Recent questions and answers

Let $a_{n}=46+8 n$ and $b_{n}=98+4 n$ be two sequences for natural numbers $n \leq 100$. Then, the sum of all terms common to both the sequences is$14900$$15000$$14798$$1...

Two people are selected at random from a group, assuming that:Each day of the year is equally likely to be a birthday.There are 365 days in a year (ignoring leap years).B...

The number of all positive integers up to $500$ with non-repeating digits is

In the following sentence, a part of the sentence is underlined following which are 4 ways afrephrasing the underlined part. Mark the most appropriate choice.Mr. Pillai, ...

A kinship diagram is a powerful visual representation used to map out relationships between individuals within a family or community. It helps to clearly illustrate how p...

The selling price of a product is fixed to ensure $40 \%$ profit. If the product had cost $40 \%$ less and had been sold for $5$ rupees less, then the resulting profit wo...

If $3^{a}=4,4^{b}=5,5^{c}=6,6^{d}=7,7^{e}=8$ and $8^{f}=9$, then the value of the product $\mathrm{abcdef}$ is

The midpoints of sides $\mathrm{AB}$, $\mathrm{BC}$, and $\mathrm{AC}$ in $\triangle \: \mathrm{ABC}$ are $\mathrm{M}, \mathrm{N}$, and $\mathrm{P}$, respectively. The me...

The average of three distinct real numbers is $28$. If the smallest number is increased by $7$ and the largest number is reduced by $10$, the order of the numbers remains...

For any non-zero real number $x$, let $f(x)+2 f\left(\frac{1}{x}\right)=3 x$. Then, the sum of all possible values of $x$ for which $f(x)=3$, is$-3$$3$$-2$$2$

If $x$ and $y$ are positive real numbers such that $\log _{x}\left(x^{2}+12\right)=4$ and $3 \log _{y} x=1$, then $x+y$ equals$11$$20$$10$$68$

If $x$ and $y$ are real numbers such that $x^{2}+(x-2 y-1)^{2}=-4 y(x+y)$, then the value $x-2 y$ is$1$$2$$-1$$0$

For what value of $k,$ expression $x^{4} – 2x^{2} + k$ will be a perfect square ?$0$$1$$-1$Cannot be determined.

When $2x + \frac{2}{x} = 3,$ then the value of $x^{3} + \frac{1}{x^{3}} + 2$ is :$7/2$$7/8$$8/7$$2/7$

Let $r$ and $c$ be real numbers. If $r$ and $-r$ are roots of $5 x^{3}+c x^{2}-10 x+9=0$, then $c$ equals$4$$-4$$-\frac{9}{2}$$\frac{9}{2}$

A boy finds the average of $10$ positive integers. Each integer contains two digits. By mistake, the boy interchanges the digits of one number say $ba$ for $ab.$ Due to t...

Let $a, b, c$ be non-zero real numbers such that $b^{2}<4 a c$, and $f(x)=a x^{2}+b x+c$. If the set $S$ consists of all integers $m$ such that $f(m)<0$, then the set $S$...

$\mathrm{A}$ trapezium $\mathrm{ABCD}$ has side $\mathrm{AD}$ parallel to $\mathrm{BC}, \angle \mathrm{BAD}=90^{\circ}, \mathrm{BC}=3 \mathrm{~cm}$ and $\mathrm{AD}=8 \ma...

Let$le(x, y) =$ least of x and y (i.e., $\min(x, y))$$me(x, y) =$ maximum of x and y (i.e., $\max(x, y))$$mo(x) = |x|$ (absolute value)For real numbers $a, b,$ which of t...

Let $\text{P, Q, S, R, T, U}$ and $\text{V}$ represent the seven distinct digits from $0$ to $6$, not necessarily in that order. If $\text{PQ}$ and $\text{RS}$ are both t...

The perimeter of a square plot is the same as that of a rectangular plot with sides $35 \; \text{m}$ and $15 \; \text{m}.$ The side of the square plot is :$25 \; \text{m}...

A number is divided into two parts in such a way that $80 \%$ of the first part is $3$ more than $60 \%$ of the $2^{\text{nd}}$ part and $80 \%$ of the $2^{\text{nd}}$ pa...

If $4.25 – \left[ 4.25 + \left\{ 4.25 – \left( 8.5 – \overline{\rm 4.25+x} \right) \right\} \right]$ the value of $x$ is :$0$$4.25$$8.5$$12.75$

Consider the following statements :$x+3$ is the factor of $x^{3} + 2x^{2} + 3x + 8.$$x-2$ is the factor of $x^{3} + 2x^{2} + 3x + 8.$Which of the statements given above i...

Julia and Angelina are team members in a project. Whenever Julia approaches Angelina for some work-related discussions. Angelina replies to her rudely and does not seem w...

Answer the question on the basis of the following table.Below is a table that lists countries region-wise. Each region-wise list is sorted, first by birth rate and then a...

Among the components of attitude ___________ is the only component that can be observed directly.CognitiveBehaviouralObservationAffective

A government is assigning each of six embassy office workers - Farr, Golden, HayaKawa, Inserra, Jones, and Kovacs to embassies. There are four embassies. Embassies L and ...

A government is assigning each of six embassy office workers - Farr, Golden, HayaKawa, Inserra, Jones, and Kovacs to embassies. There are four embassies. Embassies L and ...

Anil mixes cocoa with sugar in the ratio $3: 2$ to prepare mixture $A$, and coffee with sugar in the ratio $7: 3$ to prepare mixture $B$. He combines mixtures $A$ and $B$...

The population of a town in $2020$ was $100000$. The population decreased by $y \%$ from the year $2020$ to $2021$, and increased by $x \%$ from the year $2021$ to $2022$...