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Q 1 - Which of the following is the 16^{th} term of A.P. 5, 8, 11, 14, 17, ...?

**Answer - A**

**Explanation**

Here a = 5, d = 8 - 5 = 3, n = 16 Using formula T_{n}= a + (n - 1)d T_{16}= 5 + (16 - 1) x 3 = 50

Q 2 - Which of the following term of A.P. 4, 9, 14, 19, 24, ... is 109?

**Answer - C**

**Explanation**

Here a = 4, d = 9 - 4 = 5 Using formula T_{n}= a + (n - 1)d T_{n}= 4 + (n - 1) x 5 = 109 where 109 is the n^{th}term. => 4 + 5n - 5 = 109 => 5n = 109 + 1 => n = 110 / 5 = 22

**Answer - D**

**Explanation**

Here a = 7, d = 13 - 7 = 6, T_{n}= 205 Using formula T_{n}= a + (n - 1)d T_{n}= 7 + (n - 1) x 6 = 205 where 205 is the n^{th}term. => 7 + 6n - 6 = 205 => 6n = 205 - 1 => n = 204 / 6 = 34

Q 4 - Which of the following is the first term of A.P. if 6^{th} term is 12 and 8^{th} term is 22?

**Answer - A**

**Explanation**

Using formula T_{n}= a + (n - 1)d T_{6}= a + (6 - 1)d = 12 ...(i) T_{8}= a + (8 - 1)d = 22 ...(ii) Substract (i) from (ii) => 2d = 10 => d = 5 Using (i) a = 12 - 5d = 12 - 25 = -13

Q 5 - Which of the following is the common difference of A.P. if 6^{th} term is 12 and 8^{th} term is 22?

**Answer - B**

**Explanation**

Using formula T_{n}= a + (n - 1)d T_{6}= a + (6 - 1)d = 12 ...(i) T_{8}= a + (8 - 1)d = 22 ...(ii) Substract (i) from (ii) => 2d = 10 => d = 5

Q 6 - Which of the following is the 16^{th} term of A.P. if 6^{th} term is 12 and 8^{th} term is 22?

**Answer - C**

**Explanation**

Using formula T_{n}= a + (n - 1)d T_{6}= a + (6 - 1)d = 12 ...(i) T_{8}= a + (8 - 1)d = 22 ...(ii) Substract (i) from (ii) => 2d = 10 => d = 5 Using (i) a = 12 - 5d = 12 - 25 = -13 ∴ T_{16}= -13 + (16 - 1) x 5 = 75 - 13 = 62

Q 7 - Which of the following is the sum of first 17 term of A.P. 5, 9, 13, 17, ...?

**Answer - D**

**Explanation**

Here a = 5, d = 9 - 5 = 4, n = 17 Using formula S_{n}= (n/2)[2a + (n - 1)d] S_{17}= (17/2)[2 x 5 + (17 - 1) x 4] = (17/2)(10 + 64) = 17 x 74 / 2 = 629

Q 8 - Which of the following is the sum of the series 2, 5, 8, ..., 182?

**Answer - A**

**Explanation**

Here a = 2, d = 5 - 2 = 3, T^{n}= 182 Using formula T_{n}= a + (n - 1)d a + (n - 1)d = 182 => 2 + (n - 1) x 3 = 182 => 3n = 183 => n = 61. Using formula S_{n}= (n/2)[2a + (n - 1)d] S_{61}= (61/2)[2 x 2 + (61 - 1) x 3] = (61/2)(4 + 180) = 61 x 184 / 2 = 5612

Q 9 - What are the three numbers in A.P. if their sum is 15 and product is 80?

**Answer - B**

**Explanation**

Let've numbers are a - d, a and a + d Then a - d + a + a + d = 15 => 3a = 15 => a = 5 Now (a - d)a(a + d) = 80 => (5 - d) x 5 x (5 + d) = 80 => 25 - d^{2}= 16 => d^{2}= 9 => d = +3 or -3 ∴ numbers are either 2, 5, 8 or 8, 5, 2.

Q 10 - Which of the following is the 9^{th} term of G.P. 3, 6 , 12, 18...?

**Answer - B**

**Explanation**

Here a = 3, r = 6 / 3 = 2, T_{9}= ? Using formula T_{n}= ar^{(n - 1)}T_{9}= 3 x 2^{(9 - 1)}=3 x 2^{8}=3 x 256 =768

Q 11 - Which of the following is the first term of G.P. if 4^{th} term is 54 and 9^{th} term is 13122?

