Archives

Express 121 as the sum of 11 odd numbers.

Solution 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 121 = 112 Therefore sum of first 11 odd natural numbers is 121.... View Article

All squares are trapeziums. (True or False)

All squares are trapeziums. Ans: True All squares have two sides that are parallel to each similar to Trapezium. ... View Article

All rectangles are squares. (True or False)

All rectangles are squares. Ans: False In square all sides are equal, but in rectangle length and breadth are different. All square are... View Article

Simplify the following expression: (3 + √3) (3-√3)

(ii) (3+√3)(3-√3) On opening the brackets and solving, we get, (3+√3)(3-√3) = 32-(√3)2 = 9-3... View Article

In Fig. if AB CD, CD EF and y : z = 3 : 7, find x.

Given AB || CD and CD || EF y : z = 3 : 7 => AB || CD || EF => AB || EF So, x=z [alternate interior angles] -------------(i) Again... View Article

Simplify the following expression: (√5-√2) (√5 + √2)

(iv) (√5-√2)(√5+√2) On opening the brackets and solving, we get, (√5-√2)(√5+√2) =... View Article

Find six rational numbers between 3 and 4.

Given The numbers 3 & 4 are given Find out We have to find out 6 rational numbers between 3 and 4 Solution There are infinite rational... View Article

Solve the following equation: (7y + 4) /(y + 2) = -4/3

(7y + 4)/(y + 2) = -4/3 ⇒ 7y + 4 = -4/3 (y + 2) ⇒ 3(7y + 4) = -4(y + 2) ⇒ 21y + 12 = -4y – 8 Rearranging the equation... View Article

In the figure, DE||OQ and DF||OR, show that EF||QR.

Proof Given that In ΔPQO, DE || OQ By using Basic Proportionality Theorem, PD/DO = PE/EQ……(i) Also given that In... View Article

In Fig. if AB DE, BAC = 35° and CDE = 53°, find DCE.

AB || DE,∠BAC = 35° and ∠CDE = 53° We know that AE is a transversal of AB and DE BAC and AED are alternate interior... View Article

In the figure, if ΔABE ≅ ΔACD, show that ΔADE ~ ΔABC.

Given Given, ΔABE ≅ ΔACD. To Prove ΔADE ~ ΔABC Proof Given, ΔABE ≅ ΔACD. By CPCT, we have ∴... View Article

Solve the following equation: (3y + 4) /(2 – 6y) = -2/5

(3y + 4)/(2 – 6y) = -2/5 ⇒ 3y + 4 = -2/5 (2 – 6y) ⇒ 5(3y + 4) = -2(2 – 6y) ⇒ 15y + 20 = -4 + 12y Rearranging... View Article

Simplify the following expression: (i) (3 + √3) (2 + √2)

(i) (3+√3)(2+√2) On opening and solving the brackets, we get, (3+√3)(2+√2)=... View Article

In a ∆ABC, ∠ C = 3 ∠ B = 2 (∠A + ∠ B) . Find the three angles.

Given ∠C = 3 ∠B = 2(∠B + ∠A) Find out The angles of traingle ∠B = 2 ∠A+2 ∠B ∠B=2 ∠A ∠A – ∠B= 0-... View Article

If P(E) = 0.05, what is the probability of ‘not E’?

Probability of not happening an event is equal to 1 minus probability of happening an event. We know that, P(E)+P(not E) = 1 It is given that,... View Article

Find the square root of 900 by Division method.

Solution We have to find the square root of 900 by the long division method ∴ √900 = 30 Answer √900 =30... View Article

Find the square root of 576 by Division method.

Solution We have to find the square root of 576 by the long division method ∴ √576 = 24 Answer √576 = 24... View Article

Find the square root of 529 by Division method.

Solution We have to find the square root of 529 by the long division method ∴ √529 = 23 Answer √529 = 23... View Article

All rhombuses are parallelograms. (True or False)

All rhombuses are parallelograms. Ans: True A parallelogram has opposite sides parallel and equal in length. Here the opposite angles are equal.... View Article

In Fig., AC = AE, AB = AD and BAD = EAC. Show that BC = DE.

Solution Given AC = AE, AB = AD ∠BAD = ∠EAC To Prove Line segment BC and DE are similar i.e. BC = DE Proof ∠BAD = ∠EAC On adding ∠DAC on... View Article