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Find the area of the triangle whose vertices are: (i) (2, 3) , (-1, 0) , (2, -4) (ii) (-5, -1) , (3, -5) , (5, 2)

Area of a triangle formula = (i) (2, 3), (-1, 0), (2, -4) Substitute all the values in the above formula, we get Area of triangle = 1/2 [2 {0-... View Article

Write three numbers whose decimal expansions are non-terminating non-recurring.

Non-terminating decimals are the one that does not have an end term. It has an infinite number of terms. Example: 0.5444444…..,... View Article

In what direction does the buoyant force on an object immersed in a liquid act?

The buoyant force on an object that is immersed in a liquid will be in a vertically upward direction. When an object is immersed in a liquid it... View Article

If the diagonals of a parallelogram are equal, then show that it is a rectangle.

Given: AC = BD To Prove: ABCD is a rectangle if the diagonals of a parallelogram are equal Solution: As mentioned parallelogram, so... View Article

If the median of a distribution given below is 28.5 then, find the value of x & y.

Class Interval Frequency 0-10 5 10-20 x 20-30 20 30-40 15 40-50 Y 50-60 5 Total 60 Solution: Given Parameters, n = 60 Median... View Article

If the point (3, 4) lies on the graph of the equation 3y = ax + 7, find the value of a.

Answer: Linear equations are the equations of degree 1. It is the equation for the straight line. The standard form of linear equation is... View Article

Give two different examples of pair of (i) Similar figures (ii) Non-similar figures

Similar figures are two figures having the same shape. The objects which are of exactly the same shape and size are known as congruent objects.... View Article

Classify the following numbers as rational or irrational according to their type:

Solution: √23 = 4.79583152…… As the number is non-terminating non-recurring. It is an irrational number.... View Article

Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

Draw a circle and connect two points A and B such that AB becomes the diameter of the circle. Next, draw two tangents PQ and RS at points A and B... View Article

Why a block of plastic when released under water come up to the surface of water?

The density of plastic is lesser than that of water. Therefore, the force of buoyancy on the plastic block will be greater than the weight of the... View Article

How many sides does a regular polygon have if each of its interior angles is 165°?

Given The measure of interior angle = 165° Find out We have to find the number of sides of a polygon Formula (no. of sides) x (measure... View Article

ABC and ADC are two right triangles with common hypotenuse AC. Prove that ∠ CAD = ∠CBD.

Given: ABC and ADC are two right-angle triangles with common hypotenuse AC.To prove: ∠ADB=∠CBDSolution: ∠ABC=∠ADC=90°The... View Article

Which term of the AP: 121, 117, 113, . . ., is its first negative term? [Hint: Find n for a_n < 0]

Given that The AP series is 121, 117, 113, . . ., Thus, first term, a = 121 Common difference, d = 117-121= -4 Find out The first negative term... View Article

If two zeroes of the polynomial x⁴-6x³-26x² + 138x-35 are 2 ±√3, find other zeroes.

The given equation is a polynomial equation of degree 4, hence there will be total 4 roots. Let f(x) = x4-6x3-26x2+138x-35 Since 2 +√3 and... View Article

ABCD is a cyclic quadrilateral (see Fig.) . Find the angles of the cyclic quadrilateral.

We have to find the angles of the given quadrilateral We know that the sum of the opposite angles of a cyclic quadrilateral is 180o... View Article

Find the roots of the following equations: (i) x-1/x = 3, x ≠ 0 (ii) 1/x + 4 – 1/x-7 = 11/30, x = -4, 7

(i) x-1/x = 3 ⇒ x2 – 3x -1 = 0 On comparing the given equation... View Article

Find the smallest square number that is divisible by each of the numbers 4, 9 and 10.

Solution At first we have to find L.C.M of 4, 9 and 10 4 = 2 x 2 x 1 9 = 3 x 3 x 1 5 = 1 x 5 Hence, L.C.M = (2 × 2 × 3 x... View Article

Write the following in decimal form and say what kind of decimal expansion each has :

(i) 36/100 Solution: the remainder becomes zero. Hence, decimal expansion becomes terminating. 36/100 = 0.36 (ii)1/11 Solution:... View Article

Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°.

Given A circle with a radius 6 cm and angle of the sector is 60° Find out We have to find out the area of a sector Solution Given:... View Article

D is a point on the side BC of a triangle ABC such that ∠ADC = ∠BAC. Show that CA2 = CB.CD

Given that D is a point on the side BC of a triangle ABC such that ∠ADC = ∠BAC. To Prove CA2 = CB.CD Proof... View Article