Simplification Questions

• A and B have their annual average income Rs. 80,000. B and C have their annual average income Rs. 75,000. C and A have their annual average income Rs. 78,000. The annual income of A is ?
• In the first 10 overs of a cricket game, the run rate was only 3.2. The run rate in the remaining 40 overs to reach the target of 282 runs is
• An army lost 10% of its men in war, 10% of the remaining died due to disease and 10% of the rest were declared disabled. Thus the strength of the army was reduced to 7,29,000 active men. The original strength of the army was
• A man can cover a certain distance in 3 hours 36 minutes if he walks at the rate of 5 Km/hr. If he covers the same distance on cycle at the rate of 24 Km/hr, then the time taken by him in minutes is
• If P = 99, then the value of P(P2+ 3P + 3) is
• If x + 1x = c + 1c , then the value of x =
• A complete factorisation of x4 + 64 is
• If a + b = 1, then a4 + b4 - a3 - b3 - 2a2b2 + ab is equal to
• If a = 299, b = 298, c = 297 then the value of 2a3 + 2b3 + 2c3 - 6abc is
• If x + 1x = 3, then x18 + x12 + x6 + 1 value is
• In a circle with centre O, AB is a diameter and CD is a chord which is equal to the radius OC. AC and BD are extended in such a way that they intersect each other at a point P, exterior to the circle. The measure of ∠APB is
• If x tan 60° + cos 45° = sec 45° then the value of x2 + 1 is
• If a2sec2x - b2tan2x = c2 then the value of sec2x + tan2x is equal to (assume b2 ≠ a2 )
• (1 + sec 20° + cot 70°)(1 - cosec 20° + tan70°) is equal to
• If tan4θ + tan2θ = 1 then the value of cos4θ + cos2θ is
• The value of 8(sin6θ + cos6θ) - 12(sin4θ + cos4θ) is equal to
• An aeroplane flying horizontally at a height of 3 Km. above the ground is observed at a certain point on earth to subtend an angle of 60°. After 15 sec flight, its angle of elevation is changed to 30°. The speed of the aeroplane (taking √3 = 1.732) is
• If the angle of elevation of the sun decreases from 45° to 30°, then the length of the shadow of a pillar increases by 60m. The height of the pillar is
• The angle of elevation of the top of a tower, vertically erected in the middle of a paddy field, from two points on a horizontal line through the foot of the tower are given to be α and β (α>β). The height of the tower is h unit. A possible distance (in the same unit) between the points is
• If x2+1x2 = 98, then x3+1x3 = ?