**Q.1)** If (x – 2) and (x + 3) are the factors of the equation x^2 + k1x + k2 = 0, then what are the values of k1 and k2?

1) k1 = 6, k2 = – 1

2) k 1 = 1, k 2 = – 6

3) k 1 = 1, k2 = 6

4) k 1 = – 6, k2 = 1

**Q.2)** If (x – y) = 7, then what is the value of (x – 15)^3 – (y – 8)^3?

1) 0

2) 343

3) 392

4) 2863

**
Q.3) ** If x – y – √18 = –1 and x + y – 3√2 = 1, then what is the value of 12xy(x^2 – y^2)?

1) 0

2) 1

3) 512√2

4) 612√2

**Q.4)** If p/q = r/s = t/u = √5, then what is the value of [(3p^2 + 4r^2 + 5t^2)/(3q^2 + 4s^2 + 5u^2)]?

1) 1/5

2) 5

3) 25

4) 60

**
Q.5)** In triangle ABC, a line is drawn from the vertex A to a point D on BC. If BC = 9 cm and DC = 3 cm, then what is the ratio of the areas of triangle ABD and triangle ADC respectively?

1) 1 : 1

2) 2 : 1

3) 3 : 1

4) 4 : 1

**
Q.6)** PQR is a right angled triangle in which ∠R = 90°. If RS ⊥ PQ, PR = 3 cm and RQ = 4 cm, then what is the value of RS (in cm)?

1) 12/5

2) 36/5

3) 5

4) 2.5

**
Q.7)** In triangle PQR, A is the point of intersection of all the altitudes and B is the point of intersection of all the angle bisectors of the triangle. If ∠PBR = 105°, then what is the value of ∠PAR (in degrees)?

1) 60

2) 100

3) 105

4) 115

**Q.8)** If there are four lines in a plane, then what cannot be the number of points of intersection of these lines?

1) 0

2) 5

3) 4

4) 7

**Q.9)** What is the simplified value of cosec 2A + cot 2A?

1) sec A

2) sec (A /2)

3) cot A

4) cot2 A

**
Q.10) ** If A = 30°, B = 60° and C = 135°, then what is the value of sin^3A + cos^3B + tan^3C – 3sin A cos B tan C?

1) 0

2) 1

3) 8

4) 9