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10, 100, 200, 310, ?

(A) 400 (B) 410 (C) 420 (D) 430 Solution: By observing the series, we can find that the pattern is + 90, +100, + 110, ... So next term =... View Article

If tan(cos^-1 x) = sin(cot^-1 1/2) then x is equal to

(a) 1/√5 (b) 2/√5 (c) 3/√5 (d) √5/3 Solution: Given tan(cos-1 x) = sin(cot-1 1/2) Let cot-1 ½ = θ... View Article

The probability that a number selected at random from the numbers 1,2,3…….15 is a multiple of 4 is

(a) 4/15 (b) 1/5 (c) 2/15 (d) 1/15 Solution: Total number of outcomes = 15 From the numbers 1,2,3.......15, multiples of 4 are 4, 8 and 12.... View Article

The cost of preparing the walls of a room 12m long at the rate of Rs.1.35 per square meter is Rs. 340.20 and the cost of matting the floor at 85 paise per square metre is Rs. 91.80. Find the height of the room.

Solution: Given length of the room = 12 m Cost of matting floor = area of floor × rate per m2 Area of floor = Cost of matting floor/rate... View Article

Mitochondria are store houses of

A. Glycogen B. Glucose C. ATP D. Fats Solution: Mitochondria are known as the powerhouse of the cell because it stores ATP in it. This ATP... View Article

Solve the linear equation 3(5z-7) – 2(9z-11) = 4(8z-13)-17

Solution: 3(5z-7) - 2(9z-11) = 4(8z-13)-17 15z - 21 - 18z + 22 = 32z - 52 - 17 - 21 + 22 + 52 + 17 = 32z - 15z + 18z 35z = 70 z = 70/35 = 2... View Article

Find the HCF of 25 and 30.

(A) 25 (B) 6 (C) 1 (D) 5 Solution: HCF is the highest factor of all the common factor in the given number’ So we can factorise... View Article

Find the value of ¹⁰C₃.

Solution: nCr = n!/r!(n-r)! 10C3 = 10!/3!7! = 10×9×8/2×3 = 120 Hence the value of 10C3 = 120.... View Article

A classroom is 10 m long, 6.4 m broad and 5 m high. If each student be given 1.6 m² of the floor area, how many students can be accommodated in the room? How many cubic meters of air would each student get?

Solution: Length of classroom = 10 m Breadth of classroom = 6.4 m Height of classroom = 5 m Area of classroom = length × breadth =... View Article

Find the zeroes of the quadratic polynomial 4x²-4x-3 and verify the relationship between the zeroes and the coefficients of the polynomial.

Solution: 4x2 - 4x - 3 = 0 4x2 - 6x + 2x - 3 = 0 2x(2x - 3) +(2x - 3) = 0 (2x + 1)(2x - 3) = 0 2x = -1 or 2x = 3 x = -1/2 or x = 3/2 Sum... View Article

If we add 1 to the numerator and subtract 1 from the denominator a fraction reduces to 1. It becomes 1/2, if we only add 1 to the denominator. What is the fraction?

Solution: Let x/y be the fraction. Add 1 to the numerator and subtract 1 from the denominator. (x+1)/(y-1) = 1 => x+1 = y-1 => x = y-2... View Article

Divide the sum of 8/3 and 4/7 by the product of -3/7 and 14/9.

Solution: Sum of 8/3 and 4/7 = (8/3) + (4/7) = (56 + 12)/21 = 68/21 Product of -3/7 and 14/9 = (-3/7) × (14/9) = -3 × 2/9 =... View Article

If sin A + cos A = √2 then sin A – cos A is equal to

(a) 1 (b) 0 (c) 2 (d) none of these Answer: Given sin A + cos A = √2 Squaring both sides sin2A + cos2A + 2 sin A cos A = 2 1 -... View Article

Sum of factors of 78 are

Solution: Factors of 78 are 1, 2, 3, 6,13, 26, 39 and 78. Sum of factors = 1 + 2 + 3 + 6 + 13 + 26 + 39 + 78 = 168 Hence the sum of factors... View Article

If 2/-9 is the additive inverse of 2/q , then q is equal to

Solution: An additive inverse of a number is the value, which on adding with the original number results in zero value. For example, the... View Article

Find the equation of the straight line passing through the points (-1, 1) and (2, -4).

Solution: Given points are (-1, 1) and (2, -4). (x1, y1) = (-1, 1) and (x2, y2) = (2, -4) Slope m = (y2 - y1)/(x2 - x1) = (-4 - 1)/(2 - -1)... View Article

Prove that sin 40⁰– cos 70⁰ = √3 cos 80⁰.

Solution: Use sin A - sin B = 2 cos (A+B)/2 sin (A-B)/2 cos (90 - x) = sin x So cos 70 = cos (90 - 20) = sin 20 sin 400 - cos 700 = sin 400 -... View Article

Check which of the following are solutions of the equation x – 2y = 4 and which are not:

(a) (0, 2) (b) (2, 0) (c) (4, 0) (d) (√2, 4√2) Solution: Given x - 2y = 4…(i) Substitute given values in the equation and check whether it... View Article

Coal tar is used in the manufacture of

(A) Synthetic dyes (B) Drugs (C) Perfumes (D) All the three Solution: Coal tar is a thick dark liquid that is a by-product of the production... View Article

Duramen is?

(A) Sapwood (B) Heartwood (C) Bark (D) Periderm Solution: Duramen is the central or inner dark coloured, non-functional secondary xylem... View Article