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A rectangular piece of cardboard is 40 in. width and 50 in. length. Squares 5 in. on a side are cut out of each corner, and the remaining flaps are bent up to form an open box. The number of cubic inches in the box is

The height of the rectangular piece after being bent is 5 in.The new length of the rectangular piece is 50 - 5 - 5 = 40The new width of the... View Article

If cos x + √sin x = 0, then x

The given expression is cos x + √sin x = 0.... View Article

The value of f (999) is 1 / k, where k equals

⇒ f (1) + 2 f (2) + 3 f (3) . . . . + n f (n) = n (n + 1) f (n) . . . . . (i)Let n = n +1 in the above equation, f (1) + 2 f (2) + 3 f (3) .... View Article

The distance between – 9 and 0 is:

The distance between the points x and y that is - 9 and 0 is given by |x - y|= |- 9 - 0|= |- 9|= 9... View Article

Find the probability of a card that is selected at random from a pack of cards will be a red honour.

Total number of ways of selecting a card = 52 waysThere exist 8 honours on the 26 red cards.A red honour can be chosen in 8 ways.Probability... View Article

Find the value of log (100 / 90).

log (100 / 90)... View Article

Find the ninth term of the G.P. 1, 4, 16, 64, . . .

The given series is 1, 4, 16, 64, . . .a = 1r = 4 / 1 = 4The nth term of the GP is arn-1.n = 9The 9th term is ar8.= (1) * 48= 65536... View Article

The radian measure of 175^o 45’ is

The given expression is 175o 45’.... View Article

Find the simple interest and the amount when principal = Rs. 1500, rate = 12% p.a. and time = 3 years 3 months.

P = Rs. 1500, R = 12% p.a. and Time = 3 years 3 months.3 years 3 months = (39 / 12) = (13 / 4) SI = (P × R × T) / 100 = (1500 ×... View Article

The values of θ satisfying sin 7θ = sin 4θ – sin θ and 0 < θ < π / 2 are

The given expression is sin 7θ = sin 4θ - sin θ.... View Article

Select the odd one from the given series: 3, 7, 9, 21, 27, 66, 81, 189, 243.

3, 7, 9, 21, 27, 66, 81, 189, 243.There exist two alternate series.Series I: 3, 9, 27, 81, 243Series II: 7, 21, 66, 189In series I, the numbers... View Article

The diameter of a tennis ball is 6.58 cm. What is the volume?

The diameter of a tennis ball is 6.58 cm; the radius of the sphere is:... View Article

Three numbers are in the ratio 2 : 3 : 5 and the sum of these numbers is 800. Find the numbers.

The three numbers are in the ratio 2 : 3 : 5 and the sum of them is 800. Sum of the terms of the ratio = 2 + 3 + 5 = 10 First number = (2 / 10)... View Article

Write a statement for the equation, given below: 12y – 30 = 6.

30 less than 12 times the number y equals 6.... View Article

Determine the point in the yz-plane which is equidistant from three points A (2, 0 3), B (0, 3, 2) and C (0, 0, 1).

As the x-coordinate of every point in the yz-plane is zero. Let P (0, y, z) be a point on the yz-plane such that PA = PB = PC.... View Article

150 is what percent of 30?

Let the percentage be x.(150 / 30) × (100 / 100) = [(150 × 100) / (30)] × (1 / 100) = 500 / 100The answer is 500%.... View Article

What needs to be done for calculating the mean for a continuous series?

The midpoints need to be found by taking the average of the upper and lower limits of each class interval given. For example, if the class... View Article

The cost of 2 (1 / 3) meters of cloth is Rs. 75 (1 / 4). Find the cost of cloth per metre.

The cost of 2 (1 / 3) meters of cloth is Rs. 75 (1 / 4).The cost of 1 meter of cloth is = [Rs. 75 (1 / 4) / 2 (1 / 3)]... View Article

Express the following numbers in index form. i. Fifth root of 13 ii. Sixth root of 9 iii. Square root of 256 iv. Cube root of 17 v. Eighth root of 100 vi. Seventh root of 30

i. (13)1/5 ii. (9)1/6 iii. (256)1/2 iv. (17)1/3 v. (100)1/8 vi. (30)1/7... View Article

Factorise 2x⁴ – 32.

The given expression is 2x4 - 32.... View Article