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1. If 2 cos x + 3 cos y = 5 then 3 sin (x + 90) + 10 sin y = ?

2. Find the next number in the the below series

11, 19, 29, 41, _____

11, 19, 29, 41, _____

Explanation:

In the given series, 11, 19, 29, 41 ,

Consecutive numbers increase by 8 ,10 ,12.

Following the same pattern, the next number should increase by 14.

When we add 14 to the last number (i.e 41) we get 14+41=55

Consecutive numbers increase by 8 ,10 ,12.

Following the same pattern, the next number should increase by 14.

When we add 14 to the last number (i.e 41) we get 14+41=55

3. What is 14.5% of 4000?

Explanation:

Given

14.5% of 4000

= (14.5 /100 ) x 4000

= 0.145 x 4000

= 580

14.5% of 4000

= (14.5 /100 ) x 4000

= 0.145 x 4000

= 580

4. Find the approximate value for the expression

55.002 - 65.003 / 45.998 * 25.999 + 10.001

55.002 - 65.003 / 45.998 * 25.999 + 10.001

Explanation:

Given Question is 55.002 - 65.003 / 45.998 * 25.999 + 10.001

when we apply BODMAS RULE to the above question,

Step - 1 : (Bracket Of Division) 55 - ( 65 / 46 ) * 26 + 10 = 55 - 1.413 * 26 + 10

Step - 2 : 55 - ( 1.413 * 26 ) + 10 = 55 - 36.738 + 10 = 28.26 = (approx) 28

when we apply BODMAS RULE to the above question,

Step - 1 : (Bracket Of Division) 55 - ( 65 / 46 ) * 26 + 10 = 55 - 1.413 * 26 + 10

Step - 2 : 55 - ( 1.413 * 26 ) + 10 = 55 - 36.738 + 10 = 28.26 = (approx) 28

5. Find the next number in the the below series

6, 26, 53, 87, _____

6, 26, 53, 87, _____

Explanation:

In the given series, 6, 26, 53, 87 ,

Consecutive numbers increase by 20 ,27 ,34.

Following the same pattern, the next number should increase by 41.

When we add 41 to the last number (i.e 87) we get 41+87=128

Consecutive numbers increase by 20 ,27 ,34.

Following the same pattern, the next number should increase by 41.

When we add 41 to the last number (i.e 87) we get 41+87=128

6. Which one of the following is not a prime number?

Explanation:

91 is divisible by 7. So, it is not a prime number.

7. Find the length of the diagonal of a cuboid 12m long, 9 m broad and 8 m high.

Explanation:

Let l, b and h be the length, breadth and height of the cuboid respectively.

Diagonal = sqrt(lxl + bxb + hxh) = sqrt(12 x 12 + 9 x 9 + 8 x 8) = sqrt(144+81+64)

Diagonal = sqrt(289) = 17

Diagonal = sqrt(lxl + bxb + hxh) = sqrt(12 x 12 + 9 x 9 + 8 x 8) = sqrt(144+81+64)

Diagonal = sqrt(289) = 17

8. If a:b = 1 : 2 and b : c = 3 : 2 then a : b : c =

Explanation:

a : b = 1 : 2

=> Mulitply by "3" on both sides

=> a x 3 : b x 3 =1 x 3 : 2 x 3

=> a : b= **3 : 6**

b : c = 3 : 2

=> Mulitply by "2" on both sides

=>b x 2 : c x 2 = 3 x 2: 2 x 2

=> b : c =**6 : 4**

Now** a : b : c =3 : 6 : 4**

9. A sum of money doubles itself in 8 years. What is the rate of interest?

Explanation:

Let the principal be Rs. p, rate of interest be r and time given, t = 8.

Amount = 2p (since the money gets doubled), interest earned = p

Which means S.I = p, we know that S.I = (p x t x r) / 100

p = (p x 8 x r) / 100 => 8r/100 = 1 => r=100/8 => r = 12.5

The rate of interest is 12.5%

Amount = 2p (since the money gets doubled), interest earned = p

Which means S.I = p, we know that S.I = (p x t x r) / 100

p = (p x 8 x r) / 100 => 8r/100 = 1 => r=100/8 => r = 12.5

The rate of interest is 12.5%

10. Vinay and Vicky can complete a piece of work in 30 and 15 days repectively by working alone. After how many days 80% of the work would have got completed?

