List of practice Questions

The minute hand of a watch is $1.5 \,cm$ long. How far does its tip move in $40$ minutes? (Use $\pi = 3.14$)
The minimum value of the function $f \left(x\right)=x^{3/2}+x^{-3/2}-4\left(x+\frac{1}{x}\right)$ for all permissible real $x$, is
Duraluminium is an alloy of
Which one of the following option is true regarding the given statements ? I. The plant was introduced in India because of its beautiful flowers and shape of leaves. II. It can propagate vegetatively at a phenomenal rate and spread all over water body in a short period. III. It is very difficult to get rid off these plants.
A point moves with uniform acceleration $v_1,v_2$ and $v_3$ denote the average velocities in three successive intervals of time $t_1, t_2$ and $ t_3 $. Correct relation among the following is
$\displaystyle \lim_{x \to 0}$ $\frac{cos\,ax-cos\,bx}{cos\,cx-1}=$
Droplet infection occurs in case of
Which one of the following produces acyl halide by treatment with $ {PCl_5}$?
The electronic configuration of two elements $X$ and $Y$ is given below : $X=1s^{2}$, $2s^{2}2p^{6}$, $3s^{2}3p^{6}$, $4s^{2}$ $Y=1s^{2}$, $2s^{2}2p^{6}$, $3s^{2}3p^{5}$ The formula of the ionic compound that can be formed between these elements is
If $K_1$ and $K_2$ are the respective equilibrium constants for the two reactions. $ {XeF6_{(g)} +H2O_{(g)}<=> XeOF4_{(g)} +2HF_{(g)}}$ $ {XeO4_{(g)} +XeF6_{(g)} <=> XeOF4_{(g)} +XeO3F2_{(g)}}$ The equilibrium constant for the reaction, $ {XeO4_{(g)} +2HF_{(g)} <=> XeO3F2_{(g)} +H2O_{(g)}}$ is
When a solid sphere rolls without slipping down an inclined plane making an angle $\theta$ with the horizontal, the acceleration of its centre of mass is $a$. If the same sphere slides without friction, its acceleration $a'$ will be
The statement 'nothing lives forever, yet life continues' illustrates the role of
The number of different words that can be formed from the letters of the word so that no vowels are together is :
Which ofthe following quantities has the unit Kg $m^2\,s^{-3}\,A^{-2}$
The number of all possible matrices of order 3 $\times$ 3 with each entry 0 or 1 is
Which of the given statements are true? (i) During the development of a dicot embryo, heart- shaped embryo is followed by globular embryo. (ii) The part of embryonal axis above the level of cotyledons is epicotyl, while the part below the level of cotyledons is hypocotyl. (iii) Monocot seeds possess a single cotyledon represented by scutellum.
Which of the following is not a unit of time?
A radioactive isotope is being produced at a constant rate A .The isotope has a half -life T initially there are no nuclei ,after a times t>>T, the number of nuclei become constant .The value of this constant is
A quantity X is given by $ \varepsilon _{0} L =\frac{\Delta V}{\Delta t} $, where $e_0$ is the permittivity of free space, L is length, $\Delta V$ is potential difference and $\Delta t$ is time interval. The dimensional formula for X is the same as that of
DNA repairing is done by :
The narrowly utilitarian arguments for biodiversity conservation include which of the following from the given list ? (i) Industrial products like dyes, lubricants (ii) Ecosystem services like photosynthesis (iii) Pollinators layer of bees, birds and bats (iv) Firewood, fibre and construction material (v) The aesthetic pleasure of walking through thick woods (vi) Products of medicinal importance (vii) Watching spring flowers in full bloom
Which one of the following can also act as a lubricant in the machines?
Which one of the following cellular components of the blood is responsible for the production of antibodies?
A proton is accelerating on a cyclotron having oscillating frequency of $11\, MHz$ in external magnetic field of $1 \,T$. If the radius of its dees is $55\, cm$, then its kinetic energy (in $MeV$) is $(m_{p}=1.67 \times 10^{-27} \, kg$, $e = 1.6 \times 10^{-19}\, C)$
A proton and an $\alpha$- particle enter in a uniform magnetic field perpendicularly with same speed. The ratio of time periods of both particle $\left(\frac{T_{p}}{T_{\alpha}}\right)$ will be