List of practice Questions

If A and B are two mutually exclusive and exhaustive events with P(B)=3P(A), then what is the value of P(B)?

In a given race the odds in favour of three horses A, B, C are 1:3; 1:4; 1:5 respectively. Assuming that dead heat is impossible the probability that one of them wins is

A property dealer sells a house for ` 6,30,000 and in the bargain makes a profit of 5%. Had he sold it for ` 5,00,000, then what percentage of loss or gain he would have made?

Find the value of 1% of 1% of 25% of 1000 is

One litre of water is evaporated from 6 litres of a solution containing 5% salt. The percentage of salt in the remaining solution is

If the numerator of a fraction is increased by 200% and the denominator is increased by 200%, then resultant fraction is \(2\frac{4}{5}\). What is the original fraction?

The value of \(\frac{\frac{1}{2}+\frac{1}{2}\text{of}\frac{1}{2}}{\frac{1}{2}+\frac{1}{2}\text{of}\frac{1}{2}}\)is

Two numbers are such that the square of greater number is 504 less than 8 times the square of the other. If the numbers are in the ratio 3 : 4. Find the number.

The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and 15 as remainder. What is the smaller number ?

The last two-digits in the multiplication 122×123×125×127×129 will be

What smallest number should be added to 4456 so that the sum is completely divisible by 6?

Amongst $LiCl, RbCl, BeCl_2$ and $MgCl_2$ the compounds with the greatest and the least ionic character, respectively are :

Which one of the following molecules is paramagnetic ?

A lamp emits monochromatic green light uniformly in all directions. The lamp is $3\%$ efficient in converting electrical power to electromagnetic waves and consumes $100 \,W$ of power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of $5 \,m$ from the lamp will be nearly :

If $f$ and $g$ are differentiable functions in $(0, 1)$ satisfying $f (0) = 2 = g (1), g (0) = 0$ and $f (1) = 6$, then for some $c \in ] 0, 1 [$

For all complex numbers z of the form 1 + i$\alpha$, $\alpha$ $\epsilon$ R, if z = x + iy, then :

Let $z\ne-i$ be any complex number such that $\frac{z-i}{z+i}$ is a purely imaginary number. Then $z+\frac{1}{z}$ is :

A number $x$ is chosen at random from the set $\{1, 2, 3, 4, ....., 100\}$. Define the event: $A =$ the chosen number $x$ satisfies $\frac{\left(x-10\right)\left(x-50\right)}{\left(x-30\right)}\ge0$ Then $P(A)$ is :

Let $A$ and $B$ be two events such that $P\left(\overline{A\cup B}\right)=\frac{1}{6}, P\left(\overline{A \cap B}\right)=\frac{1}{4}$ and $P\left(\bar{A}\right)=\frac{1}{4}$ where $\overline{A}$ stands for the complement of the event $A$. Then , the events $A$ and $B$ are

In S$_N$2 reactions, the correct order of reactivity for the following compounds $CH_3Cl,CH_3CH_2Cl, (CH_3 )_2CHCl$ and (CH$_3 )_3CCl$ is

Which one of the following compounds will not be soluble in sodium bicarbonate?

Which one of the following substituents at para-position is most effective in stabilizing the phenoxide ion ?

Chloro compound of Vanadium has only spin magnetic moment of $1.73\, BM$. This Vanadium chloride has the formula : (at. no. of $V = 23$)

Among the following organic acids, the acid present in rancid butter is :

Which of the following will not show mutarotation?