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
