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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

Obtain all other zeroes of 3x⁴ + 6x³-2x²-10x-5, if two of its zeroes are √(5/3) and – √(5/3) .

The given polynomial equation is of degree 4, hence there will be total 4 roots. Given that √(5/3) and - √(5/3) are zeroes of... View Article

The following figures GUNS and RUNS are parallelograms. Find x and y. (Lengths are in cm)

(i) SG = NU and SN = GU {opposite sides of a parallelogram are equal} 3x = 18 x = 18/3 ⇒ x =6 3y – 1 = 26 and, ⇒ 3y... View Article

Find the measure of each exterior angle of a regular polygon of (i) 9 sides (ii) 15 sides

Sum of angles a regular polygon having side n = (n-2)×180° (i) Sum of angles a regular polygon having side 9 = (9-2)×180°=... View Article

ABC and DBC are two isosceles triangles on the same base BC (see Fig.) . Show that ABD = ACD.

Solution Given AB=AC,BD=DC To Prove ∠ABD = ∠ACD Proof From ∆ABD, AD=AC ∴∠1=∠2 [angle opposite... View Article

Find the surface area of a sphere of diameter: (i) 14cm (ii) 21cm (iii) 3.5cm (Assume π = 22/7)

(i) Radius of sphere, r = diameter/2 = 14/2 cm = 7 cm We know that, Surface area of sphere = 4πr²= 4×(22/7)×72 =... View Article

Find the surface area of a sphere of radius: (i) 10.5cm (ii) 5.6cm (iii) 14cm (Assume π = 22/7)

Solution: We know that, Surface area of sphere (SA) = 4πr² (i) Radius of sphere, r = 10.5 cm SA = 4×(22/7)×10.52 =... View Article

A quadrilateral ABCD is drawn to circumscribe a circle (see Fig.) . Prove that AB + CD = AD + BC

Let the P, Q, R and S be point of contacts for tangent AB, BC, CD and DA respectively . AP = AS ……..(1) BP = BQ... View Article

Find the number of terms in each of the following A.P. (i) 7, 13, 19, …, 205 (ii) 18, 15_1/2, 13, …, -47

(i) Given that The AP series 7, 13, 19, …, 205 Find out The number of terms in the series Solution First term, a = 7 Common... View Article

Show that the diagonals of a parallelogram divide it into four triangles of equal area.

Solution We have to Prove the diagonals of a parallelogram divide it into four triangles of equal area. Proof O is the mid point of AC and... View Article

From the choices given below, choose the equation whose graphs are given in the figures.

Let’s verify each given cases, whether they are satisfying the solution given on graph or not, (i) y=x Given point (1,-1) x=1 and... View Article

In the figure, altitudes AD and CE of ΔABC intersect each other at the point P. Show that:

Given Altitudes AD and CE of ΔABC intersect each other at the point P. To Prove (i) ΔAEP ~ ΔCDP(ii) ΔABD ~... View Article

ABC is an isosceles triangle with AC = BC. If AB2 = 2AC2, prove that ABC is a right triangle.

Given: ABC is an isosceles triangle with AC being equal to BC and AB square being equal to 2 AC square. i.e. AC = BC and AB2 = 2AC2 To... View Article