SSC CGL Tier I - 09 September 2024 - Shift 1
100 questions · 60 minutes · 4 subjects
SSC · Algebra practice
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English SSC CGL Tier I papers. Free 60-minute mocks, 100 questions, 200 marks; +2 correct and −0.5 incorrect. Source: SSC response sheets preserved by SSC Portal. The marked archived keys have not been independently revalidated against final SSC keys; worked explanations are pending review. A/B/C/D correspond to source options 1/2/3/4.
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Find the 23th term of the arithmetic progression 9, 18, 27, ...
Answer and explanation
Correct answer: B
nth term = a + (n−1)d = 9 + 22×9 = 207.
Find the sum of the first 12 terms of the AP with first term 9 and common difference 5.
Answer and explanation
Correct answer: C
S = n/2 [2a + (n−1)d] = 12/2 × [18 + 55] = 438.
Solve for x: 11x + 25 = 245
Answer and explanation
Correct answer: B
11x = 245 − 25 = 220, so x = 20.
If a + b = 10 and ab = 24, what is the value of a² + b²?
Answer and explanation
Correct answer: C
a² + b² = (a+b)² − 2ab = 100 − 48 = 52.
If a − b = 10 and a² + b² = 122, find ab.
Answer and explanation
Correct answer: D
ab = [a² + b² − (a−b)²]/2 = (122 − 100)/2 = 11.
If x + 1/x = 2, what is the value of x² + 1/x²?
Answer and explanation
Correct answer: D
x² + 1/x² = (x + 1/x)² − 2 = 4 − 2 = 2.
Expand and simplify: (12x + 9)² − (12x − 9)²
Answer and explanation
Correct answer: C
(p+q)² − (p−q)² = 4pq = 4×12x×9 = 432x.
What is the sum of the roots of the equation x² − (-1)x − 110 = 0?
Answer and explanation
Correct answer: A
For ax² + bx + c = 0 the sum of roots is −b/a = -1.
What is the value of sin 90°?
Answer and explanation
Correct answer: D
Standard value: sin 90° = 1.
If sin θ = 20/29 (θ acute), find cot θ.
Answer and explanation
Correct answer: A
Take the right triangle with perpendicular 20, base 21, hypotenuse 29; cot θ = 21/20.
Evaluate 15² − 20² using the identity a² − b² = (a + b)(a − b).
Answer and explanation
Correct answer: B
(15+20)(15−20) = 35 × -5 = -175.
Find the 35th term of the arithmetic progression 19, 25, 31, ...
Answer and explanation
Correct answer: C
nth term = a + (n−1)d = 19 + 34×6 = 223.
Find the sum of the first 21 terms of the AP with first term 14 and common difference 7.
Answer and explanation
Correct answer: B
S = n/2 [2a + (n−1)d] = 21/2 × [28 + 140] = 1764.
Solve for x: 3x + 10 = -26
Answer and explanation
Correct answer: A
3x = -26 − 10 = -36, so x = -12.
If 5x + 1y = 49 and 2x + 1y = 28, what is the value of x + y?
Answer and explanation
Correct answer: B
Solving the equations gives x = 7, y = 14; x + y = 21.
If a + b = 12 and ab = 27, what is the value of a² + b²?
Answer and explanation
Correct answer: B
a² + b² = (a+b)² − 2ab = 144 − 54 = 90.
If a − b = 1 and a² + b² = 25, find ab.
Answer and explanation
Correct answer: C
ab = [a² + b² − (a−b)²]/2 = (25 − 1)/2 = 12.
Expand and simplify: (6x + 11)² − (6x − 11)²
Answer and explanation
Correct answer: C
(p+q)² − (p−q)² = 4pq = 4×6x×11 = 264x.
What is the sum of the roots of the equation x² − 6x − 135 = 0?
Answer and explanation
Correct answer: B
For ax² + bx + c = 0 the sum of roots is −b/a = 6.
What is the value of cos 0°?
Answer and explanation
Correct answer: A
Standard value: cos 0° = 1.
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