List of top Mathematics Questions

If $|Z_1 - 3 - 4i| = 5$ and $|Z_2| = 15$ then the sum of the maximum and minimum values of $|Z_1 - Z_2|$ is

If $1+2i$ is a root of the equation $x^4 - 3x^3 + 8x^2 - 7x + 5 = 0$, then sum of the squares of the other roots is

If $f(x) = x^2 - 2(4K-1)x + g(K)>0$ $\forall x \in \mathbb{R}$ and for $K \in (a,b)$, and if $g(K) = 15K^2 - 2K - 7$, then

If $Z=r(\cos\theta+i\sin\theta)$, $(\theta \neq -\pi/2)$ is a solution of $x^3 = i$, then $r^9(\cos(9\theta)+i\sin(9\theta)) =$

The number of real values of 'a', for which the system of equations $2x+3y+az = 0$, $x+ay-2z=0$ and $3x+y+3z = 0$ has nontrivial solutions is

If the eight vertices of a regular octagon are given by the complex numbers $\frac{1}{x_j-2i}$ ($j=1,2,3,4,5,6,7,8$), then the radius of the circumcircle of the octagon is

If $A = \begin{pmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & x & 1 \end{pmatrix}$, $A^{-1} = \frac{1}{2} \begin{pmatrix} 1 & -1 & 1 \\ -8 & 6 & 2y \\ 5 & -3 & 1 \end{pmatrix}$ then the point $(x,y)$ lies on the curve

A is a $3 \times 3$ matrix satisfying $A^3 - 5A^2 + 7A + I = 0$. If $A^5 - 6A^4 + 12A^3 - 6A^2 + 2A + 2I = lA + mI$, then $l + m =$

\( \int_0^{\pi/2} \sqrt{\tan x} \, dx = \)

The differential equation corresponding to the family of ellipses \( \frac{x^2}{a^2} + \frac{y^2}{4} = 1 \), where 'a' is an arbitrary constant is

\( \int \frac{x+\cos x}{1-\sin x} dx = \)

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

\( \int_{-1}^{5} \frac{1}{\sqrt{20+x-x^2}} dx = \)

If \( \int x^3 \sin(3x) dx = \frac{1}{27} [f(x)\cos(3x) + g(x)\sin(3x)] + c \) then f(1)+g(1)=

The real valued function \( f(x) = \frac{x^2}{2} - \log(x^2+x+1) \) is

If \( y = x^{\log x} + (\log x)^x, x>1 \) then \( (\frac{dy}{dx})_{x=e} = \)

If the curves \(y^2=12x-3\) and \(y^2=12-kx\) cut each other orthogonally then the length of the sub tangent at (1,b) on the curve \(y^2=12-kx\) is

A rod of length 41 m with an end A on the floor and another end B on the wall perpendicular to the floor is sliding away horizontally from the wall at the rate of 3 ft/min. When the end B is at the height of 9 ft from the floor, then the rate at which the area of the triangle formed by the rod with wall and floor changes at that instant is (in ft/min)

There is a possible error of 0.02 cm in measuring the base diameter of a right circular cone as 14 cm. If the semi-vertical angle of the cone is 45°, then the approximate error in its volume is (in cu. cm)

If the angle between the planes ax-y+3z=2a and 3x+ay+z=3a is \( \frac{\pi}{3} \) then the direction ratios of the line perpendicular to the plane (a+2)x+(a-4)y+2az=a are

If [x] is the greatest integer function and \( f(x) = \begin{cases} \frac{2[x]-x}{|x|} & x \neq 0 \\ 1 & x=0 \end{cases} \) is a real valued function, then f is

If \( y = \tan^2(\cos^{-1}\sqrt{\frac{1+x^2}{2}}) \), then \( \frac{dy}{dx} = \)

If \(\alpha\) is the angle between any two diagonals of a cube and \(\beta\) is the angle between a diagonal of a cube and a diagonal of its face, which intersects this diagonal of the cube then \( \cos\alpha + \cos^2\beta = \)

If L(p,q), q>3 is one end of the latus rectum of the parabola \((y-2)^2 = 3(x-1)\) then the equation of the tangent at L to this parabola is

If the latus rectum through one of the foci of a hyperbola \( \frac{x^2}{9} - \frac{y^2}{b^2} = 1 \) subtends a right angle at the farther vertex of the hyperbola, then \(b^2 = \)