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Cartesian Product

If 3 × 5 × 7 ...

Question

If 3 × 5 × 7 + a, 5 × 7 × 11 + b and 7 × 11 × 13 + c are composite numbers, where a, b, c are distinct prime numbers, then the number of possible pairs of (a, b, c) is

यदि 3 × 5 × 7 + a, 5 × 7 × 11 + b तथा 7 × 11 × 13 + c संयुक्त संख्याएं हैं, जहाँ a, b, c भिन्न अभाज्य संख्याएं हैं, तब (a, b, c) के संभावित युग्मों की संख्या हैं

A

12

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B

15

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C

14

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D

13

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Solution

The correct option is C 14
Solution

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Similar questions

Q. In a quadratic equation ax² + bx + c = 0, where a, b and c are distinct natural numbers less than 6. If quadratic equation has real and distinct roots, then total number of possible pairs of (a, b, c) is

किसी द्विघात समीकरण ax² + bx + c = 0 में, जहाँ a, b व c भिन्न प्राकृत संख्याएं हैं जो 6 से कम हैं। यदि द्विघात समीकरण के मूल वास्तविक एवं भिन्न हैं, तब (a, b, c) के संभावित युग्मों की कुल संख्या है

Q. If 0. ABC ABC ABC ……..

= \frac{P}{Q},

where A, B and C are distinct positive real numbers and P, Q are prime numbers, then sum of all possible values of P is

यदि 0. ABC ABC ABC ……..

= \frac{P}{Q},

जहाँ A, B व C भिन्न धनात्मक वास्तविक संख्याएँ हैं तथा P, Q अभाज्य संख्याएँ हैं, तब P के सभी संभावित मानों का योगफल है

\sqrt{5 + \sqrt{16 + 6 \sqrt{7 + 4 \sqrt{3}}}} = x \sqrt{a} + y \sqrt{b} + z \sqrt{c},

where a < b < c (a, b, c are integers, b is smallest odd prime number and x, y, z are non-negative rational numbers), then

(\frac{x}{y + z})

is equal to

यदि

\sqrt{5 + \sqrt{16 + 6 \sqrt{7 + 4 \sqrt{3}}}} = x \sqrt{a} + y \sqrt{b} + z \sqrt{c},

जहाँ a < b < c (a, b, c पूर्णांक हैं, b सबसे छोटी विषम अभाज्य संख्या है तथा x, y, z अ-ऋणात्मक परिमेय संख्याएँ हैं), तब

(\frac{x}{y + z})

बराबर है

If $\frac{3 + \sqrt{5}}{2 \sqrt{5} + 3} = a + b \sqrt{5}$ , then the values of irrational numbers $a$ and $b$ are

(\frac{1}{1 + 2 i} + \frac{3}{1 - i}) (\frac{3 - 2 i}{1 + 3 i})

is reducible to

a + i b

, then values of

a

b

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