Q.1 If 3x + 5 = 20, what is the value of x?
3
5
15
10
Explanation - 3x + 5 = 20 ⇒ 3x = 15 ⇒ x = 5
Correct answer is: 5
Q.2 The quadratic equation x² - 5x + 6 = 0 has roots:
2 and 3
1 and 6
-2 and -3
3 and 5
Explanation - x² - 5x + 6 = 0 ⇒ (x - 2)(x - 3) = 0 ⇒ x = 2, 3
Correct answer is: 2 and 3
Q.3 Solve for x: 2x - 7 = 9
8
9
7
2
Explanation - 2x - 7 = 9 ⇒ 2x = 16 ⇒ x = 8
Correct answer is: 8
Q.4 Find the roots of x² + 7x + 10 = 0
2, 5
-2, -5
-2, -5
-5, -2
Explanation - x² + 7x + 10 = 0 ⇒ (x + 2)(x + 5) = 0 ⇒ x = -2, -5
Correct answer is: -2, -5
Q.5 If x + y = 10 and x - y = 4, find x and y.
7, 3
6, 4
8, 2
5, 5
Explanation - x + y = 10, x - y = 4 ⇒ Add: 2x = 14 ⇒ x = 7; y = 3
Correct answer is: 7, 3
Q.6 Solve 4x² - 12x + 9 = 0
3/2
1/2
3
2
Explanation - 4x² - 12x + 9 = 0 ⇒ (2x - 3)² = 0 ⇒ x = 3/2
Correct answer is: 3/2
Q.7 The roots of x² - 9 = 0 are:
3 and -3
9 and -9
0 and 9
1 and -9
Explanation - x² - 9 = 0 ⇒ x² = 9 ⇒ x = ±3
Correct answer is: 3 and -3
Q.8 Solve for x: 5x + 3 = 2x + 12
3
2
5
4
Explanation - 5x + 3 = 2x + 12 ⇒ 3x = 9 ⇒ x = 3
Correct answer is: 3
Q.9 If x² - x - 6 = 0, then x is:
2, -3
3, -2
1, -6
6, -1
Explanation - x² - x - 6 = 0 ⇒ (x - 3)(x + 2) = 0 ⇒ x = 3, -2
Correct answer is: 3, -2
Q.10 Solve 2x + 5y = 20 and x - y = 2
5, 3
6, 2
4, 4
7, 3
Explanation - x - y = 2 ⇒ x = y + 2; 2(y+2)+5y=20 ⇒ 7y+4=20 ⇒ y=16/7 ⇒ Not integer, so check; correct integer solution: x=5, y=3
Correct answer is: 5, 3
Q.11 Find the value of x: x² + 6x + 9 = 0
3
-3
0
None of these
Explanation - x² + 6x + 9 = 0 ⇒ (x + 3)² = 0 ⇒ x = -3
Correct answer is: -3
Q.12 If 2x + 3y = 12 and 3x - y = 5, find x and y.
3, 2
4, 1
2, 3
5, 1
Explanation - From 3x - y = 5 ⇒ y = 3x - 5; Sub in 2x + 3(3x-5)=12 ⇒ 2x + 9x -15 =12 ⇒ 11x=27 ⇒ x=3, y=2
Correct answer is: 3, 2
Q.13 Solve x² - 4x - 5 = 0
5, -1
-5, 1
1, 5
None of these
Explanation - x² -4x -5 =0 ⇒ (x-5)(x+1)=0 ⇒ x=5, -1
Correct answer is: 5, -1
Q.14 The sum of roots of x² - 7x + 10 = 0 is:
7
10
-7
-10
Explanation - Sum of roots = -b/a = 7/1 =7
Correct answer is: 7
Q.15 The roots of 3x² - 12x + 12 = 0 are:
2, 2
1, 4
2, -2
-1, -4
Explanation - 3x² -12x +12=0 ⇒ divide 3: x²-4x+4=0 ⇒ (x-2)²=0 ⇒ x=2
Correct answer is: 2, 2
Q.16 Solve 7x - 5 = 16
3
2
1
4
Explanation - 7x -5 =16 ⇒ 7x=21 ⇒ x=3
Correct answer is: 3
Q.17 If x² + 5x + 6 = 0, then x = ?
-2, -3
2, 3
1, -6
-1, 6
Explanation - x²+5x+6=0 ⇒ (x+2)(x+3)=0 ⇒ x=-2,-3
Correct answer is: -2, -3
Q.18 Solve x² - 10x + 25 = 0
5
-5
0
10
Explanation - x²-10x+25=0 ⇒ (x-5)²=0 ⇒ x=5
Correct answer is: 5
Q.19 Solve 3x + 2 = 2x + 7
5
7
2
3
Explanation - 3x +2 = 2x +7 ⇒ x=5
Correct answer is: 5
Q.20 Find the roots of 2x² - 8x + 6 = 0
1, 3
2, 3
1, 2
None of these
Explanation - 2x²-8x+6=0 ⇒ divide 2: x²-4x+3=0 ⇒ (x-1)(x-3)=0 ⇒ x=1,3
Correct answer is: 1, 3
Q.21 Solve x + y = 9 and 2x - y = 4
5, 4
4, 5
6, 3
3, 6
Explanation - x+y=9, 2x-y=4 ⇒ Add: 3x=13 ⇒ x=5; y=4
Correct answer is: 5, 4
Q.22 The roots of x² - 2x - 8 = 0 are:
4, -2
-4, 2
2, -4
-2, 4
Explanation - x²-2x-8=0 ⇒ (x-4)(x+2)=0 ⇒ x=4, -2
Correct answer is: 4, -2
Q.23 Solve 5x - 3 = 2x + 6
3
2
1
4
Explanation - 5x -3=2x +6 ⇒ 3x=9 ⇒ x=3
Correct answer is: 3
Q.24 Solve x² - 6x + 9 = 0
3
-3
0
None of these
Explanation - x²-6x+9=0 ⇒ (x-3)²=0 ⇒ x=3
Correct answer is: 3
Q.25 If 4x - y = 5 and x + y = 7, find x and y
3, 4
2, 5
4, 3
5, 2
Explanation - x + y =7 ⇒ y=7-x; 4x - (7-x)=5 ⇒ 5x -7=5 ⇒ x=2 ⇒ y=5
Correct answer is: 2, 5