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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

In Fig. lines AB and CD intersect at O. If AOC + BOE = 70° and BOD = 40°, find BOE and reflex COE.

Given AB and CD are straight lines. ∠AOC + ∠BOE = 70° ------(i) ∠BOD = 40° -------(ii) AB is a straight... View Article

If (1, 2) , (4, y) , (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.

Let A,B,C and D be the points of a parallelogram : A(1,2), B(4,y), C(x,6) and D(3,5). Since the diagonals of a parallelogram bisect each... View Article

How many litres of milk can a hemispherical bowl of diameter 10.5cm hold? (Assume π = 22/7)

Given Diameter of hemispherical bowl = 10.5 cm Radius of hemispherical bowl, r = 10.5/2 cm = 5.25 cm Formula Volume of the... View Article

AD and BC are equal perpendiculars to a line segment AB (see Fig.) . Show that CD bisects AB.

Solution Given AD and BC are equal perpendiculars to a line segment AB To Prove CD bisects AB Proof Two triangles ΔAOD and ΔBOC ∠ AOD = ∠... View Article

Find the coordinates of the point which divides the join of (- 1, 7) and (4, – 3) in the ratio 2:3.

Given, the line joining two points (-1, 7) and (4, -3) is divided by a point in the ratio of 2:3. Let us assume that P(x, y) be the required... View Article

In Fig., ABCD is a parallelogram, AE ⊥ DC and CF ⊥ AD. If AB = 16 cm, AE = 8 cm and CF = 10 cm, find AD.

(i) From the diagram we observe that trapezium ABCD and triangle PCD have a common base CD and these are lying between the same parallel... View Article

In a right triangle ABC, ∠B = 90°. a. If AB = 6 cm, BC = 8 cm, find AC b. If AC = 13 cm, BC = 5 cm, find AB

Solution (a) In right triangle ABC According to Pythagoras Theorem AC2 = AB2 + BC2 AC2 = 62 + 82... View Article

How will you describe the position of a table lamp on your study table to another person?

To describe the position of a table lamp on your study table to another person we follow the given set[s From the figure given below... View Article