**Q.1)** In the given figure, ABCD is a trapezium in which AB is the diameter of semicircle of radius 6 m. If AD = BC = 4 m, then find the length of CD.

(1) 6(2/3) m

(2) 9(1/3) m

(3) 8(3/4) m

(4) 11(1/9) m

**Q.2)** In the given figure, if measure of ∠E and ∠ F are 50° and 60° respectively, then find the measure of ∠ A.

(1) 35°

(2) 40°

(3) 30°

(4) 70°

**Q.3)** If X^2 – √3X –1 = 0 , then find the value of X^6 – (1/X^6)

1) 30√3

2) 30√7

3) 21√21

4) 24√21

**Q.4)** 17% of a number exceeds 6% of the same number is 77. The one-fourth of that number is:

1) 700

2) 175

3) 185

4) 200

**Q.5)** Simplify: (6+4√2)/(34+24√2)

1) 3+2√2

2) 3-2√2

3) 2+2√3

4) 2-2√3

**Q.6)** A number of boys raised ₹ 3,200 for a relief. If each boys gives the double coins of ₹ 1 as there was the number of number of boys ?

1) 400

2) 80

3) 40

4) 20

**Q.7) ** Pappu and Chandan are 1 km apart. They both see a balloon flying in the sky making an angle of 60º and 45º respectively. If the balloon is between them, then the height of the balloon is

1) 500(√3-1) mtr

2) 500√3(√3-1) mtr

3) 1000(√3-1) mtr

4) 500√3(√3+1) mtr

**Q.8)** If cosec A + cot A = 7 then find the value of tan A:

1) (7/24)

2) (7/8)

3) (7/16)

4) 16/63

**Q.9)** Find the value of 1-sin^2A – sec A:

1) (1+sec A) ( cos^2A +1-cos A)

2) (1-sec A) ( cos^2A + 1 + cos A)

3) (1+ sec A) (cos^2 A + 1 – cos A)

4) (1- sec A) ( cos^2 A + 1 – cos A)

**Q.10)** A work could get completed in 50 days by some persons. However, due to the absence of 5 persons, it was completed in 55 days. The original number of persons was–

1) 50

2) 55

3) 60

4) 45