# Archives

## Find the volume of the parallelopiped whose coterminous edges are represented by vector a = 2i−3j+4k, vector b = i+2j-k, vector c = 3i-j+2k.

(a) 7 (b) 8 (c) 9 (d) none of these Solution: vector a = 2i - 3j + 4k vector b = i + 2j - k vector c = 3i - j + 2k  Volume of the... View Article

## A number of friends decided to go on a picnic and planned to spend Rs. 96 on eatables. Four of them, however, did not turn up. As a consequence, the remaining ones had to contribute Rs. 4 each extra. The number of those who attended the picnic was

(A) 8 (B) 12 (C) 16 (D) 24 Solution: Let x be the number of persons. Amount spend = Rs. 96 So the contribution of each person = 96/x... View Article

## The perimeter of a certain sector of a circle of radius 5.6 m is 27.2 m. Find the area of the sector.

Solution: Let r be the radius of the circle. Given r = 5.6 Perimeter of sector = 27.2 m Perimeter of sector = 2r + length of arc 27.2 = 2r +... View Article

## The least two-digit composite number is

(A) 11 (B) 10 (C) 12 (D) 16 Solution: If a number has more than 2 factors, then it is a composite number. 11 is a prime number since it has... View Article

## Number of prime numbers between 50 to 60 is

(a) 2 (b) 3 (c) 4 (d) 1 Solution: The prime numbers between 50 and 60 are 53 and 59. Number of prime numbers between 50 and 60 = 2 Hence... View Article

## Express the given complex number in the form a+ib: 3(7 + 7i) + i(7 + i7).

Solution: Given 3(7 + 7i) + i(7 + i7) = 21 + 21i + 7i - 7 = 14 + 28i This is of the form a + ib where a = 14 and b = 28.... View Article

## 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