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Expand( 2x+3y+2z)^2 Using suitable identity.

Given, (-2x+3y+2z)2 Using the algebraic identity; ( a + b + c )² = a² + b² + c² + 2ab + 2bc + 2ac We can write the given... View Article

Find the value of x if x = root 6 + root 6 + root 6 + Infinity. Where x is a natural number.

Given, Let x = So, on squaring on both the sides: x2 = 6 + x2 = 6 + x x2 - x - 6 = 0 On solving the equation, using... View Article

The median of the following data is 525. Find the value of x and y, if the total frequency is 100.

Given, Class interval 0-100 100-200 200-300 300-400 400-500 500-600 600-700 700-800 800-900 900-1000 frequnecy 2 5 x 12... View Article

Evaluate sin 25 cos 65 + cos 25 sin 65 = ?

sin 25° cos 65° + cos 25° sin 65° = sin 25° cos (90° - 25°) + cos 25° sin (90° - 65°) = sin 25° sin... View Article

If the height of a person is 1.65m. Convert the meters (m) into centimeters (cm) and millimeters (mm).

Given, height of a person is 1.65m We need to conver the given height into centimeters and millimeters. 1 meter = 100 cm and 1000... View Article

The ratio of daily wages of two workers is 4:3 and one gets daily Rs.9 more than other. What are their daily wages?

Given, the ratio of daily wages of two workers is 4:3 Let us say, the wages of workers are 4x and 3x. As per the question, one gets daily... View Article

a^m × a^n is equal to (a) a^m+n (b) a^m-n (c) a^mn (d) a^n-m

Answer: (a) am+n By laws of exponents: am × an = am+n... View Article

Write the equation of line parallel to x axis and distance 6 unit from below the x axis.

The equation of line parallel to x axis and distance 6 unit from below the x axis is y = -6.... View Article

How many vertices does a sphere has (a) 0 (b) 1 (c)2

Answer: (a) 0 A sphere has zero vertices. A vertex is a point when two or more lines meet at a point. A sphere is round shape but does... View Article

Find the value of ( -10 –10 ) ÷ { -10 –( -10 –10 )}

( -10 –10 ) ÷ { -10 –( -10 –10 )} = (-20) ÷ { -10 - (-20)} = (-20) ÷ {-10 + 20} =... View Article

Find the square root of 49 by successive subtraction.

To find: √49 The steps to find the square root of 49 is as follows: 49 – 1 = 48 48 – 3 = 45 45 – 5 = 40 40 – 7 = 33... View Article

Show that the diagonals of a square are equal and bisect each other at right angles?

Given Let ABCD be a square and its diagonals AC and BD intersect each other at point O. To Prove AC = BD AO = OC and ∠AOB = 90° Proof In... View Article

Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.

Steps of Construction: Step 1: Draw a line segment AB of length 8 cm Step 2: Taking A as center and radius 4 cm and taking B as center and radius... View Article

A lending library has a fixed charge for the first three days and additional charge for each day thereafter. Saritha paid Rs. 27 for a book kept for seven days, while Susy paid Rs. 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.

Consider the fixed charge = Rs x Extra charge = Rs y As per the question x + 4y = 27 ----- (1) x + 2y = 21 ------(2) We get, 2y = 6 y = 3 putting... View Article

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