Numerical Ability · General Aptitude · GATE Data Science and Artificial Intelligence
Marks 1
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 ?
The sum of the following infinite series is
$$ 2+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{8}+\frac{1}{9}+\frac{1}{16}+\frac{1}{27}+\ldots $$
In an election, the share of valid votes received by the four candidates $A, B, C$, and $D$ 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 $B$ and $C$ isA $4 \times 4$ digital image has pixel intensities $(U)$ as shown in the figure. The number of pixels with $U \leq 4$ is:
| 0 | 1 | 0 | 2 |
|---|---|---|---|
| 4 | 7 | 3 | 3 |
| 5 | 5 | 4 | 4 |
| 6 | 7 | 3 | 2 |
A rectangle has a length L and a width W . where $\mathrm{L}>\mathrm{W}$. If the width, W , is increased by $10 \%$, which one of the following statements is correct for all values of L and W ?
Marks 2
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 ?
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 $A$ ?
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 ?
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 :
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 Rs $1000(X-0.2)$, what is the average amount (in she has earned per shift in the past 100 shifts?
Note : The figure shown is representative.
