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Give the geometric representations of y = 3 as an equation (i) in one variable (ii) in two variables

(i) If y = 3 is treated as an equation in one variable y only, then it has the unique solution y = 3, which is a point on the number line... View Article

If the 3rd and the 9th terms of an A.P. are 4 and − 8 respectively. Which term of this A.P. is zero.

Given that 3rd term, a3 = 4 and 9th term, a9 = −8 Find out We need to find out which term of the given series is zero... View Article

The angles of quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral.

Given The angles of quadrilateral are in the ratio 3 : 5 : 9 : 13. Find out We have to find out the angles of the quadrilateral Solution... View Article

Classify the following numbers as rational or irrational: (i) 2 -√5 (ii) (3 + √23) – √23 (iii) 2√7/7√7 (iv) 1/√2 (v) 2

(i) 2 –√5 As √5 = 2.2360678… This is non-terminating and non-recurring. It is an irrational number. On... View Article

Construct a right triangle whose base is 12cm and sum of its hypotenuse and other side is 18 cm.

Procedure 1. Draw a line segment of base BC = 12 cm 2. Measure and draw ∠B = 90° and draw the ray BX 3. Using a compass measure AB+AC = 18 cm.... View Article

Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.

Given that Second term, a2 = 14 Third term, a3 = 18 Find out We need to find the sum of first 51 terms of the given series Solution... View Article

A circle has only finite number of equal chords. Write True or False. Give reason for your answer

Write True or False: A circle has only finite number of equal chords. False There can be infinite number of equal chords in a... View Article

An A.P. consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.

Given that 3rd term, a3 = 12 50th term, a50 = 106 Find out We have to find out the 29th term Solution We know that,... View Article

Find the square root of the following decimal numbers. i. 2.56 ii. 7.29 iii. 51.84 iv. 42.25 v. 31.36

Solution We will find the square root of given decimals using the long division method (i) 2.56 Hence √2.56 = 1.6 (ii) 7.29 Hence √7.29... View Article

Give the equations of two lines passing through (2, 14) . How many more such lines are there, and why?

Given point is (2,14) x=2 and y=14 We can form various equations: y-x = 14-2 = 12 x+y = 2+14 =16 2x+y = 4+14 = 18 y-2x = 14-4 = 10... View Article

Find the area of the shaded region in Fig.if PQ = 24 cm, PR = 7 cm and O is the centre of the circle.

On applying Pythagoras theorem RQ2=RP2+PQ2 RQ2=(7)2+(24)2 RQ2=625 RQ=√625 RQ=√5*5*5*5 RQ=5*5 =25 The radius of circle =25/2cm Areas... View Article

A conical pit of top diameter 3.5m is 12m deep. What is its capacity in kiloliters? (Assume π = 22/7)

Given Radius of cone (r) = 3.5/2 m Height of cone (h) = 12 m Find out We have to find the capacity in kiloleters Solution Volume... View Article

PQR is a triangle right angled at P and M is a point on QR such that PM ⊥ QR. Show that PM^2 = QM × MR.

Given: ΔPQR is right-angled at P is a point on QR such that PM ⊥QR. To Prove: PM2 = QM × MR Proof: ΔPMQ and ΔPMR are right triangles... View Article

D and E are points on sides AB and AC respectively of ΔABC such that ar(DBC) = ar(EBC) . Prove that DE || BC.

Solution ΔDBC and ΔEBC are on the same base BC and are having equal areas. Hence, They will lie between the same parallel... View Article

The height of a cone is 15cm. If its volume is 1570cm³, find the diameter of its base. (Use π = 3.14)

Given Height of the cone, h = 15 cm The volume of cone =1570 cm3 Find out We have to find out the diameter of its base Solution Volume of... View Article

The diameter of a sphere is decreased by 25%. By what percent does its curved surface area decrease?

Given The diameter of a sphere is decreased by 25% Find out We have to find out by what per cent does its curved surface area decreases?... View Article

In the figure, ABC and AMP are two right triangles, right angled at B and M respectively, prove that:

Given ABC and AMP are two right triangles, right angled at B and M respectively To Prove (i) ΔABC ~ ΔAMP (ii) CA/PA = BC/MP Proof... View Article

What is a regular polygon? State the name of a regular polygon of (i) 3 sides (ii) 4 sides (iii) 6 sides

A polygon is a closed two-dimensional figure, which is made up of straight lines. Whenall the sides and interior angles of the polygon are... View Article

Give the geometric representations of 2x + 9 = 0 as an equation (i) in one variable (ii) in two variables

Firstly, we solve 2x + 9 = 0, to get x = -9/2 (i) If x = -9/2 is treated as an equation in one variable x only, then it has the unique... View Article

Find the cost of digging a cuboidal pit 8m long, 6m broad and 3m deep at the rate of Rs 30 per m³.

Given Length of the cuboidal pit, l = 8 m Width of the cuboidal pit, b = 6m Height of cuboidal pit, h = 3m Find out We have to... View Article