Explanation:

Let the time taken by Vinay = A days = 30 days

the time taken by Vicky = B days = 15 days

**Vinay + Vicky together can complete 100 % of the work in:**

=>**1/(A + B) = (1/A) + (1/B)**

=> 1 / (A + B) = (1 / 30) + (1 / 15)

=> 1 / (A + B) = (15 + 30) / (30 * 15)

=> 1 / (A + B) = 45 / 450

Taking reciprocal on both sides

A + B = 450/45

**A + B = 10 days**

Thus 100% of the work is completed in 10 days,

**80% of the work is completed in {(10 / 100%) * 80%} days = 8 days**

the time taken by Vicky = B days = 15 days

=>

=> 1 / (A + B) = (1 / 30) + (1 / 15)

=> 1 / (A + B) = (15 + 30) / (30 * 15)

=> 1 / (A + B) = 45 / 450

Taking reciprocal on both sides

A + B = 450/45

Thus 100% of the work is completed in 10 days,

11. Can you find the answer for the below equation

69 * 272 - 264 / 271 + 266

69 * 272 - 264 / 271 + 266

Explanation:

Given Question is 69 * 272 - 264 / 271 + 266

when we apply BODMAS RULE to the above question, we get (Bracket Of Division) 69 * 272 - ( 264/ 271 ) + 266 = 69 * 272 - 0.97+ 266 = 19033.03

when we apply BODMAS RULE to the above question, we get (Bracket Of Division) 69 * 272 - ( 264/ 271 ) + 266 = 69 * 272 - 0.97+ 266 = 19033.03

12. Find the average of first 30 multiples of 8

Explanation:

Average of first 30 natural numbers =

= 31 / 2

=

Average of first 30 multiples of 8 = ( Average of first 30 natural numbers ) * 8

= 15.5 * 8

=

The average of first 30 multiples of 8 = 124.

13. The area of a trapezium is 1586 cm² and the distance between its parallel sides is 26 cm. If one of the parallel sides is 84 cm, find the other.

14. Two liquids A and B are mixed together in the ratio 3 : 5. The average cost of liquid B is Rs 20 per liter and the average cost of the mixture is Rs. 15 per liter, then find the average cost of liquid A per liter.

Explanation:

Given, Ratio of liquids A and B =3 : 5

Average cost of liquid B per liter = Rs. 20

Average cost of mixture per liter = Rs. 15

Let the**Average cost of liquid A** per liter = **Rs. x**

According to alligation equation,

(20 - 15)/(15-x) = 3/5

=> 5 /(15-x) = 3/5

=> 5 * 5 = 3 *(15-x)

=> 25 = 45 - 3x

=> 3x = 45 - 25

=> 3x = 20

=>**x = 6.7**

Therefore,**Average cost of liquid A** **per liter** =** **Rs. x = **Rs. 6.7**

Average cost of liquid B per liter = Rs. 20

Average cost of mixture per liter = Rs. 15

Let the

According to alligation equation,

(20 - 15)/(15-x) = 3/5

=> 5 /(15-x) = 3/5

=> 5 * 5 = 3 *(15-x)

=> 25 = 45 - 3x

=> 3x = 45 - 25

=> 3x = 20

=>

Therefore,

15. The average age of a group of 10 students was 26. The average age increased by 1 year when two new students joined the group. What is the average age of the two new students who joined the group?

Explanation:

The average age of a group of 10 students is 26.

Therefore, the sum of the ages of all 10 of them

= 10 * 26

= 260

When two students joins the group, the average increase by 1.

New Average = 27

Now there are 12 students.

Therefore, sum of all the ages of 12 students

= 12 *27

= 324

Therefore, the sum of the ages of two students who joined

= 324 - 260

= 64

And the**average age** of these** two students**

=64 / 2

=**32.**

Therefore, the sum of the ages of all 10 of them

= 10 * 26

= 260

When two students joins the group, the average increase by 1.

New Average = 27

Now there are 12 students.

