The value of (1001)^{3} is

- a)1003003001
- b)1003033001
- c)100300301
- d)103003001

Correct answer is option 'A'. Can you explain this answer?

SITA DEVI answered • 11 hours ago

The value of (1001)^{3 }= 1001 × 1001 × 1001

= 1003003001

Or,

1001 = 1000 + 1

Cubing

(1001)^{3} = (1000 + 1)^{3}

We know that, (a + b)^{3} = a^{3} + b^{3 }+ 3ab (a + b)

⇒ (1001)^{3} = 1000^{3} + 1 + 3000 × (1000 + 1)

⇒ (1001)^{3 }= 1000000000 + 1 + 3003000

⇒ (1001)^{3 }= 1003003001

= 1003003001

Or,

1001 = 1000 + 1

Cubing

(1001)

We know that, (a + b)

⇒ (1001)

⇒ (1001)

⇒ (1001)

Mushahid Raza asked • 1 minute ago

Form two places, 60 km apart, A and B start towards each other and meet after 6 hours. Had A travelled with 2/3 of his speed and B travelled with double of his speed, they would have met after 5 hours. The speed of A is:

- a)4 km/hr
- b)6 kmph
- c)10 kmph
- d)12 kmph

Correct answer is option 'B'. Can you explain this answer?

SAMEER PATEL answered • 11 hours ago

Let speed of A be a kmph and speed of B be b kmph

Then we have

⇒ a + b = 60/6

⇒ a + b = 10

or 2a + 2b = 20------[1]

also,

⇒ 2/3a + 2b = 60/5 = 12--------------[2]

[1] – [2] leads to

⇒ (4/3)a = 8

a = 6 kmph

Then we have

⇒ a + b = 60/6

⇒ a + b = 10

or 2a + 2b = 20------[1]

also,

⇒ 2/3a + 2b = 60/5 = 12--------------[2]

[1] – [2] leads to

⇒ (4/3)a = 8

a = 6 kmph

SOURAV KUMAR asked • 17 minutes ago

Q. I wish to be a palaeontologist and study the structures of ancient civilisations.

- a)He said that he wish to be a palaeontologist and study the structures of ancient civilisations.
- b)He wished to be a palaeontologist and study the structures of ancient civilisations.
- c)He wishes to be a palaeontologist and study the structures of ancient civilisations.
- d)He said that he wished to be a palaeontologist and study the structures of ancient civilisations.

Correct answer is option 'D'. Can you explain this answer?

If ‘a’ and ‘b’ are two odd positive integers, by which of the following is (a^{4} – b^{4}) always divisible?

- a)3
- b)6
- c)8
- d)12

Correct answer is option 'C'. Can you explain this answer?

VIJAYATA DEVI answered • yesterday

We know that, Summation and Subtraction between two odd integers gives an even integer.

Given, a and b are two odd positive integers.

∴ a + b = 2k_{1} ……(1)

And a – b = 2k_{2 }........(2)

Where, k_{1} and k_{2}are two integers.

(1) + (2) ⇒ 2a = 2(k_{1} + k_{2}) ⇒ a = k_{1} + k_{2}

(1) - (2) ⇒ 2b = 2(k_{1} - k_{2}) ⇒ b = k_{1} - k_{2}

∴ a^{2} + b^{2}

= (k_{1} + k_{2})^{2} + (k_{1} - k_{2})^{2}

= k_{1}^{2} + k_{2}^{2} + 2k_{1}k_{2} + k_{1}^{2} + k_{2}^{2} - 2k_{1}k_{2}

= 2(k_{1}^{2} + k_{2}^{2}) ………..(3)

Given expression is,

a^{4} – b^{4}

= (a^{2} – b^{2})(a^{2} + b^{2})

= (a + b) (a - b)(a^{2} + b^{2})

Putting values from (1), (2) and (3)

= 2k_{1 }× 2k_{2} × 2(k_{1}^{2} + k_{2}^{2})

= 8× k_{1 }× k_{2} × (k_{1}^{2} + k_{2}^{2})

∴ a^{4} – b^{4 }= 8× k_{1 }× k_{2} × (k_{1}^{2} + k_{2}^{2}) is always divisible by 8.

Given, a and b are two odd positive integers.

∴ a + b = 2k

And a – b = 2k

Where, k

(1) + (2) ⇒ 2a = 2(k

(1) - (2) ⇒ 2b = 2(k

∴ a

= (k

= k

= 2(k

Given expression is,

a

= (a

= (a + b) (a - b)(a

Putting values from (1), (2) and (3)

= 2k

= 8× k

∴ a

Jais and his father has an age difference of 35 years now. After 5 years, the sum of their age is 125. What will be the age of Jais and his father after 12 years from now?

- a)51 & 85
- b)40 & 75
- c)52 & 87
- d)45 & 70

Correct answer is option 'C'. Can you explain this answer?

PRIYAM BHARDWAJ answered • yesterday

Let the present age of Jais be X years and the age of his father be Y years.

Presently, Jais and his father has an age difference of 35 years.

→ Y – X = 35. ----------- (1)

After 5 years, the sum of their ages will be 125.

→ (X + 5) + (Y + 5) = 125

→ X + Y + 10 =125

→ Y + X = 115. ----------- (2)

Adding equation (1) and (2),

Y – X + Y + X = 35 + 115

→ 2Y = 150

→ Y = 75.

Similarly, X = Y – 35 = 75 – 35 = 40.

After 12 years, Jais age is 52 (40 + 12) years and his father’s age will be 87 (75 + 12) years.

Hence, the correct answer is 52, 87.

Presently, Jais and his father has an age difference of 35 years.

