# Archives

## 07 July 2021: The Hindu Analysis

UPSC Current Affairs Preparation: The Hindu Analysis Watch expert analysis of â€˜The Hinduâ€™ dated 07th Jul 2021. Important news and views to boost... View Article

## World Heritage Convention

The World Heritage Convention is an important global conservation instrument. Such international treaties and conventions are very important for... 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 = 3y

We have to express x = 3y in the form ax + by + c = 0 and indicate the values of a, b and c in each case. Solution The equation x = 3y can... View Article

## In Fig., sides QP and RQ of Î”PQR are produced to points S and T respectively. If SPR = 135Â° and PQT = 110Â°, find PRQ.

Solution  ∠TQP = 110°, ∠SPR = 135° TQR is a Straight line (from figure) As we have studied in this chapter, TQP... View Article

## In the figure, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.

Given that A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR To Prove BC || QR Proof In ΔOPQ, AB || PQ... View Article

## If 1 part of a red pigment requires 75 mL of base, how much red pigment should we mix with 1800 mL of base?

Solution Let the parts of red pigment mix with 1800 mL base be x. Since the red pigment is in Direct proportion with parts of the base, ... View Article

## Amanâ€™s age is three times his sonâ€™s age. Ten years ago he was five times his sonâ€™s age. Find their present ages.

Solution Let the age of Aman’s son be x  Let the age of Aman will be 3x. According to the given details, the equation becomes 5(x... 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: y-2 = 0

We have to express y–2 = 0 in the form ax + by + c = 0 and indicate the values of a, b and c in each case. Solution The equation... 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: 2x = -5y

We have to express 2x = –5y in the form ax + by + c = 0 and indicate the values of a, b and c in each case. Solution The equation 2x =... View Article

## Find the area of the shaded region in Fig. if ABCD is a square of side 14 cm and APD and BPC are semicircles.

Given ABCD is a square of side 14 cm and APD and BPC are semicircles. Solution Radius =14/2=7 Area of shaded region=Area of square-Area of 2... 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: 3x + 2 = 0

We have to express 3x+2 = 0 in the form ax + by + c = 0 and indicate the values of a, b and c in each case. Solution The equation 3x+2 = 0 can... View Article

## Choose the correct choice in the following and justify: (i) 30th term of the A.P: 10,7, 4, â€¦, is (A) 97 (B) 77 (C) âˆ’77 (D) âˆ’87

The correct answer is option C -77 Given that A.P. = 10, 7, 4, … Find out 30th term Solution We know that from given series... View Article

## A machine in a soft drink factory fills 840 bottles in six hours. How many bottles will it fill in five hours?

Solution Let the number of bottles filled = n Number of bottles 840 a Time in hours 06 5 The ratio of hours and... View Article

## An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.

Given The length of two equal sides of an isosceles triangle is 12 cm. Perimeter = 30 cm. Find out We have to determine the area of a... View Article

## How many diagonals does each of the following have? a) A convex quadrilateral (b) A regular hexagon (c) A triangle

a) A convex quadrilateral:2. b) A regular hexagon: 9    c) A triangle: 0... 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: -2x + 3y = 6

We have to express –2x+3y = 6 in the form ax + by + c = 0 and indicate the values of a, b and c in each case. Solution The equation... View Article

## Tick the correct answer and justify: In Î”ABC, AB = 6âˆš3 cm, AC = 12 cm and BC = 6 cm. The angle B is: (A) 120Â° (B) 60Â° (C) 90Â° (D) 45Â°

Given In ΔABC, AB = 6√3 cm, AC = 12 cm and BC = 6 cm. Find out We have to find the measure of angle B On applying pythagoras... View Article

## In each of the following find the value of â€˜kâ€™, for which the points are collinear. (i) (7, -2) , (5, 1) , (3, -k) (ii) (8, 1) , (k, -4) , (2, -5)

(i) For collinear points, area of triangle formed by them is always zero. Let points (7, -2) (5, 1), and (3, k) are vertices of a triangle. Area... View Article

## Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.

Let us assume ABCD be a quadrilateral and P, Q, R and S are the mid points of AB, BC, CD and DA respectively. Now, From ΔACD, R and S are... View Article

## Prove that the sum of the squares of the sides of rhombus is equal to the sum of the squares of its diagonals.

Given: ABCD is a rhombus To prove: AB2 + BC2 + CD2 + DA2 Poof: ABCD is rhombus and let diagonals AC and BD bisect... View Article