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In Fig. OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the (i) quadrant OACB, (ii) shaded region.

Solution Radius of the quadrant = 3.5 cm = 7/2 cm (i) Area of shaded region=Area of quadrant =1/4πr2 =1/4*22/7*3.5*3.5 =38.5/4 =9.625... View Article

In the following figure, E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If AD ⊥ BC and EF ⊥ AC, prove that ΔABD ~ ΔECF.

Given that Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of ΔPQR To... View Article

The measures of two adjacent angles of a parallelogram are in the ratio 3 : 2. Find the measure of each of the angles of the parallelogram.

In parallelogram ABCD. Let the measures of two adjacent angles ∠A be 3x Let the measure of ∠B be 2x ∠A + ∠B = 180°... View Article

Is it possible to have a regular polygon with measure of each exterior angle as 22°? Can it be an interior angle of a regular polygon? Why?

(a) given here, measure of exterior angle = 22° We know that (no. of sides) x (measure of exterior angle) = 360° On... View Article

Find the number of digits in the square root of each of the following numbers (without any calculation) . i. 144 ii. 4489 iii. 27225 iv. 390625

Solution If n is the number of digits in a square number then The number of digits in the square root can be calculated as n/2 if n is even... View Article

Find the distance between the points (0, 0) and (36, 15) . Can you now find the distance between the two towns A and B discussed in Section 7.2.

Let us consider, town A at point (0, 0). Therefore, town B will be at point (36, 15). Distance between points (0, 0) and (36, 15) can be obtained... View Article

Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number.

No, the square roots of all positive integers in not irrational. For example √9 = 3, √25 = 5, hence square roots of all positive... View Article

Two APs have the same common difference. The difference between their 100th term is 100, what is the difference between their 1000th terms?

Given that Two APs have the same common difference. The difference between their 100th term is 100, Find out We need to find out the difference... View Article

In an isosceles triangle ABC, with AB = AC, the bisectors of B and C intersect each other at O. Join A to O. Show that: (i) OB = OC (ii) AO bisects A

Solution Given AB = AC and The bisectors of B and C intersect each other at O To Prove (i) OB = OC (ii) AO bisects A Proof (i) OB =... View Article

If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.

Solution Given: ABCD is a cyclic quadrilateral. Diagonals of ABCD are also diameters of circle.To prove: ABCD is a rectangle ProofAC=BD... View Article

ABC is a right-angled triangle and O is the mid-point of the side opposite to the right angle. Explain why O is equidistant from A, B and C.

Solution Construction: Draw two lines AD and DC such that AD II BC and AB II DC AD = BC , AB = DC Since, ABCD is a rectangle. Opposite... View Article

Find the area of the shaded region in Fig. if radii of the two concentric circles with centre O are 7 cm and 14 cm respectively and AOC = 40°.

Given, Angle made by sector = 40°, Radius the inner circle = r = 7 cm, Radius of the outer circle = R = 14 cm Find out We have to find the... View Article

Find the sum of the following APs. (i) 2, 7, 12 ,…., to 10 terms. (ii) − 37, − 33, − 29 ,…, to 12 terms (iii) 0.6, 1.7, 2.8 ,…….., to 100 terms (iv) 1/15, 1/12, 1/10, …… , to 11 terms

(i) Given, 2, 7, 12 ,…, to 10 terms For this A.P., first term, a = 2 And common difference,... View Article

Rashmi has a road map with a scale of 1 cm representing 18 km. She drives on a road for 72 km. What would be her distance covered in the map?

Solution Let the distance covered on the map is x cm Since distance covered on road is directly proportional to the distance covered on... View Article

ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.

Given P, Q, R and S are the mid points of Rectangle ABCD. Construction: Join AC and BD To Prove: PQRS is a rhombus. Proof We... View Article

Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB = 2CD, find the ratio of the areas of triangles AOB and COD.

Given Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. AB = 2CD Find out We have to find the ratio of the... View Article

A capsule of medicine is in the shape of a sphere of diameter 3.5mm. How much medicine (in mm³) is needed to fill this capsule? (Assume π = 22/7)

Given Diameter of capsule = 3.5 mm Radius of capsule, say r = diameter/ 2 = (3.5/2) mm = 1.75mm Find out We have to find out how much... View Article

In Fig., ABCD is a parallelogram and BC is produced to a point Q such that AD = CQ. If AQ intersect DC at P, show that ar (BPC) = ar (DPQ) . [Hint : Join AC.]

Solution Given: From the given diagram ABCD is a ||gm AD=CQ To prove: ar.(BPC)=ar.(DPQ) Construction: Join AC. Proof: ACQD... View Article

The base of an isosceles triangle is 4/3 cm. The perimeter of the triangle is 62/15 What is the length of either of the remaining equal sides?

Solution Given The base of an isosceles triangle is 4/3 cm. The perimeter of the triangle is 62/15 cm Find out We have to determine... View Article

If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side.

Solution Given: AB and AC are diameters of two circlesTo prove: The point of intersection is D, which lies on the BC.Construction:... View Article

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