GATE Overflow for GATE ESE - Recent activity in Quantitative Aptitude

Edited: GATE ES 2026 | GA | Question: 9

Fri, 03 Apr 2026 08:37:42 +0000

Circles $C_{1}, C_{2}$, and $C_{3}$, with centers $O_{1}, O_{2}$, and $O_{3}$, and radii $r_{1}, r_{2}$, and $r_{3}$, respectively, touch each other as shown in the following figure. Given $r_{1}=2 \mathrm{~cm}$, $r_{2}=1 \mathrm{~cm}$ and the angle $\angle O_{1} O_{3} O_{2}$ is $90^{\circ}, r_{3}=$ $\_\_\_\_$ $\mathrm{cm}$.

$\dfrac{1}{2}(-3+\sqrt{17})$
$\dfrac{1}{2}(3+\sqrt{17})$
$\dfrac{1}{2}(-2+\sqrt{17})$
$\dfrac{1}{2}(-3+2 \sqrt{17})$

Answered: GATE ES 2025 | GA Question: 7

Tue, 26 Aug 2025 14:40:38 +0000

Drawn using Excalidraw

Edited: GATE ES 2025 | Question: 52

Mon, 02 Jun 2025 20:05:29 +0000

A street sweeping machine starts from point $P$ and ends at $S$, as shown in the network of streets below. It sweeps all the streets at least once.

Length of the streets, in km , are shown on the network. The minimum distance travelled by the sweeping machine for completing the job of sweeping all the street is $\_\_\_\_\_\_$ km. (rounded off to nearest integer)

Edited: GATE ES 2025 | GA Question: 10

Mon, 02 Jun 2025 15:48:05 +0000

The number of patients per shift $(X)$ consulting Dr. Gita in her past $100$ shifts is shown in the figure. If the amount she earns is ₹ $1000(X-0.2)$, what is the average amount (in ₹) she has earned per shift in the past $100$ shifts?

Note: The figure shown is representative.

$6,100$
$6,300$
$6,000$
$6,500$

Edited: GATE ES 2025 | GA Question: 9

Mon, 02 Jun 2025 15:46:54 +0000

If a real variable $x$ satisfies $3^{x^{2}}=27 \times 9^{x}$, then the value of $\frac{2^{x^{2}}}{\left(2^{x}\right)^{2}}$ is:

$2^{-1}$
$2^{0}$
$2^{3}$
$2^{15}$

Edited: GATE ES 2025 | GA Question: 5

Mon, 02 Jun 2025 15:43:40 +0000

A rectangle has a length $\text{L}$ and a width $\text{W}$ , where $\text{L>W}$. If the width, $\text{W}$, is increased by $10 \%$, which one of the following statements is correct for all values of $\text{L}$ and $\text{W}$?

Perimeter increases by $10 \%$.
Length of the diagonals increases by $10 \%$.
Area increases by $10 \%$.
The rectangle becomes a square.

Edited: GATE ES 2025 | GA Question: 3

Mon, 02 Jun 2025 15:37:52 +0000

A $4 \times 4$ digital image has pixel intensities $(U)$ as shown in the figure. The number of pixels with $U \leq 4$ is:

$$\begin{array}{|l|l|l|l|} \hline 0 & 1 & 0 & 2 \\ \hline 4 & 7 & 3 & 3 \\ \hline 5 & 5 & 4 & 4 \\ \hline 6 & 7 & 3 & 2 \\ \hline \end{array}$$

$3$
$8$
$11$
$9$

Recategorized: GATE ES 2024 | GA Question: 5

Mon, 21 Apr 2025 17:05:15 +0000

In an election, the share of valid votes received by the four candidates $\text{A, B, C}$, and $\mathrm{D}$ is represented by the pie chart shown. The total number of votes cast in the election were $1,15,000$, out of which $5,000$ were invalid.

Based on the data provided, the total number of valid votes received by the candidates $\mathrm{B}$ and $\mathrm{C}$ is

$45,000$
$49,500$
$51,750$
$54,000$

Recategorized: GATE ES 2024 | GA Question: 4

Mon, 21 Apr 2025 17:05:12 +0000

The sum of the following infinite series is
\[
2+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{8}+\frac{1}{9}+\frac{1}{16}+\frac{1}{27}+\cdots
\]

$11 / 3$
$7 / 2$
$13 / 4$
$9 / 2$

Recategorized: GATE ES 2024 | GA Question: 3

Mon, 21 Apr 2025 17:05:10 +0000

How many $4$-digit positive integers divisible by $3$ can be formed using only the digits $\{1,3,4,6,7\}$, such that no digit appears more than once in a number?

$24$
$48$
$72$
$12$

Recategorized: GATE ES 2024 | GA Question: 8

Mon, 21 Apr 2025 17:04:56 +0000

Person $1$ and Person $2$ invest in three mutual funds $\text{A, B}$, and $\text{C}$. The amounts they invest in each of these mutual funds are given in the table

	Mutual fund A	Mutual fund B	Mutual fund C
Person 1	$10,000$	$20,000$	$20,000$
Person 2	$20,000$	$15,000$	$15,000$

At the end of one year, the total amount that Person $1$ gets is ₹$500$ more than Person $2$. The annual rate of return for the mutual funds $\text{B}$ and $\mathrm{C}$ is $15 \%$ each. What is the annual rate of return for the mutual fund $\mathrm{A}$ ?