Therefore, sum of all the ages of 12 students

= 12 *27

= 324

Therefore, the sum of the ages of two students who joined

= 324 - 260

= 64

And the

=64 / 2

=

16. If sec x = 9x + 1 / 36 x, then evaluate sec x + tan x

17. The sum of the linear factors of x^2 - 10 x+ 21 = 0 is

Explanation:

x^2 - 10x + 21

= x^2 - 2 (5x) + 21

= x^2 - 2 (5) x + 21

= x^2 - 2(5) x + 5^2 + 21 - 25

=x^2 -2(5)(x) + 5^2 - 4

= (x-5)^2 - 4

= (x-5)^2 - 2^2

= ( (x-5) - 2 ) x ((x-5) + 2)

= (x - 5 - 2) x (x - 5 + 2)

=(x-7) x (x-3)

The two linear factors are x - 3 and x - 7

Sum is x - 3 + x - 7 = 2x - 10 = 2(x-5)

= x^2 - 2 (5x) + 21

= x^2 - 2 (5) x + 21

= x^2 - 2(5) x + 5^2 + 21 - 25

=x^2 -2(5)(x) + 5^2 - 4

= (x-5)^2 - 4

= (x-5)^2 - 2^2

= ( (x-5) - 2 ) x ((x-5) + 2)

= (x - 5 - 2) x (x - 5 + 2)

=(x-7) x (x-3)

The two linear factors are x - 3 and x - 7

Sum is x - 3 + x - 7 = 2x - 10 = 2(x-5)

18. In an arithmetic progression the first term is 9 and its common difference is 6. If the general term is (a_n) , find a_24 - a_12.

Explanation:

Given a = 9 and common difference = 6.
General Term a_n = a +(n-1)d
a_n = 9 + 6(n-1) = 6n + 3
a_24 = 144 + 3=147
a_12 = 72 + 3 = 75
a_24 - a_12 = 72

19. 3x^2 - 10x + 8 = 0,

3y^2 + 8y - 16 = 0

3y^2 + 8y - 16 = 0

Explanation:

3x^2 - 10x + 8 = 0

=> Sum of roots = -10 => [- 6 - 4 = -10]

=> Product of roots = 24 => [-6 * -4 = 24]

Thus, the roots are -6, -4

=>3x^2 - 6x - 4x + 8 = 0

=> 3x(x - 2) - 4(x - 2) = 0

=>(x - 2) (3x - 4) = 0

=> x = 2, 4/3

=>**x = 2, 1.33**

Given, 3y^2 + 8y - 16 = 0

=> Sum of roots = 8 => [12 - 4 = 8]

=> Product of roots = -48 => [12 * -4 = -48]

Thus, the roots are 12, -4

=> 3y^2 + 12y - 4y - 16 = 0

=> 3y(y + 4) -4(y + 4) = 0

=>(y + 4) (3y -4) = 0

=> y = -4, 4/3

=>**y = -4, 1.33**

Put on number line

-4, 1.33, 2

Thus,** X >= Y**

=> Sum of roots = -10 => [- 6 - 4 = -10]

=> Product of roots = 24 => [-6 * -4 = 24]

Thus, the roots are -6, -4

=>3x^2 - 6x - 4x + 8 = 0

=> 3x(x - 2) - 4(x - 2) = 0

=>(x - 2) (3x - 4) = 0

=> x = 2, 4/3

=>

Given, 3y^2 + 8y - 16 = 0

=> Sum of roots = 8 => [12 - 4 = 8]

=> Product of roots = -48 => [12 * -4 = -48]

Thus, the roots are 12, -4

=> 3y^2 + 12y - 4y - 16 = 0

=> 3y(y + 4) -4(y + 4) = 0

=>(y + 4) (3y -4) = 0

=> y = -4, 4/3

=>

Put on number line

-4, 1.33, 2

Thus,

20. Two concentric circles have radius 12 and 10 cm. Find the area between these circles.

21. A farmer has a square shaped field whose sides measure 40m each. In the middle of his field, he has a Square shaped room (each side measuring 34m) Find the area of cultivable land?

