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ABCD is a rectangle in which diagonal AC bisects ∠A as well as ∠C. Show that: (i) ABCD is a square (ii) Diagonal BD bisects ∠B as well as ∠D.

A rectangle ABCD such that AC bisects ∠A as well as ∠C, so ∠BAC = ∠DAC and, ∠DCA = ∠BCA... View Article

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (see Fig.) . Show that (i) ΔAPB ≅ ΔCQD (ii) AP = CQ

Solution ABCD is a parallelogram DP = BQ (i) ∆APB ≅ ∆CQD (i) In ∆APB and ∆CQD, we have ∠APB = ∠CQD [Each 90°] AB = CD [ Opposite sides of... View Article

The diameter of a metallic ball is 4.2cm. What is the mass of the ball, if the density of the metal is 8.9 g per cm²? (Assume π = 22/7)

Given Diameter of a metallic ball = 4.2 cm The radius of the metallic ball, r = 4.2/2 cm = 2.1 cm Solution We know that volume of the... View Article

Top surface of a raised platform is in the shape of a regular octagon as shown in the figure. Find the area of the octagonal surface.

Solution: Octagon having eight equal sides, each 5 m. (given) Divide the octagon as shown in the below figure, 2 trapeziums whose parallel... View Article

A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.

Given Radius of the sphere (R) = 4.2 cm Radius of cylinder (r) = 6 cm Find out We have to find the height of the cylinder Solution let... View Article

Give examples of polynomials p(x) , g(x) , q(x) and r(x) , which satisfy the division algorithm and (i) deg p(x) = deg q(x) (ii) deg q(x) = deg r(x) (iii) deg r(x) = 0

Dividend = Divisor × Quotient + Remainder ∴ p(x) = g(x)×q(x)+r(x) Where r(x) = 0 or degree of r(x)< degree of g(x).... View Article

For the following A.P.s, write the first term and the common difference. (i) 3, 1, – 1, – 3 … (ii) -5, – 1, 3, 7 … (iii) 1/3, 5/3, 9/3, 13/3 …. (iv) 0.6, 1.7, 2.8, 3.9 …

(i) 3, 1, –1, –3… First term = a = 3,Common difference (d) = Second term – first term = Third term – second term... View Article

Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

Considering, ∆OAP and ∆OBP OA = OB …………..(radius of large circle) OP = OP... View Article

The ages of Rahul and Haroon are in the ratio 5:7. Four years later the sum of their ages will be 56 years. What are their present ages?

Solution Let the ages of Rahul and Haroon be ‘5p’ and ‘7p’. Four years later, The ages of Rahul and Haroon will be (5p... View Article

A chord of a circle, which is twice as long as its radius, is a diameter of the circle. Write True or False. Give reason for your answer

Write True or False: A chord of a circle, which is twice as long as its radius, is a diameter of the circle. True. Any chord whose... View Article

Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts. Give the justification of the construction

Procedure A line segment with a measure of 7.6 cm length is divided in the ratio of 5:8 as follows. 1. Draw line segment AB with the length... View Article

Express 0.99999…. in the form p/q . Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.

Lets’s assume x = 0.99999…… 10x = 9.99999…. Hence, 10x – x = (9.99999…..) –... View Article

A child has a die whose six faces show the letters as given below: The die is thrown once. What is the probability of getting (i) A? (ii) D?

The total number of possible outcomes (or events) = 6 P(E) = (Number of favourable outcomes/ Total number of outcomes) (i) The total number... View Article

Find the area of a rhombus if its vertices are (3, 0) , (4, 5) , (-1, 4) and (-2,-1) taken in order. [Hint: Area of a rhombus = 1/2(product of its diagonals)

Let us assume that A(3, 0), B (4, 5), C( – 1, 4) and D ( – 2, – 1) are the vertices of a rhombus ABCD Length of the diagonal AC= Length of... View Article

Show that a₁, a₂ … , a_n , … form an AP where an is defined as below (i) a_n = 3 + 4n (ii) a_n = 9−5n Also find the sum of the first 15 terms in each case.

(i) Given an = 3+4n Find out We have to find the sm of first 15 terms a1 = 3+4(1) = 7 a2 = 3+4(2) = 3+8 = 11 a3 = 3+4(3)... View Article

How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions 5.5 cm × 10 cm × 3.5 cm?

We know that coins are cylindrical in shape Given So, height (H) of the cylinder = 2 mm = 0.2 cm Radius (r) of circular end of coins = 1.75/2 =... View Article

In Fig. ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region.

Solution Area of segment=Area of quadrant -Area of ∆BAC =1/4πr2-1/2*AC*AB =1/4*22/7*14*14-1/2*14*14 =11*14-98 =154-98 =56 cm2 Semicircle R=?... View Article

Gravitational force acts on all objects in proportion to their masses. Why then does a heavy object not fall faster than a light object?

All objects fall from the top with a constant acceleration called acceleration due to gravity (g). This is constant on earth and therefore the... View Article

. In a cricket match, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary.

Given As per the given parametersTotal number of balls batswoman plays = 30 Numbers of boundary hit by batswoman = 6 Find outWe have... View Article

Find the capacity in litres of a conical vessel with (i) radius 7cm, slant height 25 cm (ii) height 12 cm, slant height 12 cm (Assume π = 22/7)

Volume of cone (V) = (1/3) × πr2h (i) Given Radius of cone (r) = 7 cm Slant height of cone (l) = 25 cm h =... View Article

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