Jamb Mathematics Past Questions For Year 1981
Question 31
The area of a circular plate is one-sixteenth the surface area of a ball of a ball, If the area of the plate is given as P cm^2, then the radius of the ball is
- A. \(\frac{2P}{\pi}\)
- B. \(\frac{P}{\sqrt{\pi}}\)
- C. \(\frac{P}{\sqrt{2\pi}}\)
- D. 2\(\frac{P}{\pi}\)
Question 32
Show that \(\frac{\sin 2x}{1 + \cos x}\) + \(\frac{sin2 x}{1 - cos x}\) is
- A. sin x
- B. cos²x
- C. 2
- D. 3
Question 33
The first term of an Arithmetic progression is 3 and the fifth term is 9. Find the number of terms in the progression if the sum is 81
- A. 12
- B. 27
- C. 9
- D. 4
- E. 36
Question 34
Simplify T = \(\frac{4R_2}{R_1^{-1} + R_2^{-1} + 4R_3^{-1}}\)
- A. \(\frac{4R_1 \times R_2 R_3}{R_2R_3 + R_1R_3 + 4R_1 R_2}\)
- B. \(\frac{R_1 R_2 R_3}{R_2R_3 + R_1R_2 + 4R_1 R_2}\)
- C. \(\frac{16R_1 R_2 R_3}{R_2R_3 + R_1R_2 + R_1 R_2}\)
- D. \(\frac{4R_1 R_2 R_3}{4R_2R_3 + R_1R_2 + 4R_1 R_2}\)
Question 35
If b = a + cp and r = ab + \(\frac{1}{2}\)cp\(^2\), express b\(^2\) in terms of a, c, r.
- A. b² = aV + 2cr
- B. b² = ar + 2c²r
- C. b² = a² = \(\frac{1}{2}\) cr²
- D. b² = \(\frac{1}{2}\)ar² + c
- E. b² = 2cr - a²
