List of practice Questions

Fill in the blank with most appropriate word
_______ means the ridiculous and miserable failure.

Fill in the blank with most appropriate word
He looks at everything from a personal point of view

Fill in the blank with most appropriate word
Docile person is _______

By understanding the relationship between the first and the second word find the most related word for the third word
Monkey : Chatter :: Elephant : ?

By understanding the relationship between the first and the second word find the most related word for the third word
Shooting : Bullet : : Archery : ?

By understanding the relationship between the first and the second word find the most related word for the third word
Carpenter : Furniture : : Sculptor : ?

By understanding the relationship between the first and the second word find the most related word for the third word
Ornithology : Birds : : Entomology : ?

By understanding the relationship between the first and the second word find the most related word for the third word
Patricide : Father : : Sororicide : ?

$\quad\int_{0}^{1} \left[f \left(x\right)g'' \left(x\right)-f''\left(x\right)g \left(x\right)\right]$ dx is equal to : [Given f(0) = g(0) = 0]

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 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

If $z=\frac{7-i}{3-4i} \, then\, z^{14}=$

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

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

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-

The solution of the differential equation log x $\frac{d y}{d x}+\frac{y}{x} =$ sin 2x is

Value of $\int\limits_{0}^{\pi /2} \frac{\sqrt{sin x}}{\sqrt{sin x}\sqrt{cos x}} $ dx is

An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail 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 :

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 :

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 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)

The total number of terms in the expansion of ${(x+a)^{47} - (x-a)^{47}}$ after simplification is