GATE Overflow for GATE XE - Recent activity in Quantitative Aptitude

Edited: GATE XE 2026 | Question: 179

Thu, 02 Apr 2026 11:15:22 +0000

A radioactive isotope sample has a decay constant $\lambda= 2.31 \times 10^{-4} \text{year}^{-1}$. Initially the sample contains $8000 \times 10^{15}$ atoms. The sample decays to $25 \%$ of its initial value. The number of years it takes to decay to this stage is closest to ________.

$3000$
$6000$
$900$
$2600$

Edited: GATE XE 2026 | Question: 150

Thu, 02 Apr 2026 10:23:20 +0000

If $20$ wave crests pass a fixed point in an interval of $5$ minutes, then the frequency of the wave (in Hertz) is $\_\_\_\_$. (rounded off to three decimal places)

Answered: GATE XE 2025 | Question: 10

Fri, 31 Oct 2025 14:07:45 +0000

According to Heron's formula

area (triangle) = sqrt{s(s-a)(s-b)(s-c)}

s=(a+b+c)/2

a=13, b=14, c=15, therefore s=21, and area= 84

area of triangle = 1/2 (base*altitude)

84 = 1/2 (14*altitude)

therefore altitude = 12 (C)

Edited: GATE XE 2025 | Question: 94

Sun, 29 Jun 2025 17:10:01 +0000

A tank of $4 \: \mathrm{~m}^{3}$ contains an ideal gas mixture of $60 \%$ hydrogen and $40 \%$ nitrogen by volume at $100 \: \mathrm{kPa}$ and $300 \: \mathrm{K}$. Nitrogen is added to the tank such that the composition changes to $50 \%$ nitrogen by volume, with a final temperature of $300 \: \mathrm{K}$. The amount of nitrogen (in $\mathrm{kmol}$) to be added is $\_\_\_\_\_\_$ (rounded off to three decimal places).

Use: Universal gas constant $\left(R_{u}\right)=8.314 \mathrm{~kJ} / \mathrm{kmol}-\mathrm{K}$

Edited: GATE XE 2025 | Question: 9

Sun, 29 Jun 2025 11:12:31 +0000

A business person buys potatoes of two different varieties $\text{P}$ and $\text{Q}$, mixes them in a certain ratio and sells them at ₹ $192$ per kg.

The cost of the variety $\text{P}$ is ₹ $800$ for $5$ kg.

The cost of the variety $\text{Q}$ is ₹ $800$ for $4$ kg.

If the person gets $8 \%$ profit, what is the $\text{P:Q}$ ratio (by weight)?

$5:4$
$3:4$
$3:2$
$1:1$

Edited: GATE XE 2025 | Question: 5

Sun, 29 Jun 2025 10:44:06 +0000

A bag contains Violet (V), Yellow (Y), Red (R), and Green (G) balls. On counting them, the following results are obtained:

The sum of Yellow balls and twice the number of Violet balls is $50$.
The sum of Violet and Green balls is $50$.
The sum of Yellow and Red balls is $50$.
The sum of Violet and twice the number of Red balls is $50$.

Which one of the following Pie charts correctly represents the balls in the bag?

Edited: GATE XE 2025 | Question: 3

Sun, 29 Jun 2025 10:13:00 +0000

An electricity utility company charges ₹$7$ per kWh (kilo watt-hour). If a $40$ -watt desk light is left on for $10$ hours each night for $180$ days, what would be the cost of energy consumption? If the desk light is on for $2$ more hours each night for the $180$ days, what would be the percentage-increase in the cost of energy consumption?

₹ $604.8 ; 10 \%$
₹ $504 ; 20 \%$
₹ $604.8 ; 12 \%$
₹ $720 ; 15 \%$

Recategorized: GATE XE 2022 | GA Question: 2

Mon, 05 May 2025 12:41:35 +0000

$x: y: z=\frac{1}{2}: \frac{1}{3}: \frac{1}{4}$.

What is the value of $\frac{x+z-y}{y}$ ?

$0.75$
$1.25$
$2.25$
$3.25$

Recategorized: GATE XE 2022 | GA Question: 7

Mon, 05 May 2025 12:41:24 +0000

In a partnership business the monthly investment by three friends for the first six months is in the ratio $3: 4: 5$. After six months, they had to increase their monthly investments by $10 \%, 15 \%$ and $20 \%$, respectively, of their initial monthly investment. The new investment ratio was kept constant for the next six months.

What is the ratio of their shares in the total profit $\text{(in the same order)}$ at the end of the year such that the share is proportional to their individual total investment over the year?

$22: 23: 24
$22: 33: 50
$33: 46: 60
$63: 86: 110$

Recategorized: GATE XE 2023 | Question: 63

Mon, 05 May 2025 12:19:15 +0000

Recategorized: GATE XE 2023 | GA Question: 3

Mon, 05 May 2025 12:13:39 +0000

A 'frabjous' number is defined as a $3$ digit number with all digits odd, and no two adjacent digits being the same. For example, $137$ is a frabjous number, while $133$ is not. How many such frabjous numbers exist?

$125$
$720$
$60$
$80$

Recategorized: GATE XE 2023 | GA Question: 7

Mon, 05 May 2025 12:13:28 +0000

Ankita has to climb 5 stairs starting at the ground, while respecting the following rules:
1. At any stage, Ankita can move either one or two stairs up.
2. At any stage, Ankita cannot move to a lower step.

Let $F(N)$ denote the number of possible ways in which Ankita can reach the $N^{\text {th }}$ stair. For example, $F(1)=1, F(2)=2, F(3)=3$.

The value of $F(5)$ is

Recategorized: GATE XE 2024 | GA Question: 3

Mon, 05 May 2025 10:51:34 +0000

In an engineering college of $10,000$ students, $1,500$ like neither their core branches nor other branches. The number of students who like their core branches is $1 / 4^{\text {th }}$ of the number of students who like other branches. The number of students who like both their core and other branches is $500$.
The number of students who like their core branches is

$1,800$
$3,500$
$1,600$
$1,500$

Recategorized: GATE XE 2024 | GA Question: 4

Mon, 05 May 2025 10:51:29 +0000

For positive non-zero real variables $x$ and $y$, if
\[
\ln \left(\frac{x+y}{2}\right)=\frac{1}{2}[\ln (x)+\ln (y)]
\]
then, the value of $\frac{x}{y}+\frac{y}{x}$ is

$1$
$1 / 2$
$2$
$4$

Recategorized: GATE XE 2024 | GA Question: 7

Mon, 05 May 2025 10:51:26 +0000

A person sold two different items at the same price. He made $10 \%$ profit in one item, and $10 \%$ loss in the other item. In selling these two items, the person made a total of

$1 \%$ profit
$2 \%$ profit
$1 \%$ loss
$2 \%$ loss