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Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.

Given AM and DN are the medians of triangles ABC and DEF respectively and ΔABC ~ ΔDEF. To Prove The ratio of the areas of two similar... View Article

The sum of the third and the seventh terms of an AP is 6 and their product is 8. Find the sum of first sixteen terms of the AP.

Given that The sum of the third and the seventh terms of an AP is 6 and their product is 8 Find out The sum of the first sixteen terms of the AP.... View Article

State whether the following statements are true or false: Every natural number is a whole number. Give reasons for your answers.

True Explanation: The natural numbers starts from 1, 2, 3, 4 …..The whole number starts from 0, 1, 2, 3 , 4 …..Here we can... View Article

The diagonals of a quadrilateral ABCD intersect each other at the point O such that AO/BO = CO/DO. Show that ABCD is a trapezium.

Given, Quadrilateral ABCD where AC and BD intersects each other at O such that, AO/BO = CO/DO. To prove ABCD is a trapezium Proof Construction... View Article

The ages of Hari and Harry are in the ratio 5:7. Four years from now the ratio of their ages will be 3:4. Find their present ages.

Solution Let the age of Hari be 5x Let the age of Harry be 7x. 4 years later, The age of Hari = 5x + 4 The age of Harry = 7x + 4 According... View Article

Observe the following pattern and supply the missing numbers. 112 = 121 1012 = 10201 101012 = 102030201 10101012 = ……………………… …………2 = 10203040504030201

Solution From the given pattern, we note that the middle digit is 4, then the number to be squared is 10101 and its square is... View Article

The sum of 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the A.P.

Given that The sum of the 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 44 Find out First three terms of AP... View Article

In Fig. the side QR of ΔPQR is produced to a point S. If the bisectors of PQR and PRS meet at point T, then prove that QTR = 1/2 QPR.

Given: T is the bisector of ∠PQR and ∠PRS, To Prove: ∠QTR = ½ ∠QPR Proof: From ΔPQR. ... View Article

If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D, prove that AB = CD (see Fig) .

Solution Given : Two concentric circles with O. A line intersect them at A, B, C, and D To prove: AB=CD... View Article

A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?

Solution Side of a square = 60 m Length, l = 80 m According to the given details, Perimeter of rectangular field = Perimeter of... View Article

State whether the following statements are true or false: Every irrational number is a real number. Give reasons for your answers.

True Irrational numbers are the number that cannot be written in the form of p/q , p and q are the integers and q ≠ 0.Examples of irrational... View Article

If the lateral surface of a cylinder is 94.2cm² and its height is 5cm, then find (i) radius of its base (ii) its volume.[Use π = 3.14]

Given Lateral surface of cylinder = 94.2 cm2 Height of cylinder (h) = 5 cm Solution (i) radius of its base The lateral surface is of... View Article

Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a football game?

The tossing of a coin is estimated to be a fair way of determining which team should get the ball at the beginning of a football game as we know... View Article

State whether the following statements are true or false: Every real number is an irrational number. Give reasons for your answers.

FalseEvery irrational number is a real number but every real number is not an irrational number as real numbers include both rational and... View Article

Find the values of k for each of the following quadratic equations, so that they have two equal roots. (i) 2x² + kx + 3 = 0 (ii) kx (x – 2) + 6 = 0

(i) 2x2 + kx + 3 = 0 On comparing the given equation with ax2 + bx + c = 0, we get, a =... View Article

In Fig. POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that ROS = 1/2 (QOS – POS) .

Given, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. To Prove: ROS = 1/2 (QOS - POS) .... View Article

What is the sum of the measures of the angles of a convex quadrilateral? Will this property hold if the quadrilateral is not convex?

Let us assume ABCD as a convex quadrilateral. From the figure, we indicate that the quadrilateral ABCD is formed by two triangles, i.e.... View Article

In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.

To prove: 3AB2 = 4AE2 Proof: Let each side of one equilateral ∆ = a BE = 1/2a -[perpendicular bisects the side in on an... View Article

What could be the possible ‘one’s’ digits of the square root of each of the following numbers? i) 9801 ii) 99856 iii) 998001 iv) 657666025

Solution i. 9801 Unit place digit of the number is 1 We know that 12 = 1 & 92 = 81 whose unit place is 1 Therefore, one’s... View Article

Which one of the following options is true, and why? y = 3x + 5 has 1) A unique solution 2) Only two solutions 3) Infinitely many solutions

Given Linear equation: y = 3x + 5 Let us asume x = 0, Therefore y = 3 × 0 + 5 = 0 + 5 = 5 Hence, (0, 5) is one solution Now,... View Article

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