→ Y – X = 35. ----------- (1)

After 5 years, the sum of their ages will be 125.

→ (X + 5) + (Y + 5) = 125

→ X + Y + 10 =125

→ Y + X = 115. ----------- (2)

Adding equation (1) and (2),

Y – X + Y + X = 35 + 115

→ 2Y = 150

→ Y = 75.

Similarly, X = Y – 35 = 75 – 35 = 40.

After 12 years, Jais age is 52 (40 + 12) years and his father’s age will be 87 (75 + 12) years.

Hence, the correct answer is 52, 87.

Shagun Singh asked • 6 hours ago

Read each sentence to find out whether there is any grammatical error in it. The error, if any will be in one part of the sentence. If there is no error choose option 4 ‘No error’ as the answer.

Q. They also impart him (1)/ with priceless knowledge about (2)/ ethics and morals right from the beginning. (3)/ No error (4)

- a)They also impart him
- b)with priceless knowledge about
- c)ethics and morals right from the beginning
- d)No error

Correct answer is option 'B'. Can you explain this answer?

SOURAV KUMAR asked • 8 hours ago

Q. The rich man (1)/ killed him (2)/ and his own children (3)/ No error (4)

- a)The rich man
- b)killed him
- c)and his own children
- d)No error

Correct answer is option 'B'. Can you explain this answer?

DEEKSHA KUMARI asked • 9 hours ago

The building is not safe and must be _________ down.

- a)pull
- b)pulling
- c)pulled
- d)pulls

Correct answer is option 'C'. Can you explain this answer?

NAVEEN KUMAR asked • 11 hours ago

SOURAV KUMAR asked • 12 hours ago

Q. He sorry (1)/for his misbehavior (2)/ and swore not to do it again (3)

- a)only 1
- b)only 2
- c)both 1 and 3
- d)No error

Correct answer is option 'A'. Can you explain this answer?

SOURAV KUMAR asked • 13 hours ago

Q. If you see a bad habit begin to develop, try to **nip it in the bud** so that it does not become ingrained.

- a)To stop it at an early stage.
- b)Consulted one another
- c)Listen to
- d)Strange

Correct answer is option 'A'. Can you explain this answer?

Biologics Inc. asked • 14 hours ago

एक आदमी 6 किमी उत्तर की तरफ चलता है, तब वह वहाँ से बाएँ मुड़ता है और 4 किमी चलता है.वह पुनः बाएँ मुड़ता है और 6 किमी चलता है.वहां से वह अपने दाएँ ओर मुड़ता है और 6 किमी चलता है.तब वह अपने शुरू आती स्थान से किस दिशा तथा कितने दूरी पर है?

- a)10 किमी तथा पश्चिम
- b)6 किमी तथा दक्षिण
- c)4 किमी तथा दक्षिण
- d)8 किमी तथा पश्चिम

Correct answer is option 'A'. Can you explain this answer?

Abhishek Kamboj asked • 14 hours ago

एक व्यक्ति तीन विभिन्न योजनाओं के तहत 6 वर्ष, 10 वर्ष तथा 12 वर्ष के लिए क्रमश 10%, 12% तथा 15% की दर से धन निवेश करता है यदि व्यक्ति को प्रत्येक योजना का पूर्ण होने पर समान ब्याज धन प्राप्त होता है तो तीनो योजनाओं के तहत निवेश किये गए धन का अनुपात ज्ञात कीजिये?

- a)6:3:2
- b)2:3:4
- c)3:4:6
- d)3:4:2

Correct answer is option 'A'. Can you explain this answer?

SOURAV KUMAR asked • 18 hours ago

The statistical study of changing human populations

- a)demography
- b)lexicography
- c)zoology
- d)petrology

Correct answer is option 'A'. Can you explain this answer?

SOURAV KUMAR asked • yesterday

Q. Success usually (comes down to choosing) the pain of discipline over the ease of distraction

- a)comes up to choosing
- b)comes ahead of choosing
- c)brings about
- d)No improvement

Correct answer is option 'D'. Can you explain this answer?

SOURAV KUMAR asked • yesterday

Meticulous

- a)Intrepid
- b)Ignorant
- c)Scrupulous
- d)Notorious

Correct answer is option 'C'. Can you explain this answer?

SOURAV KUMAR asked • yesterday

Q. He did not know (1)/that the seeds were dry(2)/ when he sow them(3).

- a)only 1
- b)only 2
- c)only 3
- d)Both 1 and 3

Correct answer is option 'C'. Can you explain this answer?

Ashish Goyal asked • yesterday

- a)Judgeing him
- b)prevailed upon the father
- c)and he sentenced his son to death
- d)No error

Correct answer is option 'B'. Can you explain this answer?

Tech Mahe asked • yesterday

Q. As she had visited __quite____ number of__ places, she knew the routes well.

- a)Quite much
- b)Quite a number of
- c)Quite number in
- d)No replacement

Correct answer is option 'B'. Can you explain this answer?

SOURAV KUMAR asked • yesterday

Anju is younger than Preeti. Mohan and Jayant are older than Preeti but younger than Sudha who is of the same age as Sridhar. Hence, Sridhar is__

- a)Older than Anju
- b)Younger than Anju
- c)Younger than Mohan
- d)Younger than Preeti

Correct answer is option 'A'. Can you explain this answer?

SOURAV KUMAR asked • yesterday

Q. I really wish that I could babysit for you tonight, but I'm afraid my **hands are full** at the moment.

- a)To have good prospects in the competition
- b)Very busy
- c)Adopting a threatening attitude
- d)Turn pale

Correct answer is option 'B'. Can you explain this answer?

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