Jamb Mathematics Questions
Question 536:
Rationalize the denominator of the expression \(\frac{6 + 2\sqrt{5}}{4 - 3\sqrt{6}}\)
- A \(\frac{12+ 4\sqrt{5 + 7} 5 + 6\sqrt{3}}{39}\)
- B \(\frac{-(24 + 18\sqrt{6} + 8\sqrt{5} + 6\sqrt{30})}{39}\)
- C \(\frac{24 + 3\sqrt{6 + 8} 5 + 6\sqrt{30}}{19}\)
- D \(\frac{-15 + 3\sqrt{5 + 18} 5 + 6\sqrt{30}}{36}\)
- E \(\frac{-(12 + 4\sqrt{5} +9\sqrt{6} + 3\sqrt{30})}{19}\)
Question 537:
Simplify \(\frac{5^x \times 25^{x - 1}}{125^{x + 1}}\)
- A 5<sup style='font-size: smaller;'>2x + 1</sup>
- B 5<sup style='font-size: smaller;'>x + 1</sup>
- C 5<sup style='font-size: smaller;'>-5</sup>
- D 5<sup style='font-size: smaller;'>2</sup>
- E 5<sup style='font-size: smaller;'>3</sup>
Question 538:
A steel ball of radius 1 cm is dropped into a cylinder of radius 2cm and height 4cm. If the cylinder is now filled with water, what is the volume of the water in the cylinder?
- A \(\frac{44}{3}\)\(\pi\)cm<sup style='font-size: smaller;'>3</sup>
- B 12\(\pi\)cm<sup style='font-size: smaller;'>3</sup>
- C \(\frac{38}{3}\)\(\pi\)cm<sup style='font-size: smaller;'>3</sup>
- D \(\frac{40}{3}\)\(\pi\)cm<sup style='font-size: smaller;'>3</sup>
- E \(\frac{32}{33}\)\(\pi\)cm<sup style='font-size: smaller;'>3</sup>
Question 539:
Simplify \(\frac{x^2 + y^2 + xy}{x + y}\) - \(\frac{x^2 + y^2}{x - y}\)
- A \(\frac{x^2 + y^2} {(x - y)^2}\)
- B \(\frac{2y^3} {y^2 - x^2}\)
- C \(\frac{3x^2 + y^2} {(2x - y)^2}\)
- D \(\frac{x^2 + y^2} {(x^2 - y)}\)
Question 540:
A ladder resting on a vertical wall makes an angles whose tangent is 2.4 with the ground. If the distance between the foot of the ladder and the wall is 50cm, What is the length of the ladder?
- A 1m
- B 1.1m
- C 1.2m
- D 0.9m
- E 1.3m