List of top Mathematics Questions

The volume V and depth x of water in a vessel are connected by the relation $V=5x-\frac{x^{2}}{6} $ and the volume of water is increasing, at the rate of $5 cm^{3}/sec,$ when x = 2 cm. The rate at which the depth of water is increasing, is
The value of x obtained from the equation $\begin{vmatrix}x+\alpha&\beta&\gamma\\ \gamma&x+\beta&\alpha\\ \alpha&\beta&x+\gamma\end{vmatrix}=0$ will be
The area bounded by f (x) $=x^{2}, 0 \le x \le 1, g\left(x\right)=x+2,1\le x\le2$ and x- axis is
If $z=\frac{7-i}{3-4i} \, then\, z^{14}=$
Equation $\frac{1}{r}=\frac{1}{8}+\frac{3}{8} cos\, \theta represents$
Let A be the centre of the circle $x^{2}+y^{2}-2x-4y-20=0,$ and B( 1,7) andD(4,-2) are points on the circle then, if tangents be drawn at B and D, which meet at C, then area of quadri 1 ateral A BCD is-
Value of $\int\limits_{0}^{\pi /2} \frac{\sqrt{sin x}}{\sqrt{sin x}\sqrt{cos x}} $ dx is
The solution of the differential equation log x $\frac{d y}{d x}+\frac{y}{x} =$ sin 2x is
A straight line parallel to the line 2x - y + 5 = 0 is also a tangent to the curve $y^{2}=4x+5.$ Then the point of contact is
Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in $s m$) of the flower-bed, is :
An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is :
Let $a, b, c \, \in \, R$. If $f(x) = ax^2 + bx + c$ is such that $a + b + c = 3$ and $f (x + y) = f (x) + f (y) + xy, \forall \, x, y \, \in \, R,$ then $\displaystyle\sum^{10}_{n = 1} f(n)$ is equal to :
The integral $\int \sqrt{ 1 + 2 \cot \, x (cosec \, x + \cot \, x) } dx \, \left( 0 < x < \frac{\pi}{2} \right)$ is equal to : (where $C$ is a constant of integration)
If for $x \epsilon \left(0, \frac{1}{4}\right) ,$ the derivative of $ \tan^{-1} \left(\frac{6x \sqrt{x}}{1-9x^{3}}\right) $ is $\sqrt{x} . g(x)$, then $g(x)$ equals :
The total number of terms in the expansion of ${(x+a)^{47} - (x-a)^{47}}$ after simplification is
A focal chord of the parabola y2 = 8x in inclined to x-axis at an angle tan-13. Then its length is equal to:
The equation of a circle passing through the point (1, 1) and the point of intersection of the circles x2 + y2 + 13x - 3y = 0 and 2x2 + 2y2 + 4x - 7y -25 = 0 is
If \(\Delta=\begin{vmatrix} 1&2&3\\2&5&7\\3&9&13 \end{vmatrix}\) and \(\Delta'=\begin{vmatrix} 7&20&29\\2&5&7\\3&9&13 \end{vmatrix}\) then
The middle term in the expansion of \(( x + \frac{1}{x} )^{2n}\) is \(1.3.5 . . .\) \(\frac{(2n-1)}{2n\ !}\)
If the three successive coefficients in the binomial expansion of (1+x)n are 28,56 and 70 respectively then n equals
If P(A) = 1/3, P(B) = 3/4 and P(A∪B)= 11/12, then P(A/B) is
The geometric mean 3,32 ..... 3n is
what is the product of three Geometric mean between 4 and 1/4 ?
If the sum of first n positive integer is 1/(5) times the sume of their squares, then n equals
A unit vector coplanar with \(\overrightarrow{i}+\overrightarrow{j}+2\overrightarrow{k}\) and \(\overrightarrow{i}+2\overrightarrow{j}+\overrightarrow{k}\) and perpendicular to \(\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}\) is