These questions are based on the situation given below:
A rectangle PRSU is divided into two smaller rectangles PQTU and QRST by the line TQ. \( PQ = 10 \, \text{cm}, \quad QR = 5 \, \text{cm}, \quad RS = 10 \, \text{cm} \). Points A, B, F are within the rectangle PQTU and, points C, D, E are within the rectangle QRST. The closest pair of points among the pairs \( (A, C), (A, D), (A, E), (F, C), (F, D), (F, E), (B, C), (B, D), (B, E) \) are \( \frac{10}{\sqrt{3}} \, \text{cm} \) apart.
Which of the following statements is necessarily true?
Show Hint
- The closest pair of points among the six given points cannot be (F, C).
- Distance between A and B is greater than distance between F and C.
- The closest pair of points among 6 given points (C,D), (D,E) or (C,E).
- None of the above.
The Correct Option is A
Solution and Explanation
AB \(>\) AF; CD \(>\) DE \(>\) CE, BF = \( 6\sqrt{5} \) cm. Which is the closest pair of points among all 6 given points?
Show Hint
- B, F
- C, D
- A, B
- None of these
The Correct Option is B
Solution and Explanation
Top Questions on Geometry
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Questions Asked in CAT exam
- The passage given below is followed by four summaries. Choose the option that best captures the essence of the passage.
In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
Cultural appropriation occurs when elements from a particular culture are borrowed without proper understanding, respect, or acknowledgment. This leads to the commodification of sacred symbols, the reinforcement of stereotypes, and the erasure of the cultural context from which these elements originated. It is essential to recognize that the impact of cultural appropriation extends beyond the realm of artistic expression, influencing societal perceptions and perpetuating power imbalances.- CAT - 2025
- Para Summary
- The number of distinct integers $n$ for which $\log_{\left(\frac14\right)}(n^2 - 7n + 11)>0$ is:
- CAT - 2025
- Linear Inequalities
- In the set of consecutive odd numbers $\{1, 3, 5, \ldots, 57\}$, there is a number $k$ such that the sum of all the elements less than $k$ is equal to the sum of all the elements greater than $k$. Then, $k$ equals?
- CAT - 2025
- Number Systems
- The number of distinct pairs of integers $(x, y)$ satisfying the inequalities $x>y \ge 3$ and $x + y<14$ is:
- CAT - 2025
- Number Systems
For any natural number $k$, let $a_k = 3^k$. The smallest natural number $m$ for which \[ (a_1)^1 \times (a_2)^2 \times \dots \times (a_{20})^{20} \;<\; a_{21} \times a_{22} \times \dots \times a_{20+m} \] is:
- CAT - 2025
- Linear Inequalities