**Answer - A**

**Explanation**

Using formula T_{n}= ar^{(n - 1)}T_{4}= ar^{(4 - 1)}= 54 => ar^{3}= 54 ...(i) T_{9}= ar^{(9 - 1)}= 13122 => ar^{8}= 13122 ...(ii) Dividing (ii) by (i) => r^{5}= 13122 / 54 = 243 = (3)^{5}=> r = 3 Using (i) a x 27 = 54 => a = 2

Q 12 - Which of the following is the common ratio of G.P. if 4^{th} term is 54 and 9^{th} term is 13122?

**Answer - B**

**Explanation**

Using formula T_{n}= ar^{(n - 1)}T_{4}= ar^{(4 - 1)}= 54 => ar^{3}= 54 ...(i) T_{9}= ar^{(9 - 1)}= 13122 => ar^{8}= 13122 ...(ii) Dividing (ii) by (i) => r^{5}= 13122 / 54 = 243 = (3)^{5}=> r = 3

Q 13 - Which of the following is the 6^{th} term of G.P. if 4^{th} term is 54 and 9^{th} term is 13122?

**Answer - C**

**Explanation**

Using formula T_{n}= ar^{(n - 1)}T_{4}= ar^{(4 - 1)}= 54 => ar^{3}= 54 ...(i) T_{9}= ar^{(9 - 1)}= 13122 => ar^{8}= 13122 ...(ii) Dividing (ii) by (i) => r^{5}= 13122 / 54 = 243 = (3)^{5}=> r = 3 Using (i) a x 27 = 54 => a = 2 ∴ T_{6}= ar^{(6 - 1)}= 2 x (3)^{5}= 2 x 243 = 486

Q 14 - Sum of two numbers is 80. If three times of first number is same as five times of the second number, what are the numbers?

**Answer - A**

**Explanation**

Let the numbers are y and 80 - y. Then 3y = 5(80-y) => 8y = 400 ∴ y = 50 and second number = 80 - 50 = 30.

Q 15 - What is the number if its third is greater than its fifth by 16?

**Answer - B**

**Explanation**

Let the number be y. Then (y / 3) - (y / 5) = 16 => 5y - 3y = 16 x 15 = 240 => 2y = 240 ∴ y = 120

Q 16 - What is the largest number among the three consecutive multiples of 3 if there sum is 90?

**Answer - C**

**Explanation**

Let the numbers be 3y , 3y + 3, 3y + 6 Now 3y + 3y + 3 + 3y + 6 = 90 => 9y = 81 => y = 9 => largest number = 3y + 6 = 3 x 9 + 6 = 33

Q 17 - Find is the positive integer if fifteen times of it is less than its square by 16.

**Answer - D**

**Explanation**

Let the positive integer by y. Then y^{2}- 15y = 16 => y^{2}- 15y - 16 = 0 => y^{2}- 16y + y - 16 = 0 => y(y-16) + (y-16) = 0 => (y+1)(y-16)= 0 ∴ y = 16. as -1 is not a positive integer.

Q 18 - Find is the positive integer if twenty-three times of it is more than its square by 63.

**Answer - A**

**Explanation**

Let the positive integer by y. Then 23y - 2y^{2}= 63 => 23y - 2y^{2}- 63 = 0 => 2y^{2}- 23y + 63 = 0 => 2y^{2}- 14y - 9y + 63 = 0 => 2y(y-7) - 9(y-7)= 0 => (2y-9)(y-7)= 0 ∴ y = 7. as 9/2 is not an integer.

Q 19 - Find the smallest of three numbers if numbers are in ratio of 3:2:5 and sum of their squares is 1862.

**Answer - B**

**Explanation**

Let've number as 3y, 2y and 5y. Then 9y^{2}+ 4y^{2}+ 25y^{2}= 1862. => 38y^{2}= 1862 => y^{2}= 1862 / 38 = 49 => y = 7 ∴ smallest number = 2y = 2 x 7 = 14.

Q 20 - Sum of digits of a two digit number is 10. If digits are interchanged, obtained number is 54 less than original number. What is the number?

**Answer - C**

**Explanation**

Let the ten's digit is x and unit digit of number is y. Then x + y = 10 ...(i) (10x + y) - (10y - x) = 54 => 9x - 9y = 54 => x - y = 6 ...(ii) Adding (i) and (ii) 2x = 16 => x = 8 Using (i) y = 10 - x = 2 ∴ number is 82.

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