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Day 117: SSC CGL Tier II Quant

5 questions. Try each one first, then open its answer.

  1. Question 1

    Surds, Indices and Simplification. Asked once: 15 Nov 2020 Tier II

    4
    If 4553=1a+1b+1c−25\frac{45}{53} = \frac{1}{a + \frac{1}{b + \frac{1}{c - \frac{2}{5}}}}, where a, b and c are positive integers, then what is the value of (4a−b+3c)(4a - b + 3c)?

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  2. Question 2

    Triangles. Asked once: 29 Jan 2022 Tier II

    35
    SS and TT are points on the sides PQPQ and PRPR, respectively, of △PQR\triangle PQR such that PS×PR=PQ×PTPS \times PR = PQ \times PT. If ∠Q=96∘\angle Q = 96^\circ and ∠PST=∠PRQ+34∘\angle PST = \angle PRQ + 34^\circ, then ∠QPR=?\angle QPR = ?

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  3. Question 3

    Triangles. Asked once: 29 Jan 2022 Tier II

    33
    In △LMN\triangle LMN, LM=52LM = 5\sqrt{2} cm, LN=13LN = 13 cm and ∠LMN=135∘\angle LMN = 135^\circ. What is the length (in cm) of MNMN?

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  4. Question 4

    Triangles. Asked once: 29 Jan 2022 Tier II

    7
    OO is a point in the interior of △ABC\triangle ABC such that OA=12OA = 12 cm, OC=9OC = 9 cm, ∠AOB=∠BOC=∠COA\angle AOB = \angle BOC = \angle COA and ∠ABC=60∘\angle ABC = 60^\circ. What is the length (in cm) of OBOB?

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  5. Question 5

    Triangles. Asked once: 29 Jan 2022 Tier II

    98
    In ΔABC\Delta ABC, ∠A=66∘\angle A = 66^\circ and ∠B=50∘\angle B = 50^\circ. If the bisectors of ∠B\angle B and ∠C\angle C meet at PP, then, ∠BPC−∠PCA=\angle BPC - \angle PCA = ?

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