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Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

Draw a circle and connect two points A and B such that AB becomes the diameter of the circle. Next, draw two tangents PQ and RS at points A and B... View Article

Why a block of plastic when released under water come up to the surface of water?

The density of plastic is lesser than that of water. Therefore, the force of buoyancy on the plastic block will be greater than the weight of the... View Article

How many sides does a regular polygon have if each of its interior angles is 165°?

Given The measure of interior angle = 165° Find out We have to find the number of sides of a polygon Formula (no. of sides) x (measure... View Article

ABC and ADC are two right triangles with common hypotenuse AC. Prove that ∠ CAD = ∠CBD.

Given: ABC and ADC are two right-angle triangles with common hypotenuse AC.To prove: ∠ADB=∠CBDSolution: ∠ABC=∠ADC=90°The... View Article

Which term of the AP: 121, 117, 113, . . ., is its first negative term? [Hint: Find n for a_n < 0]

Given that The AP series is 121, 117, 113, . . ., Thus, first term, a = 121 Common difference, d = 117-121= -4 Find out The first negative term... View Article

If two zeroes of the polynomial x⁴-6x³-26x² + 138x-35 are 2 ±√3, find other zeroes.

The given equation is a polynomial equation of degree 4, hence there will be total 4 roots. Let f(x) = x4-6x3-26x2+138x-35 Since 2 +√3 and... View Article

ABCD is a cyclic quadrilateral (see Fig.) . Find the angles of the cyclic quadrilateral.

We have to find the angles of the given quadrilateral We know that the sum of the opposite angles of a cyclic quadrilateral is 180o... View Article

Find the roots of the following equations: (i) x-1/x = 3, x ≠ 0 (ii) 1/x + 4 – 1/x-7 = 11/30, x = -4, 7

(i) x-1/x = 3 ⇒ x2 – 3x -1 = 0 On comparing the given equation... View Article

Find the smallest square number that is divisible by each of the numbers 4, 9 and 10.

Solution At first we have to find L.C.M of 4, 9 and 10 4 = 2 x 2 x 1 9 = 3 x 3 x 1 5 = 1 x 5 Hence, L.C.M = (2 × 2 × 3 x... View Article

Write the following in decimal form and say what kind of decimal expansion each has :

(i) 36/100 Solution: the remainder becomes zero. Hence, decimal expansion becomes terminating. 36/100 = 0.36 (ii)1/11 Solution:... View Article

Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°.

Given A circle with a radius 6 cm and angle of the sector is 60° Find out We have to find out the area of a sector Solution Given:... View Article

D is a point on the side BC of a triangle ABC such that ∠ADC = ∠BAC. Show that CA2 = CB.CD

Given that D is a point on the side BC of a triangle ABC such that ∠ADC = ∠BAC. To Prove CA2 = CB.CD Proof... View Article

Which of the following cannot be the probability of an event? (A) 2/3 (B) -1.5 (C) 15% (D) 0.7

The probability of any event (E) always lies between 0 and 1 i.e. 0 ≤ P(E) ≤ 1. So, from the above options, option (B) -1.5 cannot be the... View Article

Line segment joining the centre to any point on the circle is a radius of the circle.

Write True or False: (i) Line segment joining the centre to any point on the circle is a radius of the circle. True Any line segment... View Article

Can you suggest some changes in your school which would make it environment-friendly?

Few important changes that can help make schools more environment-friendly include: Providing a desk for students and teachers to... View Article

Find the smallest square number that is divisible by each of the numbers 8, 15 and 20.

Solution At first we have to find L.C.M of we have to find L.C.M of 8, 15 and 20 8 = 1 x 2 x 2 x 2 15 = 1 x 5 x 3 20 = 1 x 2 x 5 x 2... View Article

How many sides does a regular polygon have if the measure of an exterior angle is 24°?

Given The measure of exterior angle = 24° Find out We have to find the number of sides of a polygon Formula (no. of sides) x (measure of... View Article

Determine the A.P. whose third term is 16 and the 7th term exceeds the 5th term by 12.

Given that Third term, a3 = 16 The 7th term exceeds the 5th term by 12=>a7 − a5 = 12 Find out We have to find out the AP series... View Article

Let ΔABC ~ ΔDEF and their areas be, respectively, 64 cm^2 and 121 cm^2. If EF = 15.4 cm, find BC.

Given: ΔABC ~ ΔDEF and their areas are, respectively, 64 cm2 and 121 cm2. Area of ΔABC = 64 cm2 Area of ΔDEF = 121 cm2 EF = 15.4 cm To Find:... View Article

In Figure, ABC is a triangle in which ∠ ABC < 90° and AD ⊥ BC. 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