SSC CGL 2026: Original Mock Test Questions with Explanations

Question 1 (Advance Algebra): If $x + rac{1}{x} = 3$, find the value of $x^5 + rac{1}{x^5}$.

Step-by-Step Solution:

Recall the standard algebraic identity: $x^5 + rac{1}{x^5} = (x^2 + rac{1}{x^2})(x^3 + rac{1}{x^3}) - (x + rac{1}{x})$.

• Step A: $x^2 + rac{1}{x^2} = 3^2 - 2 = 9 - 2 = 7$.
• Step B: $x^3 + rac{1}{x^3} = 3^3 - 3(3) = 27 - 9 = 18$.
• Step C: Multiply the two results: $7 imes 18 = 126$.
• Step D: Subtract $(x + rac{1}{x})$: $126 - 3 = 123$.

Answer: 123.

Question 2 (Geometry - Tangents): Two concentric circles have radii of 13 cm and 5 cm. What is the length of the chord of the larger circle that touches the smaller circle as a tangent?

Step-by-Step Solution:

• Let $O$ be the common center. Let $AB$ be the chord of the outer circle tangent to the inner circle at point $P$.
• The radius $OP$ is perpendicular to chord $AB$ and bisects it into two equal segments ($AP = PB$).
• In right-angled triangle $ riangle OPA$, hypotenuse $OA = 13 ext{ cm}$ (radius of outer circle) and perpendicular $OP = 5 ext{ cm}$ (radius of inner circle).
• By the Pythagorean Theorem: $AP = sqrt{13^2 - 5^2} = sqrt{169 - 25} = sqrt{144} = 12 ext{ cm}$.
• Total chord length $AB = 2 imes AP = 2 imes 12 = 24 ext{ cm}$.

Answer: 24 cm.

Question 3 (Syllogisms):
Statements:
1. All metals are conductors.
2. Some conductors are liquids.
Conclusions:
I. Some liquids are metals.
II. Some conductors are metals.
Which conclusion(s) logically follow?

Explanation:

• From Statement 1 ('All metals are conductors'), the valid converse is 'Some conductors are metals' (Conclusion II is unconditionally TRUE).
• No direct link exists between 'liquids' and 'metals' in the premises; a Venn diagram can satisfy both statements with zero overlap between liquids and metals. Conclusion I is NOT necessarily true.

Answer: Only Conclusion II follows.

Question 4 (Error Spotting):
"Neither the manager nor the employees was present at the annual board meeting." Find the grammatical error.

Explanation: Under the Rule of Proximity for correlative conjunctions (either...or, neither...nor), the verb must agree in number with the subject closest to it. Here, 'the employees' (plural) is closest to the verb. The singular auxiliary 'was' must be corrected to the plural 'were'.

Corrected Sentence: "Neither the manager nor the employees were present at the annual board meeting."

Question 5 (Indian Polity): Under which Article of the Constitution of India can the President declare a Financial Emergency?

Explanation: Part XVIII of the Constitution contains the Emergency Provisions. Article 352 governs National Emergency (war/external aggression/armed rebellion); Article 356 governs President's Rule in States; Article 360 empowers the President to proclaim a Financial Emergency if the financial stability or credit of India is threatened.

Answer: Article 360.