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On dividing x³-3x² + x + 2 by a polynomial g(x) , the quotient and remainder were x-2 and -2x + 4, respectively. Find g(x) .

Given, Dividend, p(x) = x3-3x2+x+2 Quotient = x-2 Remainder = –2x+4 We have to determine the value of Divisor, g(x)... View Article

Radha made a picture of an aeroplane with coloured paper as shown in Fig Find the total area of the paper used.

For the triangle I section: Solution Area of triangle can be calculated by Heron’s Formula, where a = 5 cm... View Article

How does the force of gravitation between two objects change when the distance between them is reduced to half?

When the distance between the two objects is halved, the gravitational force becomes four times. Proof According to the universal law of... View Article

The following table gives the distribution of a life time of 400 neon lamps. Find the median lifetime of a lamp.

Lifetime (in hours) Number of lamps 1500-2000 14 2000-2500 56 2500-3000 60 3000-3500 86 3500-4000 74 4000-4500 62 4500-5000 48... View Article

The number of students in a hostel, speaking different languages is given below. Display the data in a pie chart.

Solution: 00

l and m are two parallel lines intersected by another pair of parallel lines p and q (see Fig.) . Show that ΔABC ΔCDA.

Solution Given l and m are two parallel lines p and q are another pair of parallel lines To Prove... View Article

Is it possible to design a rectangular park of perimeter 80 and area 400 m²? If so find its length and breadth.

Let the length and breadth of the park be l and b. Perimeter of the rectangular park = 2 (l + b)... View Article

In Figure, ABD is a triangle right angled at A and AC ⊥ BD. Show that (i) AB2 = BC × BD (ii) AC2 = BC × DC (iii) AD2 = BD × CD

ABD is a triangle right angled at A and AC ⊥ BD. To Prove (i) AB2 = BC × BD(ii) AC2 = BC × DC(iii)... View Article

n Fig. D is a point on hypotenuse AC of ∆ABC, such that BD ⊥AC, DM ⊥ BC and DN ⊥ AB. Prove that: (i) DM2 = DN . MC (ii) DN2 = DM . AN.

Given D is a point on hypotenuse AC of ∆ABC, such that BD ⊥AC, DM ⊥ BC and DN ⊥... View Article

The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.

Given that The altitude of a right triangle is 7 cm less than its base. The hypotenuse is 13 cm,... View Article

Without doing any calculation, find the numbers which are surely not perfect squares. i) 153 ii) 257 iii) 408 iv) 441

Solution We know that natural numbers ending with the digits 0, 2, 3, 7 and 8 are not perfect squares.... View Article

AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD (see Fig.) . Show that A > C and B > D.

Solution Given From ΔABD, AB < AD < BD So, ADB < ABD — (i) (Since angle opposite to longer side... View Article

In Fig., a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. (Use π = 3.14)

Solution By Pythagoras theorem, OB2=DA2+AB2 BO2=(20)2+(20)2 OB2=400+400 OB2=800 OB=√800 OB=√(2*2*2*2*5*5) OB=2*2*5√2 OB=20√2 Area of the quadrant = (πR2)/4 cm2 = (3.14/4)×(20√2)2 cm2 =... View Article

Express the linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case: x -(y/5) -10 = 0

We have to express x –(y/5)–10 = 0 in the form ax + by + c = 0 and indicate the... View Article

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