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Write the following cubes in expanded form: (i) (2x + 1)^3 (ii) (2a – 3b)^3 (iii) [3x/2 + 1]^3 (iv) [x – 2y/3]^3.

(i) (2x + 1)³ Using identity: (a + b)³ = a³+ b³+ 3ab(a + b) (2x + 1)³ = (2x)³ + 1³ + (3×2x×1)(2x... View Article

Find the zeroes of the polynomial x^2+1/6x-2 and verify the relation between the coefficient and zeroes of the polynomial.

x2 + 1/6(x) - 2 = 0 6x2 + x - 12 = 0 6x2 - 8x + 9x - 12 = 0 (6x2 - 8x) + (9x - 12) = 0 2x(3x - 4) + 3(3x + 4) = 0 (3x - 4)(2x + 3) = 0 x =... View Article

Convert the following ratios to percentages? (a) 3:4 (b) 2:3

(a) Given, the ratio is 3:4 3:4 = 3/4 Percentage = 3/4 x 100 = 3 x 25 = 75% (b) Given, the ratio is 2:3 2:3 = 2/3 Percentage = 2/3 x 100 = 200/3%... View Article

What is formula of x²+y²?

Since we know, (x+y)2 = x2 + y2 + 2xy Therefore, the formula of x2 + y2 is: x2 + y2 = (x+y)2 - 2xy... View Article

Square of 42 without actual multiplication.

Given, the number is 42. We need to square the number 42. We can use the identity: (a+b)2 = a2 + b2 + 2ab, to find the square of 42. 42 = 40 +... View Article

Angle between minute hand and hour hand at 5 oclock is?

At 5 O’clock, the hour hand is at 5 and the minute hand is at 12. Between the two hands, there is 5 hours difference and total we have 12... View Article

In a class of 40 student 1/5 of total number of students like to study English and 2/5 of the total number of students like to study mathematics and the remaining like to study science . How many student like to study English? How many student like to study mathematics? What fraction of total number of student like to study science?

Given, total students = 40 1/5 students like to study English Number of students who like to study English = 1/5 x 40 = 8 2/5 students like to... View Article

A milkman sold two of his buffaloes for Rs 20000 each.On one he made a gain of 5% and on the other a loss of 10%.Find his overall gain or loss.(Find CP of each).

Selling price of 1st buffalo = Rs.20000 He made a gain of 5% in 1st buffalo Cost price of 1st buffalo = (100/105) x 20000 = Rs. 19047.62... View Article

Arrange the following numbers in ascending order: 847, 9754, 8320, 571.

Ascending order:571, 847, 8320, 9754.... View Article

1/2 of 10. How to solve it?

1/2 of 10 (1/2) x 10 Since, 2 x 5 = 10 Therefore, (1/2) x 10 = 5... View Article

Choose the odd one out from given four choices: (a) 13 – 21 (b) 51 – 23 (c) 16 – 24 (d) 19 – 27

Answer: (c) 16 - 24 The odd one from the given choices is 16 - 24. All pairs are odd numbers whereas 16, 24 are even numbers. If a number is... View Article

Linear equation in one variable has? (A) One Solution (B) Two Solution

Answer: (A) One Solution Linear equation in one variable has one solution.... View Article

A man can row 5 kmph in still water.if the river is running at 1kmph,it takes 75min to go to a place and come back. How far is the place?

Let us say, distance = x Upstream Speed = 5 - 1 => 4 Downstream Speed = 5 + 1 => 6 75 minutes in hours = 5/4 hours As per the given... View Article

Solve the solution 1+4+7+10………….+x = 287

Given, 1+4+7+10.............+x = 287 We need to find the value of x. First term,a = 1 Common difference = 4-1 = 3 Sn = 287 Using the... View Article

Ritu can row downstream 20 km in 2 hour, and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current.

Let, speed of Ritu in still water = x km/hr speed of current = y km/hr Thus, speed downstream =(x+y) km/hr speed upstream =(x−y) km/hr... View Article

Perimeter of a circle is called its:

The perimeter of a circle is called its circumference. The formula of the circumference is: C = 2πr where r is the radius.... View Article

The distance of a point from the Y-axis is called its y-coordinate. True or False.

False. The distance of a point from the y - axis is called its x-coordinate, or abscissa, and the distance of the point from the x-axis is... View Article

A cistern can be filled by two pipes a and b in 10 and 15 hours respectively and is then empited by a tap in 8 hours.If all the taps are opened,then cistern will be fill in how many hours?

Pipe 'a' fills the cistern in 10 hours, so in 1 hour the part of cistern filled by pipe a= 1/10 Pipe 'b' fills the csitern in 15 hours, so in 1... View Article

Write a quadratic polynomial whose zeroes are 2 and -6.

Let α and β are the zeroes of a quadratic equation. α=2 and β=−6 Sum of roots =... View Article

Find the equivalent fraction of 3/5 having denominator 20

Let the required fraction is x/20. Thus, 3/5 is equivalent to x/20 3/5 = x/20 x = 12 Therefore, the required fraction is 12/20.... View Article