1 red, 3 white, 2 blue flags in a line, no adjacent same colour, ends different. How many arrangements?
Show Hint
- 6
- 4
- 10
- 2
The Correct Option is B
Solution and Explanation
Top Questions on Number System
Find the residue of \( (67 + 89 + 90 + 87) \pmod{11} \):
- CUET (PG) - 2025
- Mathematics
- Number System
Match List-I with List-II and choose the correct option:
LIST-I (Infinite Series) LIST-II (Nature of Series) (A) \( 12 - 7 - 3 - 2 + 12 - 7 - 3 - 2 + \dots \) (II) oscillatory (B) \( 1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \dots \) (IV) conditionally convergent (C) \( \sum_{n=0}^{\infty} \left( (n^3+1)^{1/3} - n \right) \) (I) convergent (D) \( \sum_{n=1}^{\infty} \frac{1}{n \left( 1 + \frac{1}{n} \right)} \) (III) divergent
Choose the correct answer from the options given below:- CUET (PG) - 2025
- Mathematics
- Number System
Match List-I with List-II and choose the correct option:
LIST-I (Set) LIST-II (Supremum/Infimum) (A) \( S = \{2, 3, 5, 10\} \) (III) Sup S = 10, Inf S = 2 (B) \( S = (1, 2] \cup [3, 8) \) (IV) Sup S = 8, Inf S = 1 (C) \( S = \{2, 2^2, 2^3, \dots, 2^n, \dots\} \) (II) Sup S = 5, Inf S = -5 (D) \( S = \{x \in \mathbb{Z} : x^2 \le 25\} \) (I) Inf S = 2
Choose the correct answer from the options given below:- CUET (PG) - 2025
- Mathematics
- Number System
Which of the following are correct?
A. A set \( S = \{(x, y) \mid xy \leq 1 : x, y \in \mathbb{R}\} \) is a convex set.
B. A set \( S = \{(x, y) \mid x^2 + 4y^2 \leq 12 : x, y \in \mathbb{R}\} \) is a convex set.
C. A set \( S = \{(x, y) \mid y^2 - 4x \leq 0 : x, y \in \mathbb{R}\} \) is a convex set.
D. A set \( S = \{(x, y) \mid x^2 + 4y^2 \geq 12 : x, y \in \mathbb{R}\} \) is a convex set.
- CUET (PG) - 2025
- Mathematics
- Number System
If p is a prime number and a group G is of the order p2, then G is:
- CUET (PG) - 2025
- Mathematics
- Number System
Questions Asked in CAT exam
- Let $x$, $y$, and $z$ be real numbers satisfying
\(4(x^2 + y^2 + z^2) = a,\)
\(4(x - y - z) = 3 + a.\)
Then $a$ equals ?- CAT - 2024
- Algebra
- The sum of all real values of $k$ for which $(\frac{1}{8})^k \times (\frac{1}{32768})^{\frac{4}{3}} = \frac{1}{8} \times (\frac{1}{32768})^{\frac{k}{3}}$ is
- CAT - 2024
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- ABCD is a rectangle with sides AB = 56 cm and BC = 45 cm, and E is the midpoint of side CD. Then, the length, in cm, of radius of incircle of \(\triangle ADE\) is
- CAT - 2024
- Mensuration
When $10^{100}$ is divided by 7, the remainder is ?
- CAT - 2024
- Basics of Numbers
- If $(a + b\sqrt{n})$ is the positive square root of $(29 - 12\sqrt{5})$, where $a$ and $b$ are integers, and $n$ is a natural number, then the maximum possible value of $(a + b + n)$ is ?
- CAT - 2024
- Algebra