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Convert 6 radians into degree measure.

Solution: We know that π radian = 1800 So 1 radian = 180/π degree Here we have to convert 6 radians into degree measure. So 6 radian =... View Article

A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?

(a) 6 min to empty (b) 6 min to fill (c) 9 min to empty (d) 9 min to fill Solution: Since pipe B is faster, the tank will be emptied. Work... View Article

Which of the following rational number does not have a reciprocal.

(a) 1 (b) -1 (c) 0 (d) none of the above Solution: The reciprocal of a number is nothing but the multiplicative inverse of that number such... View Article

The ratio of the volume of a cylinder: volume of cone: volume of the hemisphere of same radius and same height is

(a) 1:2:3 (b) 3:1:2 (c) 1:1:1 (d) 2:3:1 Solution: Let r be radius and h be the height of the cylinder, cone, and hemisphere. Given radius... View Article

Find the area of the following triangles.

(a) b = 4 cm, h = 3 cm (b) b = 5 cm, h = 3.2 cm (c) b = 3 cm, h = 4 cm (d) b = 3 cm, h = 2 cm Solution: We know the area of a triangle =... View Article

A statue, 1.6m tall, stands on the top of pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60⁰ and from the same point, the angle of elevation of the top of the pedestal is 45⁰. Find the height of the pedestal.

(a) height of the pedestal = 0.2(√7 - 1)m (b) height of the pedestal = 0.8(√3 + 1)m (c) height of the pedestal = 1.6(√5 + 1)m (d) height of... View Article

Find the value of 64^-2/3.

Solution: 64-2/3 = (43)-2/3 = 4-2 = 1/42 = 1/16 Hence 64-2/3 = 1/16... View Article

Solve following equation: -x²+ x – 2 = 0

(a) (1 ± √7i)/2 (b) (-1 ± √7i)/2 (c) (2 ± √7i)/2 (d) (-2 ± √7i)/2 Solution: Given -x2 +... View Article

Solve for x: cos (sin^-1 x) = 1/7

Solution: cos (sin-1 x) = 1/7 Put sin-1 x = k x = sin k x2 = sin2k => 1-x2 = 1 - sin2 k => 1-x2 = cos2k …(i) cos k =... View Article

Estimate the sum to the nearest hundred. 458 + 324

Solution: Estimated value of 458 to nearest hundred = 500 Estimated value of 324 to nearest hundred = 300 Estimated sum = 500 + 300 = 800... View Article

One root of the equation (x + 1)(x + 3)(x + 2)(x + 4) = 120 is

(A) -1 (B) 2 (C) 0 (D) 1 Solution: Given (x + 1)(x + 3)(x + 2)(x + 4) = 120 Substitute the values in the equation and check. (A) Put x =... View Article

Fill in the blanks using the correct form of the verbs: My sister already the food.

(A) is; cooking (B) has; cooked (C) was; cooked (D) did; cooked Solution: My sister has already cooked the food. Hence option B is the answer.... View Article

Change the following statement into passive voice: Those who worked hard seldom obtained good marks.

(A) Good marks were seldom being obtained by those who worked hard. (B) Good marks are seldom obtained by those who worked hard. (C) Seldom had... View Article

If sec C is m/2√2, then m is

(a) 1 (b) 3 (c) 7 (d) none of these Solution: From the fig, triangle BDC is a right angled triangle. Using Pythagoras theorem, DC2 = 122... View Article

There are three boys and two girls. A committee of two is to be formed. Find the probability of the event that the committee contains at least one girl.

Solution: Number of boys = 3 Number of girls = 2 Total number of people = 3+2 = 5 Find the number of outcomes such that the committee of two... View Article

Evaluate the following using suitable identity: 213×187

Solution: 213×187 = (200 + 13)×(200 - 13) = 2002 - 132 = 40000 - 169 = 39831 Hence 213×187 = 39831.... View Article

Given a metal pipe 77 cm long and inner diameter is 4 cm and outer diameter is 4.4 cm. Find the outer curved surface area of the pipe.

Solution: Height of pipe = 77 cm Outer diameter = 4.4 cm So outer radius = 2.2 cm Curved surface area of the cylinder = 2πrh =... View Article

If x_i > 0, i = 1,2, 3, … 50 and x₁ + x₂ + x₃ + …+x₅₀ = 50, then the minimum value of (1/x₁) + (1/x₂) + ….+ (1/x₅₀) equals

(a) 50 (b) 502 (c) 503 (d) none of these Solution: We know AM ≥ HM (x1 + x2 + x3 + …+x50)/50 ≥ 50/[((1/x1) + (1/x2) +... View Article

Factorise a³ – 1/a³ – 2a + 2/a.

Solution: We know a3- b3 = (a - b)(a2 + ab + b2) a3 - 1/a3 - 2a + 2/a = (a - 1/a)(a2 + 1 + 1/a2) - 2(a - 1/a) = (a - 1/a)(a2 + 1 + 1/a2 - 2)... View Article

How many coins 1.75 cm in diameter and 2 mm thick must be melted to form a cuboid of dimensions 11 cm × 10cm × 7cm?

Solution: Diameter of coin = 1.75 cm Radius of coin = 1.75/2 cm Height = 2 mm = 0.2 cm Volume of coin = πr2h =... View Article