Geometry · SSC CGL previous year questions

2023 24 questions

1. Q522023 · 26 Jul 2023 · Shift 2

   For congruent triangles ΔABC and ΔDEF, which of the following statement is correct?

   
   1. A.Option 1
   2. B.Option 2
   3. C.Option 3
   4. D.Option 4
   Show answer

   Answer: B

2. Q592023 · 26 Jul 2023 · Shift 2

   ΔABC is a right triangle. If ∠B = 90° and tan A = , then the value of sin A cos C + cos A sin C is :

   
   1. A.Option 1
   2. B.Option 2
   3. C.Option 3
   4. D.Option 4
   Show answer

   Answer: A

3. Q682023 · 26 Jul 2023 · Shift 2

   In a right triangle for an acute angle x, if sin x = , then find the value of cosx.

   
   1. A.Option 1
   2. B.Option 2
   3. C.Option 3
   4. D.Option 4
   Show answer

   Answer: D

4. Q642023 · 26 Jul 2023 · Shift 3

   In a triangle ABC, the three angles are x, y and y + 10°. Also, 2x - 4y = 20°. Which type of triangle is ABC?

   1. A.Equilateral
   2. B.Obtuse
   3. C.Acute
   4. D.Right-angled
   Show answer

   Answer: D

5. Q592023 · 26 Jul 2023 · Shift 4

   In the figure, PT is a tangent. If TP = 12 cm, PB = x + 7 cm and PA = x cm, then find the value of x.

   
   1. A.9
   2. B.6
   3. C.7
   4. D.5
   Show answer

   Answer: A

6. Q632023 · 26 Jul 2023 · Shift 4

   Find the value of x in the given figure where TF ( tangent on point T) = 15 cm, FB = 2x + 3 cm, FA = 9 cm.

   
   1. A.21 cm
   2. B.18 cm
   3. C.15 cm
   4. D.11 cm
   Show answer

   Answer: D

7. Q622023 · 25 Jul 2023 · Shift 2

   The three sides of two triangles are 4, 5 and 6 cm. Select the INCORRECT statement.

   1. A.The angle opposite to the greater side in those triangles will be greater.
   2. B.The area of the two triangles will be different.
   3. C.The two triangles are congruent.
   4. D.The two triangles are scalene triangles.
   Show answer

   Answer: B

8. Q722023 · 25 Jul 2023 · Shift 3

   If , where θ is an acute angle, then the value of sin (θ + 30°) is:

   
   1. A.Option 1
   2. B.Option 2
   3. C.Option 3
   4. D.Option 4
   Show answer

   Answer: D

9. Q552023 · 24 Jul 2023 · Shift 3

   If ΔABC and ΔDEF are congruent triangles, then which of the following is FALSE?

   1. A.The ratio of AC to DF is 2 ∶ 1.
   2. B.The perimeter of both the triangles is equal.
   3. C.AB = DE, and BC = EF.
   4. D.The ratio of the angles in both the triangles is the same.
   Show answer

   Answer: A

10. Q672023 · 24 Jul 2023 · Shift 3

    The centroid of an equilateral triangle PQR is L. If PQ = 6 cm, the length of PL is:

    
    1. A.2 cm
    2. B.4 cm
    3. C.5 cm
    4. D.3 cm
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    Answer: A

11. Q682023 · 24 Jul 2023 · Shift 4

    In the given figure, chords XY and PQ intersect each other at point L. Find the length of XY (in cm).

    
    1. A.21
    2. B.20
    3. C.22
    4. D.23
    Show answer

    Answer: C

12. Q592023 · 21 Jul 2023 · Shift 2

    If Δ ABC is right angled at B, AB = 12 cm and ∠CAB = 60°, determine the length of BC.

    1. A.12√2 cm
    2. B.12
    3. C.12√3 cm
    4. D.24√3 cm
    Show answer

    Answer: C

13. Q552023 · 21 Jul 2023 · Shift 3

    In ΔXYZ, right angled at Y, if sin X = , find the value of cos X cos Z + sin X sin Z.

    
    1. A.Option 1
    2. B.Option 2
    3. C.Option 3
    4. D.Option 4
    Show answer

    Answer: A

14. Q682023 · 21 Jul 2023 · Shift 4

    PQR is a triangle right angled at Q and PQ ∶ QR = 3 ∶ 4. What is the value of sin P + sin Q + sin R?

    
    1. A.Option 1
    2. B.Option 2
    3. C.Option 3
    4. D.Option 4
    Show answer

    Answer: C

15. Q592023 · 20 Jul 2023 · Shift 2

    Suppose Δ PQR and Δ STU are congruent triangles under ASA. If ∠PQR = 60°, ∠PRQ = 30° and ∠STU = 60°, find ∠TSU.

    1. A.90°
    2. B.75°
    3. C.60°
    4. D.45°
    Show answer

    Answer: A

16. Q622023 · 20 Jul 2023 · Shift 3

    The three sides of a triangle are 12, 17 and x units. Which of the following options is correct?

    1. A.5 < x < 29
    2. B.5 ≤ x < 29
    3. C.5 ≤ x ≤ 29
    4. D.5 < x ≤ 29
    Show answer

    Answer: A

17. Q632023 · 20 Jul 2023 · Shift 4

    In a right-angle triangle, the hypotenuse is 5 cm and the base is 3 cm. If one angle is θ, then tan θ is equal to :

    
    1. A.Option 1
    2. B.Option 2
    3. C.Option 3
    4. D.Option 4
    Show answer

    Answer: A

18. Q552023 · 19 Jul 2023 · Shift 3

    The following pie chart shows the annual expenditure on different items. What is the minimum angle in the given pie chart?

    
    1. A.36°
    2. B.45°
    3. C.32°
    4. D.30°
    Show answer

    Answer: A

19. Q592023 · 19 Jul 2023 · Shift 3

    For any acute angle θ, sin θ + sin²θ = 1, then the value of cos²θ + cos4θ = ________.

    1. A.0
    2. B.1
    3. C.2
    4. D.−1
    Show answer

    Answer: B

20. Q632023 · 19 Jul 2023 · Shift 4

    In the shown figure, BC is a chord and CD is a tangent through the point C. If ∠AOC = 112°, then find ∠ACD.

    
    1. A.63°
    2. B.59°
    3. C.65°
    4. D.56°
    Show answer

    Answer: D

21. Q592023 · 18 Jul 2023 · Shift 3

    If sin (5x - 25°) = cos(5y + 25°), where 5x - 25° and 5y + 25° are acute angles,then the value of (x + y) is:

    1. A.50°
    2. B.40°
    3. C.18°
    4. D.16°
    Show answer

    Answer: C

22. Q512023 · 17 Jul 2023 · Shift 2

    The lengths of the three sides of a triangle are 30 cm, 42 cm and x cm. Which of the following is correct?

    1. A.12 ≤ x < 72
    2. B.12 > x > 72
    3. C.12 < x < 72
    4. D.12 ≤ x ≤ 72
    Show answer

    Answer: C

23. Q682023 · 14 Jul 2023 · Shift 2

    Let ABC, PQR be two congruent triangles such that angle A = angle P = 90°. If BC = 13 cm, PR = 5 cm, find AB.

    1. A.12 cm
    2. B.8 cm
    3. C.10 cm
    4. D.5 cm
    Show answer

    Answer: A

24. Q542023 · 14 Jul 2023 · Shift 3

    What is the central angle corresponding to the sector indicating the expenses incurred on Health?

    
    1. A.72°
    2. B.54°
    3. C.110°
    4. D.108°
    Show answer

    Answer: D