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Find the height of the cylinder whose volume if 1.54 m² and diameter of the base is 140 cm.

Given Volume of cylinder = 1.54 m3 Diameter of cylinder = 140 cm Find out We have to find out the height of the cylinder Solution... View Article

Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42cm.

Given The length of the two sides is given as 18 cm and 10 cm respectively. Perimeter = 42 cm. Find out We have to determine the area of a... View Article

In Fig. if PQ ST, PQR = 110° and RST = 130°, find QRS. [Hint : Draw a line parallel to ST through point R.]

Solution: Construct a line XY parallel to PQ. We have to find the value of ∠QRS PQ || ST [Given] and XY || ST [... View Article

If the volume of a right circular cone of height 9cm is 48πcm3, find the diameter of its base.

Given Height of cone (h) = 9 cm Volume of cone (V) = 48π cm3 Find out We have to find the diameter of its base Solution V = (1/3)... View Article

Given a parallelogram ABCD. Complete each statement along with the definition or property used.

Solution (i) AD = BC {Opposite sides of a parallelogram are equal} (ii) ∠DCB = ∠DAB {Opposite angles of a parallelogram are... View Article

Fifteen years from now Ravi’s age will be four times his present age. What is Ravi’s present age?

Solution Let the present age of Ravi be ‘G’. Fifteen years later, Ravi age will be (G+15) years. Accordding to the given... View Article

Is zero a rational number? Can you write it in the form p/q where p and q are integers and q ≠ 0?

A number is said to be a rational number if it can be written in the form of p/q, where p and q are integers and q ≠ 0 We can write 0... View Article

In Figure, ABC is a triangle in which ∠ABC > 90° and AD ⊥ CB produced. Prove that AC2 = AB2 + BC2 + 2 BC.BD.

Given ABC is a triangle in which ∠ABC > 90∘ and AD⊥CB is produced. To Prove AC2= AB2+ BC2 – 2 BC.BD. Proof... View Article

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