendicular distance from the focus of an ellipse $\frac{x^2}{9} + \frac{y^2}{b^2} = 1$ ($b<3$) to its corresponding directrix is $\frac{4}{\sqrt{5}}$, then the slope of the tangent to this ellipse drawn at $(\frac{3}{\sqrt{2}}, \frac{b}{\sqrt{2}})$ is

The length of the chord of the ellipse $\frac{x^2}{4} + y^2 = 1$ formed on the line $y = x+1$ is

Let P, Q, R, S be the points of intersection of the circle $x^2 + y^2 = 4$ and the hyperbola $xy = \sqrt{3}$. If P = $(\alpha,\beta)$ and $\alpha>\beta>0$, then the equation of the tangent drawn at P to the hyperbola is

If the foot of the perpendicular drawn from the point (2,0,-3) to the plane $\pi$ is (1,-2,0) and the equation of the plane is $ax+by-3z+d=0$ then $a+b+d=$

If $2x-3y+5=0$ and $4x-5y+7=0$ are the equations of the normals drawn to a circle and (2,5) is a point on the given circle, then the radius of the circle is

The line $4x-3y+2 = 0$ intersects the circle $x^2+y^2-2x+6y+c=0$ at two points A, B and AB=8. If (1,k) is a point on the given circle and $k>0$, then $k =$

If $(\alpha,\beta)$ is the centre of the circle which passes through the point (1,-1) and cuts the circles $x^2 + y^2+2x-3y-5=0$, $x^2+y^2-3x+2y+1=0$ orthogonally, then $\alpha-5\beta =$

The number of normals that can be drawn through the point (2,0) to the parabola $y^2 = 7x$ is