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A sphere of diameter 5cm is dropped into a cylindrical vessel partly filled with water. The diameter of the base of the vessel is 10cm. If the sphere is completely submerged, by how much will the level of water rise?

Solution: Diameter of sphere = 5 cm Radius of sphere, r = 5/2 = 5/2 cm The diameter of the base of the vessel = 10 cm Radius of the base of... View Article

The total surface area of a cube is 216 cm² then its volume is

(a) 216 (b) 144 (c) 196 (d) 212 Solution: Given TSA of cube = 216 cm3 => 6a2 = 216 => a2 = 216/6 = 36 => a = 6 Volume of a cube... View Article

An integer is chosen at random from 1 to 50. Find the probability that the number is

i) Divisible by 5 ii) A perfect cube iii) A prime number Solution: Total number of outcomes = 50 i) Numbers divisible by 5 in 1 to 50 = 5,... View Article

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

Archives

A sphere of diameter 5cm is dropped into a cylindrical vessel partly filled with water. The diameter of the base of the vessel is 10cm. If the sphere is completely submerged, by how much will the level of water rise?

The total surface area of a cube is 216 cm² then its volume is

An integer is chosen at random from 1 to 50. Find the probability that the number is

10, 100, 200, 310, ?

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

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

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.

Mitochondria are store houses of

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

Find the HCF of 25 and 30.

Find the value of ¹⁰C₃.

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?

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

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?

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

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

Sum of factors of 78 are

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

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

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

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