List of practice Questions

The average of 11 numbers is 10.9. If the average of the first six numbers is 10.5 and that of the last six numbers is 11.4, then the middle number is :

A and B rent a pasture for 10 months; A puts in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A?

A can do a piece of work in 25 days and B in 20 days. They work together for 5 days and then A goes away. In how many days will B finish the remaining work ?

A bag contains 100 tickets numbered 1, 2, 3, .... 100. If a ticket is drawn out of it at random, what is the probability that the ticket drawn has the digit 2 appearing on it?

A bag contains 5 white and 3 black balls, and 4 are successively drawn out and not replaced. What’s the chance of getting different colours alternatively?

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