List of practice Questions

There are $10$ persons including $3$ ladies. A committee of $4$ persons including at least one lady is to be formed. The number of ways of forming such a committee is

For an isolated system, ∆U=0, what will be ∆S ?

Find the perimeter of each of the following shapes : 

1. A triangle of sides 3 cm, 4 cm and 5 cm. 
2.  An equilateral triangle of side 9 cm. 
3.  An isosceles triangle with equal sides 8 cm each and third side 6 cm.

A road roller takes 750 complete revolutions to move once over to level a road. Find the area of the road if the diameter of a road roller is 84 cm and length is 1 m.

If $ \overrightarrow{a},\text{ }\overrightarrow{b},\text{ }\overrightarrow{c} $ are non-coplanar and $ (\overrightarrow{a}+\lambda \overrightarrow{b}).[(\overrightarrow{b}+3\overrightarrow{c})\times (\overrightarrow{c}\times 4\overrightarrow{a})]=0, $ then the value of $ \lambda $ is equal to

The image of the interval [-1, 3] under the mapping $f : R\rightarrow R$ given by $f \left(x\right)=4x^{3}-12x$ is

If $A$ and $B$ are square matrices of the same order and if $A=A^{T},B=B^{T},$ then $\left(ABA\right)^{T}=$

If $ x={{\sin }^{-1}}(3t-4{{t}^{3}}) $ and $ y={{\cos }^{-1}}(\sqrt{1-{{t}^{2}}}), $ then $ \frac{dy}{dx} $ is equal to

How did Mandela’s ‘hunger for freedom’ change his life?

How did Douglas overcome his fear of water?

Classify the following reactions in one of the reaction type studied in this unit
a) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{Br}+\mathrm{HS}^{-} \rightarrow \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{SH}+\mathrm{Br}^{-}\)
b) \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{C}=\mathrm{CH}_{2}+\mathrm{HCl} \rightarrow\left(\mathrm{CH}_{3}\right)_{2} \mathrm{ClC}-\mathrm{CH}_{3}\)
c) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{Br}+\mathrm{HO}^{-} \rightarrow \mathrm{CH}_{2}=\mathrm{CH}_{2}+\mathrm{H}_{2} \mathrm{O}+\mathrm{Br}^{-}\)
d) \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}-\mathrm{CH}_{2} \mathrm{OH}+\mathrm{HBr} \rightarrow\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CBrCH}_{2} \mathrm{CH}_{3}+\mathrm{H}_{2} \mathrm{O}\)

If $ l,m $ and $ n $ are real numbers such that $ {{l}^{2}}+{{m}^{2}} $ $ +{{n}^{2}}=0, $ then $ \left| \begin{matrix} 1+{{l}^{2}} & lm & ln \\ lm & 1+{{m}^{2}} & mn \\ ln & mn & 1+{{n}^{2}} \\ \end{matrix} \right| $ is equal to

If $p :$ It is snowing, $q :$ I am cold, then the compound statement "It is snowing and it is not that I am cold" is given by

If sin $\left(\theta-\phi\right) = n \, sin (\theta - \phi),n \ne1,$ then the value of $\frac{\tan\theta}{\tan\phi}$ is equal to

If the projection of the vector $\vec {a}$ on $\vec{b}$ is $ \overrightarrow{a} $ on $ \overrightarrow{b} $ is $ |\overrightarrow{a}\times \overrightarrow{b}| $ and if $ 3\overrightarrow{b}=\vec{i}+\vec{j}+\vec{k}, $ then the angle between $ \vec{a} $ and $ \vec{b} $ is

If $\begin{vmatrix}3i&-9i&1\\ 2&9i&-1\\ 10&9&i\end{vmatrix} = x + iy $, then

If $xy\, = \,A \,sinx \,+ \,B \,cos \,x$ is the solution of the differential equation $x\frac{d^{2}y}{dx^{2}}-5a\frac{dy}{dx}+xy=0$ then the value of $a$ is equal to

If $ y={{\sin }^{2}}{{\cot }^{-1}}\sqrt{\frac{1+x}{1-x}}, $ then $ \frac{dy}{dx} $ is equal to

In a certain town $25\%$ families own a cell phone, $15\%$ families own a scooter and $65\%$ families own neither a cell phone nor a scooter. If $1500$ families own both a cell phone and a scooter, then the total number of families in the town is

In the expansion of $ {{(1+x+{{x}^{2}}+{{x}^{3}})}^{6}}, $ the coefficient of $ {{x}^{14}} $ is

Let $A (6, -1), B (1, 3)$ and $C (x, 8)$ be three points such that $AB = BC$. The values of $x$ are

The domain of the function $f\left(x\right) = sin^{-1}\left(\frac{x+5}{2}\right)$ is

The general solution of the differential equation $(x + y + 3) \,\frac{dy}{dx}\, =\,1$ is

The principal argument of the complex numb $Z=\frac{1+\sin \frac{\pi}{3}+i \cos\frac{\pi}{3} }{1+\sin \frac{\pi}{3} - i \cos\frac{\pi}{3} }$ is