What are the dimensions (length, breadth and height, respectively) of a cuboid with volume 720 cu cm, surface area 484 sq cm and the area of the base 72 sq cm?

Correct Answer: 150

Explanation:

3-digit number divisible by 6 are: 102, 108, 114,... , 996

This is an A.P. in which a = 102, d = 6 and l = 996

Let the number of terms be n. Then t_n = 996.

∴ a + (n - 1)d = 996

⟹ 102 + (n - 1) x 6 = 996

⟹ 6 x (n - 1) = 894

⟹ (n - 1) = 149

⟹ n = 150

∴ Number of terms = 150.

Correct Answer: 34

Explanation:

Given that,
x = ( ?2 + 1 ) / ( ?2 - 1 )
Expanding given equation by multiplying and dividing with ?2 + 1
we will get,
? x = ( ( ?2 + 1 ) / ( ?2 - 1 ) ) x ( ( ?2 + 1 ) / ( ?2 + 1 ) )
? x = ( ?2 + 1 ) x ( ?2 + 1 ) / ( ?2 - 1 ) x ( ?2 + 1 )
? x = ( ?2 + 1 ) ² / ( ?2 - 1 ) x ( ?2 + 1 ) [ Use the formula (A + B)(A - B) = A² - B² ]
? x = ( ?2 + 1 ) ² / ( ?2² - 1² ) [ Use the formula (A + B)² = A² + 2AB + B² ]
? x = ( 2 + 1 + 2?2 ) / (2 - 1)
? x = 3 + 2?2 .....................(i)
and given in question x - y = 4 ?2
? y = x - 4?2
Put the value of x [ from Equation (i) ]
? y = 3 + 2?2 - 4?2
? y = 3 - 2?2
Now, x² + y² = (3 + 2?2)² + (3 - 2?2)
Use the Algebra formula and solve the equation.
[ Use the formula (A + B)² = A² + 2AB + B² ]
[ Use the formula (A - B)² = A² - 2AB + B² ]

? x² + y² = 9 + 8 + 12?2 + 9 + 8 - 12?2
? x² + y² = 34

Correct Answer: 45°

Explanation:

Correct Answer: 1540

Explanation:

(2 ² + 4 ² + 6 ² + ... + 20 ² ) = (1 x 2) ² + (2 x 2) ² + (2 x 3) ² + ... + (2 x 10) ²

= (2² x 1²) + (2² x 2²) + (2² x 3²) + ... + (2² x 10²)

= 2² x [1² + 2² + 3² + ... + 10²]

[	Ref: (12 + 22 + 32 + ... + n2) =	1	n(n + 1)(2n + 1)	]
		6

=	❨	4 x	1	x 10 x 11 x 21	❩
			6

= (4 x 5 x 77)

= 1540.

Correct Answer: 5/16

Explanation:

Given expression can be written as
= 1/(1 x 4) + 1/(4 x 7) + 1/(7 x 10) + 1/(10 x 13) + 1/(13 x 16)
= 1/3{ 3/(1 x 4) + 3/(4 x 7) + 3/(7 x 10) + 3/(10 x 13) + 3/(13 x 16) }
= 1/3{ (4 - 1)/(1 x 4) + (7 - 4)/(4 x 7) + (10 - 7 )/(7 x 10) + (13 - 10)/(10 x 13) + (16 - 13/(13 x 16) }
= 1/3[(1 - 1/4) + (1/4 - 1/7) + (1/7 - 1/10) + (1/10 - 1/13) + (1/13 - 1/16)]
= 1/3[1 - 1/4 + 1/4 - 1/7 + 1/7 - 1/10 + 1/10 - 1/13 + 1/13 - 1/16]
= 1/3[1 - 1/16]
= 1/3[ (16 - 1)/16]
= 1/3[ (15)/16]
= 1 x 15/ 3 x 16
= 5/16

Correct Answer: 4 pm

Explanation:

Correct Answer: 2638800

Explanation:

8796 x 223 + 8796 x 77	= 8796 x (223 + 77)   [Ref: By Distributive Law ]
	= (8796 x 300)
	= 2638800

Correct Answer: -2/a

Explanation:

Given, x + a/x = 1
? x² + a = x .................(i)
? x² - x = -a ................(ii)
Now, ( x² + x + a ) / ( x³ - x²)
( x² + a + x ) / ( x³ - x²)
= ( x + x )/ x(x² - x) [from Eq. (i)]
= 2x/x(-a) [from Eq. (ii) ]
= 2/-a
= -2/a

Correct Answer: 16 4 minutes past 9. 11

Explanation:

Correct Answer: 6

Explanation:

Marking (/) those which are are divisible by 3 by not by 9 and the others by (X), by taking the sum of digits, we get:s

2133 → 9 (X)

2343 → 12 (/)

3474 → 18 (X)

4131 → 9 (X)

5286 → 21 (/)

5340 → 12 (/)

6336 → 18 (X)

7347 → 21 (/)

8115 → 15 (/)

9276 → 24 (/)

Required number of numbers = 6.