Explanation:

Let the side of bigger Square be x and side of smaller square be y. Then area between them = x^2 - y ^2

Substituting x = 40m and y = 34 we get the required cultivable land = 40^2 - 34^2 = (40+34) x (40-34) (using a^2-b^2 formulae)

= (74) x (6) = 444

Substituting x = 40m and y = 34 we get the required cultivable land = 40^2 - 34^2 = (40+34) x (40-34) (using a^2-b^2 formulae)

= (74) x (6) = 444

22. Can you find the answer for the below equation

85 / 176 + 175 * 174 - 171

85 / 176 + 175 * 174 - 171

Explanation:

Given Question is 85 / 176 + 175 * 174 - 171

when we apply BODMAS RULE to the above question, we get (Bracket Of Division) ( 85 / 176 ) + 175 * 174 - 171 = 0.48+175*174-171 = 30279.48

when we apply BODMAS RULE to the above question, we get (Bracket Of Division) ( 85 / 176 ) + 175 * 174 - 171 = 0.48+175*174-171 = 30279.48

23. Can you find the answer for the below equation

68 / 177 * 167 + 172 - 163

68 / 177 * 167 + 172 - 163

Explanation:

Given Question is 68 / 177 * 167 + 172 - 163

when we apply BODMAS RULE to the above question, we get (Bracket Of Division) ( 68 / 177 ) * 167 + 172 - 163 = 0.38*167+172-163 = 73.16

when we apply BODMAS RULE to the above question, we get (Bracket Of Division) ( 68 / 177 ) * 167 + 172 - 163 = 0.38*167+172-163 = 73.16

24. Given that x + 1/x = 3 then evaluate x^3 + 1/x^3 = ?

25. Find the next number in the the below series

24, 40, 57, 75, _____

24, 40, 57, 75, _____

Explanation:

In the given series, 24, 40, 57, 75 ,

Consecutive numbers increase by 16 ,17 ,18.

Following the same pattern, the next number should increase by 19.

When we add 19 to the last number (i.e 75) we get 19+75=94

Consecutive numbers increase by 16 ,17 ,18.

Following the same pattern, the next number should increase by 19.

When we add 19 to the last number (i.e 75) we get 19+75=94

26. Find the next number in the the below series

12, 39, 68, 99, _____

12, 39, 68, 99, _____

Explanation:

In the given series, 12, 39, 68, 99 ,

Consecutive numbers increase by 27 ,29 ,31.

Following the same pattern, the next number should increase by 33.

When we add 33 to the last number (i.e 99) we get 33+99=132

Consecutive numbers increase by 27 ,29 ,31.

Following the same pattern, the next number should increase by 33.

When we add 33 to the last number (i.e 99) we get 33+99=132

27. Can you find the value for the expression:

5 + 55 + 555+ 5555 + 55555

5 + 55 + 555+ 5555 + 55555

Explanation:

Given expression is

5 + 55 + 555+ 5555 + 55555

By adding each and every number together we get,

= 60 + 555 + 5555 + 55555

= 615 + 5555 + 55555

= 6170 + 55555

=**61725**

5 + 55 + 555+ 5555 + 55555

By adding each and every number together we get,

= 60 + 555 + 5555 + 55555

= 615 + 5555 + 55555

= 6170 + 55555

=

28. A rectangular Table has a length of 30 units, and breadth of 23 units. Compute its perimeter ?

Explanation:

Perimeter of Rectangle = 2 x (length + breadth)

= 2 x (30 + 23) = 106

= 2 x (30 + 23) = 106

29. If the number 481 * 673 is completely divisible by 9, then the smallest whole number in place of * will be:

Explanation:

Sum of digits = (4 + 8 + 1 + x + 6 + 7 + 3) = (29 + x), which must be divisible by 9.
x = 7

30. In an arithmetic progression the first term is 7 and its common difference is 6. If the general term is (a_{n}) , find a_{21} - a_{16}

Explanation:

Given a = 7 and common difference = 6.

General Term a_{n} = a +(n-1)d

=> a_{n} = 7 + 6(n-1) = 6n + 1

a_{21} = 126 + 1=127

a_{16} = 96 + 1 = 97

**a**_{21} - a_{16} = 30

General Term a

=> a

a

a