1
GATE AI 2024
MCQ (Single Correct Answer)
+2
-0

The probability of a boy or a girl being born is $\frac{1}{2}$. For a family having only three children, what is the probability of having two girls and one boy ?

A
$\frac{3}{8}$
B
$\frac{1}{8}$
C
$\frac{1}{4}$
D
$\frac{1}{2}$
2
GATE AI 2024
MCQ (Single Correct Answer)
+2
-0

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

Mutual
found A
Mutul
fund B
Mutul
fund C
Person 1 Rs.
10,000
Rs.
20,000
Rs.
20,000
Person 2 Rs.
20,000
Rs.
15,000
Rs.
15,000

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

A
$7.5 \%$
B
$10 \%$
C
$15 \%$
D
$20 \%$
3
GATE AI 2024
MCQ (Single Correct Answer)
+2
-0

Visualize two identical right circular cones such that one is inverted over the other and they share a common circular base. If a cutting plane passes through the vertices of the assembled cones, what shape does the outer boundary of the resulting cross-section make ?

A
A rhombus
B
A triangle
C
An ellipse
D
A hexagon
4
GATE AI 2025
MCQ (Single Correct Answer)
+2
-0

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 :

A
$2^{-1}$
B
$2^0$
C
$2^3$
D
$2^{15}$