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Draw the graph of the following linear equations in two variables: x + y = 4

To draw the graph x+y=4, we have to find the values which x and y can have, satisfying the equation. We can check that when, x = 0, y =... View Article

In Fig. if PQ ⊥ PS, PQ SR, SQR = 28° and QRT = 65°, then find the values of x and y.

PQ ⊥ PS, PQ || SR, ∠SQR = 28° and ∠QRT = 65° x + SQR = QRT (Alternate angles since QR is transversal)... View Article

Check whether (5, – 2) , (6, 4) and (7, – 2) are the vertices of an isosceles triangle.

We know that the two sides of an isosceles triangle are equal. To verify whether the given points are vertices of an isosceles triangle, we... View Article

Simplify and solve the following linear equation: 3(5z – 7) – 2(9z – 11) = 4(8z – 13) – 17

3(5z – 7) – 2(9z – 11) = 4(8z – 13) – 17 => 15z – 21 – 18z + 22 = 32z – 52 – 17... View Article

If the zeroes of the polynomial x³-3x² + x + 1 are a – b, a, a + b, find a and b.

p(x) = x3-3x2+x+1 Zeroes are given as a – b, a, a + b On comparision the given polynomial with general expression, we get;... View Article

Find the sums given below: (i) 7 + 10_1/2 + 14 + … + 84 (ii) 34 + 32 + 30 + ……….. + 10 (iii) − 5 + (− 8) + (− 11) + ………… + (− 230)

(i) First term, a = 7 nth term, an = 84 common difference d= a2- a1= 10( 1/2) - 7= 21/2 - 7 = 7/2 Let 84 be the nth term of this... View Article

Find the mean salary of 60 workers of a factory from the following table:

Solution: Salary (xi) Number of workers (fi) fixi 3000 16 48000 4000 12 48000 5000 10 50000 6000 8 48000 7000 6 42000 8000 4... View Article

Express the following in the form p/q, where p and q are integers and q 0.

(i) Assume that x = 0.666… Then,10x = 6.666… Lets’s take, x = 0.66666…… 10x = 6.666….... View Article

Sum of two numbers is 95. If one exceeds the other by 15, find the numbers.

Solution Let one of the numbers be ‘x’. Then, the other number becomes (x + 15) As per the given data the equation becomes, x +... View Article

Draw the graph of the following linear equations in two variables: 3 = 2x + y

To draw the graph 3=2x+y, we have to find the values which x and y can have, satisfying the equation. We can check that when, x = 0, y =3, When x... View Article

Give five examples of data that you can collect from your day-to-day life

Five examples from day-to-day life are listed below 1. Number of children present in an apartment 2. Number of shops present in my... View Article

Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.

Given dataCommon difference, d = 7 22nd term, a22 = 149 Find out Sum of first 22 term, S22 = ? Solution We know that By the... View Article

Find the volume of a sphere whose surface area is 154 cm². (Assume π = 22/7)

Given Surface area of sphere =154 cm2 Find out We have to find out the volume of the sphere Solution Let us say that the radius of a... View Article

Find the radius of a sphere whose surface area is 154 cm². (Assume π = 22/7)

Given The surface area of sphere is 154 cm² Find out We have to find out the radius of the sphere Solution Let the radius of the sphere be... View Article

Find the square roots of 100 and 169 by the method of repeated subtraction.

Solution For 100 100 – 1 = 99 [1] 99 – 3 = 96 [2] 96 – 5 = 91 [3] 91 – 7 = 84 [4] 84 – 9 = 75 [5] 75 – 11 = 64 [6] 64 – 13 = 51 [7] 51... View Article

A circle is a plane figure. Write True or False. Give reason for your answer

Write True or False: A circle is a plane figure. True. A circle is a 2d figure and it can be drawn on a plane. A circle is also termed... View Article

Find the 31st term of an A.P. whose 11th term is 38 and the 16th term is 73.

Given that, 11th term, a11 = 38 16th term, a16 = 73 Find out We have to find out the 31st term We know that,... View Article

Consider the following parallelograms. Find the values of the unknown x, y, z

Solution: (i) y = 100° {opposite angles of a parallelogram} x + 100° = 180° {Adjacent angles of a parallelogram} ⇒ x =... View Article

Solve 2x + 3y = 11 and 2x – 4y = – 24 and hence find the value of ‘m’ for which y = mx + 3.

2x + 3y = 11…………………………..(I) 2x – 4y =... View Article

Why will a sheet of paper fall slower than one that is crumpled into a ball?

A sheet of paper falls slower than the crumpled ball. A sheet of paper has a larger surface area when compared to a crumpled paper ball. A... View Article