Objective Math MCQs for LT Grade, TGT, PGT Exams

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Prepare for competitive teaching exams like LT Grade, TGT, and PGT with these selected objective type mathematics questions. This set includes solved MCQs from previous years (Q.1 to Q.24) with accurate answers to help you understand the exam pattern and improve your speed and accuracy.

Level 4: Last Years Trends – Questions and Answers

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Level 4: Last Years Trends – Questions and Answers

1. The sum of the radii of inscribed and circumscribed circles for an n sided regular polygon of side a, is: (A.I.E.E.E. 2003)

  • (a) a/4 cot(π/2n)
  • (b) a cot(π/n)
  • (c) a/2 cot(π/2n)
  • (d) a cot(π/2n)

2. The upper 3/4th portion of a vertical pole subtends an angle tan−1(3/5) at a point in the horizontal plane through its foot and at a distance 40 m from the foot. A possible height of the vertical pole is: (A.I.E.E.E. 2003)

  • (a) 80 m
  • (b) 20 m
  • (c) 40 m
  • (d) 60 m

3. If in a triangle ABC, a·cos²(C/2) + c·cos²(A/2) = (3b/2), then the sides a, b, and c:

  • (a) satisfy a + b = c
  • (b) are in A.P.
  • (c) are in G.P.
  • (d) are in H.P.

4. The trigonometric equation sin⁻¹(x) = 2·sin⁻¹(a) has a solution for: (A.I.E.E.E. 2003)

  • (a) |a| ≥ 1/√2
  • (b) |a| < 1/√2
  • (c) all real values of a
  • (d) |a| < 1/2

5. Which of the following pieces of data does NOT uniquely determine acute-angled triangle ABC (R being the radius of the circumcircle)? (I.I.T. Screening 2002)

  • (a) a, sin A, sin B
  • (b) a, b, c
  • (c) a, sin B, R
  • (d) a, sin A, R

6. The number of integral value of k, for which the equation 7·cos x + 5·sin x = 2k + 1 has a solution is: (I.I.T. Screening 2002)

  • (a) 4
  • (b) 8
  • (c) 10
  • (d) 12
OBJECTIVE MCQ

OBJECTIVE MCQ

7. In a triangle ABC with sides a, b, c, r₁ > r₂ > r₃ (which are the ex-radii), then:
(a) a < b < c
(b) c < b < a
(c) a > b > c
(d) a < b > c
Answer: (a)
8. The sides of a triangle are 3x + 4y, 4x + 3y and 5x + 5y where x, y > 0. The triangle is:
(a) acute angled
(b) obtuse angled
(c) right angled
(d) none of these
Answer: (a)
9. If sin 45° cos² 60° tan² 60° cosec 30° sec 30° = x, then x =
(a) 2
(b) 4
(c) 8
(d) 32
Answer: (d)
10. A circular wire of radius 7 cm is cut and bent again into an arc of a circle of radius 12 cm. The angle subtended by the arc at the centre is:
(a) 180°
(b) 210°
(c) 240°
(d) 270°
Answer: (b)
11. The angles of a triangle are in the ratio 1 : 3 : 5. Then the greatest angle is:
(a) 5π/9
(b) π/9
(c) 7π/9
(d) 11π/9
Answer: (a)
12. If tan A + cot A = 4, then tan² A + cot² A is equal to:
(a) 110
(b) 191
(c) 194
(d) 195
Answer: (d)
13. If tan(θ/2) = t, then (1 − t²)/(1 + t²) is equal to:
(a) cos θ
(b) sin θ
(c) sec θ
(d) cos 2θ
Answer: (a)
14. The period of the function y = sin 2x is:
(a) 2π
(b) π
(c) π/2
(d) 2π²
Answer: (b)
15. If the angle of elevation of the top of a tower at a distance 500 metres from its foot is 30°, then the height of the tower is:
(a) 500
(b) 500√3
(c) √3/500
(d) 500/√3
(e) None of these
Answer: (e)
16. In triangle ABC, a(a² + b² − c²) cos A + b(b² + c² − a²) cos B + c(c² + a² − b²) cos C is equal to:
(a) 3abc
(b) 2abc
(c) abc
(d) 4abc
Answer: (c)
17. The measures of the sides of a triangle are 3, 5 and 7. The greatest angle is:
(a) 60°
(b) 90°
(c) 100°
(d) 120°
Answer: (d)
18. If tan⁻¹x + tan⁻¹y + tan⁻¹z = π, then x + y + z is equal to:
(a) 0
(b) 1
(c) xyz
(d) 2xyz
Answer: (a)
19. If θ = sin⁻¹(sin(−60°)), then one of the possible values of θ is:
(a) π/3
(b) 2π/3
(c) π/2
(d) −π/3
Answer: (d)
20. If in a triangle ABC, cos A = cos B cos C, then cot A is equal to:
(a) 1
(b) 3
(c) 4
(d) 5
(e) 2
Answer: (e)
21. cos(π/12) + cos(π/4) + cos(5π/12) =
(a) 1/2
(b) (3 + √3)/2
(c) 3
(d) 2
Answer: (b)
22. If α < β < π/2, then the largest angle of a triangle whose sides are 1, sin x, cos x is:
(a) π/2
(b) π − x
(c) x
(d) None of these
Answer: (c)
23. If cos⁻¹(√p + cos⁻¹(√(1 − p²)) = 3π/4, then the value of p is:
(a) −1/2
(b) −1
(c) 1/2
(d) √2/2
Answer: (d)
24. If tan⁻¹((x + 1)/(x − 1)) + tan⁻¹((x − 1)/(x + 1)) = tan⁻¹(7), then the value of x is:
(a) −2
(b) −1
(c) 2
(d) 1
Answer: (c)

Objective Math MCQs for LT Grade, TGT, PGT Exams


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