Math Test & Practice Question For OPSC ASO Exam

Math Test & Practice Question 

Linear & Quadratic Equation 

Some Important Question of Quadratic and Linear equation . Important Question For OPSC ASO And Odisha Govt. Exams . 

1. If the equations 14x + 8y + 5 = 0 and 21x - ky - 7 = 0 have no solution, then the value of k is:

A) 12

B) -12

C)   8

D) -16

2.For a pair of equation to be consistent and dependent, the pair must have: 

A) no solution 

B) unique solution 

C) infinitely many solutions 

D) none of these

3.The value of k, for which the system of equations x + (k + l)y = 5 and (k + l)x + 9y = 8k – 1 has infinitely many solutions is

A) 2

B) 3

C) 4

D) 5

4.If a(a + b + c) = 126, b(a + b + c) = 147 and c(a + b + c) = 168, then value of (a + b + c) = ?

A) 23

B) 21

C) 41

D) 22

5.If (ab)2 + (cb)2 + 2ab2c = 324, then find the value of ab + bc

A) +18

B) -18

C) +22

D) Both 1 & 2

6.If 3^ (x – y) = 27 and 3^(x + y) = 243, then x is equal to:

A. 0

B. 2

C. 4

D. 6

7.What is the relation between X & Y

6x2 – 23√3x + 60 = 0

II. 2y2 + 3 √3y – 15 = 0

A)if x > y

B) if x ≤ y 

C) if x ≥ y

D) if x < y

8.I. 2x2 + 3x – 35 = 0 

II. 4y2 + 10y – 104 = 0 

A)if x > y

B) if x ≤ y 

C) if x ≥ y

D) CND

9.I. 35x2 + 13x – 90 = 0 

II. 7y2 + 24y + 20 = 0 

A)if x > y

B) if x ≤ y 

C) if x ≥ y

D) CND

10.If the roots of ax2 + bx + c = 0 are in the ratio m : n, then

(a) mna² = (m + n) c²
(b) mnb² = (m + n) ac
(c) mn b² = (m + n)² ac
(d) mnb² = (m – n)² ac

11.α And β  are the roots of 4x² + 3x + 7 = 0, then the value of 1/α+1/β is

A) -3/4

B) -3/7

C) 3/7

D) 4/7

12.If the roots of px2 + qx + 2 = 0 are reciprocal of each other, then

A) P = 0
B) p = -2
C) p = ±2
D) p = 2

13. The equation 12x² + 4kx + 3 = 0 has real and equal roots, if
(a) k = ±3
(b) k = ±9
(c) k = 4
(d) k = ±2

14. If the roots of the equations ax² + 2bx + c = 0 and bx² – 2√ac x + b = 0 are simultaneously real, then
(a) b = ac
(b) b2 = ac
(c) a2 = be
(d) c2 = ab

15.2x² – 3x + 5 = 0 , What is the Nature of The Roots ? 

A) The roots are Real and Equal.

B) The two roots are Real and Unequal.

C) No Real roots exist.

D) None of these  

16.The equation 2x² + kx + 3 = 0 has two equal roots, then the value of k is

A) ±√6

B) ± 4

C) ±3√2

D) ±2√6

Complete Solution Of These Questions .