List of practice Questions

The value of $\left| \frac{1+ i \sqrt{3}}{\left( 1 + \frac{1}{i+1}\right)^2} \right|$ is

The sum of the first n terms $ \frac {1^2}{1} +\frac {1^2+2^2}{1+2}+ \frac {1^2 +2^2+3^2}{1+2+3}+$ $\dots$ is

The complex, $[Pt(Py)(NH_3)Br\,Cl]$ will have how many geometrical isomers?

A radioactive nucleus of mass $M$ emits a photon of frequency $\upsilon$ and the nucleus recoils. The recoil energy will be

Which one of the following is present as an active ingredient in bleaching powder for bleaching action?

Agarose extracted from sea weeds finds used in

Three of the following pairs of the human skeletal parts are correctly matched with their respective inclusive skeletal category and one pair is not matched. Identify the non-matching pair. .

	Pair of skeletal parts	Category
(a)$\,\,$	Sternum and ribs$\,\,$	Axial skeleton
(b)$\,\,$	Clavicle and glenoid cavity$\,\,$	Pelvic girdle
(c)$\,\,$	Flumerus and ulna$\,\,$	Appendicular skeleton
(d)$\,\,$	Malleus and stapes$\,\,$	Ear ossicles

Which one of the following is the most wide accepted method of contraception in India at present?

A TV tower has a height 150 m. What is the total population covered by the TV tower, if the population density around the TV tower is $10^3\, km^{-2}?$ Radius of the earth is $6.4\times10^{6}m$

An electric dipole is placed in an uniform electric field with the dipole axis making an angle $ \theta $ with the direction of the electric field. The orientation of the dipole for stable equilibrium is

A radioactive nucleus of mass number $A$, initially at rest, emits an $ \alpha$ - particle with a speed $v$. The recoil speed of the daughter nucleus will be

A constant torque of $ 3.14\,Nm $ is exerted on a pivoted wheel. If the angular acceleration of the wheel is $ 4\pi \,rad/s^{2}, $ then the moment of Inertia of the wheel is

The rms velocity of hydrogen is $\sqrt {7}$ times the rms velocity of nitrogen. If $T$ is the temperature of the gas, which of the following is true?

A particle of charge $e$ and mass $m$ moves with a velocity $v$ in a magnetic field $B$ applied perpendicular to the motion of the particle. The radius $r$ of its path in the field is

If $\alpha , \beta ,\gamma$ are the roots of $x^3-2x+1=0$, then the value of $(\sum \frac {1} {\alpha +\beta -\gamma}$) is

If the focii of $\frac {x^2}{16}+\frac{y^2}{4}=1 $ and $\frac {x^2}{a^2}-\frac{y^2}{3}=1 $ coincide, then value of $a$ is

Locus of a point which moves such that its distance from the $X-axis$ is twice its distance from the line $x - y = 0$ is

If $y =\frac{\sec x +\tan x}{\sec x - \tan x} $ , then $\frac{dy}{dx} = $

Let [ ?] denote the greatest integer function and $f (x) = [\tan^2 x]$. Then

Ratio of radiant energy emitted per unit area per second by two stars is 16 : 81. The ratio of wavelengths at which intensity of radiant energy is maximum is given by?

The dissociation constant of a weak base is $ {1 \times 10^{-5}}$ at 25?C. The pH of its 0.1 M solution at the same temperature.will be .