$7.5 \%$
$10 \%$
$15\%$
$20\%$

Recategorized: GATE ES 2023 | GA Question: 10

Mon, 21 Apr 2025 17:01:39 +0000

A square with sides of length $6 \mathrm{~cm}$ is given. The boundary of the shaded region is defined by two semi-circles whose diameters are the sides of the square, as shown.

The area of the shaded region is __________ $\mathrm{cm}^2$.

$6 \pi$
$18$
$20$
$9 \pi$

Recategorized: GATE ES 2023 | GA Question: 9

Mon, 21 Apr 2025 17:01:36 +0000

The digit in the unit's place of the product $3^{999} \times 7^{1000}$ is ___________.

Recategorized: GATE ES 2023 | Question: 52

Mon, 21 Apr 2025 16:59:00 +0000

Ms. Anita uses a BS-IV two wheeler petrol scooter, with a mileage of $50 \mathrm{~km} / \mathrm{L}$, to travel $30 \mathrm{~km}$ every day. She exchanges this two wheeler with an electric scooter, which consumes electricity at $0.1 \mathrm{kWh} / 10 \mathrm{~km}$. Assuming the cost of petrol and electricity are fixed at Rs. $90$ per L and Rs. $3.5$ per kWh, respectively, and maintenance cost of both BS-IV two wheeler and electric scooter is negligible, the operational cost saved in a year by Ms. Anita is___________ $\text{(in Rs., in integer).}$

Recategorized: GATE ES 2023 | Question: 54

Mon, 21 Apr 2025 16:58:54 +0000

An adult of $65 \mathrm{~kg}$ weight and life span of 65 years drinks water for 5 years, which is contaminated with toluene of concentration $0.15 \mathrm{mg} / \mathrm{L}$. For toluene, reference dose is $0.200 \mathrm{mg} / \mathrm{kg}$-d. The person drinks $2 \mathrm{~L}$ of water per day. The hazard quotient from the toluene exposure for the adult will be _________ $\text{(rounded off to three decimal places).}$

Recategorized: GATE ES 2022 | GA Question: 2

Mon, 21 Apr 2025 16:45:18 +0000

A sum of money is to be distributed among $\text{P, Q, R and S}$ in the
proportion $5: 2: 4: 3$, respectively.
If R gets ₹ 1000 more than S, what is the share of Q (in ₹)?

500
1000
1500
2000

Recategorized: GATE ES 2022 | GA Question: 3

Mon, 21 Apr 2025 16:45:13 +0000

A trapezium has vertices marked as $\mathrm{P}, \mathrm{Q}, \mathrm{R}$ and $\mathrm{S}$ $\text{(in that order anticlockwise).}$ The side PQ is parallel to side SR. Further, it is given that, $\mathrm{PQ}=11 \mathrm{~cm}, \mathrm{QR}=4 \mathrm{~cm}, \mathrm{RS}=6 \mathrm{~cm}$ and $\mathrm{SP}=3 \mathrm{~cm}$.
What is the shortest distance between PQ and SR (in cm )?

$1.80$
$2.40$
$4.20$
$5.76$

Recategorized: GATE ES 2022 | GA Question: 7

Mon, 21 Apr 2025 16:45:05 +0000

Consider the following inequalities.

$2 x-1>7
$2 x-9<1$

Which one of the following expressions below satisfies the above two inequalities?

$x \leq-4$
$-4$
$4$
$x \geq 5$

Recategorized: GATE ES 2021 | GA Question: 2

Mon, 21 Apr 2025 15:43:12 +0000

$p$ and $q$ are positive integers and $\frac{p}{q}+\frac{q}{p}=3$ \end{tabular} then, $\frac{p^{2}}{q^{2}}+\frac{q^{2}}{p^{2}}=$

$3$
$7$
$9$
$11$

Recategorized: GATE ES 2021 | GA Question: 1

Mon, 21 Apr 2025 15:43:10 +0000

The current population of a city is $11,02,500$. If it has been increasing at the rate of $5 \%$ per annum, what was its population $2$ years ago?

$9,92,500$
$9,95,006$
$10,00,000$
$12,51,506$

Recategorized: GATE ES 2021 | GA Question: 9

Mon, 21 Apr 2025 15:42:50 +0000

The number of minutes spent by two students, $X$ and $Y$, exercising every day in a given week are shown in the bar chart above.

The number of days in the given week in which one of the students spent a minimum of $10 \%$ more than the other student, on a given day, is

Recategorized: GATE ES 2021 | Question: 21

Mon, 21 Apr 2025 15:41:52 +0000

Consider the following equation:
$x^{3}-10 x^{2}+31 x-30=0$
Which of the following is/are the root(s) of the above equation?

Recategorized: GATE ES 2021 | Question: 41

Mon, 21 Apr 2025 15:40:58 +0000

If $f(x)+3 f(g(x))=x-2$
where $g(x)=\frac{3 x+1}{x-3}$
then the value of the ratio $\frac{f(5)}{f(8)}$ is _________.

$\text{(answer in integer)}$

Recategorized: GATE ES 2021 | Question: 48

Mon, 21 Apr 2025 15:40:32 +0000

The net profit expected from a manufacturing unit is ₹$6000$ per year. The operational life of the unit is $15$ years. Assuming a fixed discount rate of $8 \%$ per annum, the net present worth of the profit earned over the operational life is ₹ ________$\text{(answer in integer)}$.