**Question 1 :**

Find the maximum value of quadratic function

n ^{2} - 6n - 55

(A) -64 (B) 55 (C) -48

**Solution :**

We have a formula to find the maximum value of a quadratic equation.

x-coordinate of maximum value = -b/2a

a = 1, b = -6 and c = -55

-b/2a = - (-6)/2(1)

= 6/2

= 3

Maximum value = f(3)

= (3)^{2} - 6(3) - 55

= 9 - 18 - 55

= 9 - 73

= -64

Hence the maximum value is -64.

**Question 2 :**

Find a rational number between 3/4 and 4/5

(A) 21/40 (B) 31/40 (C) 41/40

**Solution :**

Let a = 3/4 and b = 4/5

Formula to find rational number between two rational numbers

= (1/2)(a + b)

= (1/2) (3/4 + 4/5)

L.C.M of 4 and 5 is 20.

= (1/2) (15/20 + 16/20)

= (1/2) [(15 + 16)/20]

= (1/2) (31/20)

= 31/40

Hence the required rational number between the given rational numbers is 31/40.

**Question 3 :**

Simplify (1 - (1/2)) + (3/4 - 1/4)

(A) 1 (B) 0 (C) 2

**Solution :**

= (1 - (1/2)) + (3/4 - 1/4)

= (2-1)/2 + [(3 - 1)/4]

= 1/2 + [(3 - 1)/4]

= (1/2) + (2/4)

= (2 + 2)/4

= 1

Hence the answer is 1.

**Question 4 :**

Cube root of 125/256

(A) 5/4 (B) 25/4 (C) 5/6

**Solution :**

∛(125/256)

To find cube root of the given fraction, we have to decompose both numerator and denominators into prime factors.

= ∛(5⋅ 5 ⋅ 5) / (2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 3 ⋅ 3)

We may group them as triples.

= 5/6

**Question 5 :**

Find the smallest number by which 81 must be divided to obtain a perfect cube.

(A) 2 (B) 3 (C) 4

To find the number required to divide 81 such that the quotient is a perfect cube, we have to decompose 81 into prime factors. = ∛81 = ∛(3⋅3⋅3⋅3) When we group the prime factors inside the cube root as triples, we left over with 3. That is 3. So, 3 is the smallest number required to divide 81 so that the quotient is a perfect cube. |

**Question 6 :**

Find the fifth term of the sequence whose second term is 8 and third term is 14.

**Solution :**

Second term = 8

Third term = 14

General term of the arithmetic sequence :

a _{n} = a + (n - 1) d

Second term (a + d) = 8 ---(1)

Third term (a + 2d) = 14 ----(2)

(1) - (2)

a + d - (a + 2d) = 8 - 14

-d = -6

d = 6

By applying the value of d in (1), we get the value of a

a + 6 = 8

a = 8 - 6

a = 2

Fifth term = a + 4d

= 2 + 4(6)

= 2 + 24

= 26

So, the fifth term is 26.

**Question 7 :**

Find AC when AB = 15 cm, AD = 10 cm, AE = 8 cm

(A) 12 cm (B) 10 cm (C) 13 cm

**Solution :**

AB = AD + DB

15 = 10 + DB

DB = 15 - 10

DB = 5

10/5 = 8/EC

EC = 8/2 = 4

AC = AE + EC

AC = 8 + 4 = 12

So, length of AC is 12 cm.

**Question 8 :**

Angle ABC measures 250°, find the measure of minor of arc AC.

(A) 150° (B) 110° (C) 140°

**Solution :**

Measure of minor arc = 360 - 250

= 110°

**Question 9 :**

Find the mean of all odd numbers between 80 and 88.

(A) 84 (B) 30 (C) 62

**Solution :**

Odd numbers between 80 and 88 are

81, 83, 85, 87

Mean of above numbers = (81 + 83 + 85 + 87) / 4

= 336/4

= 84

**Question 10 :**

The number of times a particular observation occur in a data is called its __________

(A) Frequency (B) Mean (C) Median

**Solution :**

The number of times a particular observation occur in a data is called its frequency.

(1) 15 (2) 260 days (3) 279 km (4) 70 meter (5) 45° and 60° |
(6) 12% (7) 12 cm (8) 110° (9) 84 (10) Frequency |

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