Q) If sin θ = , prove that . Ans: Let’s start LHS: = = ∵ 1- cos2 θ= sin2 θ ∴ LHS = = = = = cot θ ∵ sin θ = ∴ cot θ = ∴ LHS = = RHS Hence Proved !

If sin θ = 3/4, prove that Root [(cosec 2θ − cot 2 θ} / (sec 2 θ − 1)] = √7 / 3 Read More »

Q) If sin θ = , prove that . Ans: Let’s start LHS: = = ∵ 1- cos2 θ= sin2 θ ∴ LHS = = = = = cot θ ∵ sin θ = ∴ cot θ = ∴ LHS = = RHS Hence Proved !

If sin θ = 3/4, prove that Root [(cosec 2θ − cot 2 θ} / (sec 2 θ − 1)] = √7 / 3 Read More »

Q) In the given figure, tangents PQ and PR are drawn to a circle such that ∠RPQ = 300. A chord RS is drawn parallel to tangent PQ. Find the ∠RQS. Ans: In △PRQ, PQ and PR are tangents from an external point P to circle. ∴ PR = PQ Since the angles opposites to equal sides

In the given figure, tangents PQ and PR are drawn to a circle such that ∠RPQ = 30 . Read More »

Q) Mrs. Gupta arranged some snacks for her child’s birthday party. After the guest left she had some food left over. She did not want to waste food and so she contacted a local NGO. She gave 60 pieces of pastries,168 pieces of cookies, and 330 chocolate bars to the team. Now the NGO workers want

Mrs. Gupta arranged some snacks for her child’s birthday party. Read More »

Q) If a, b and c are the sides of a right angled triangle, where c is hypotenuse, then prove that the radius of the circle whichtouches the sides of the triangle is given by r = Ans: Let’s consider a right angled triangle ABC with sides a, b & c.Its ∠ A is right angle

If a, b and c are the sides of a right angled triangle, where c is hypotenuse, Read More »

Q) A number consists of two digits. Where the number is divided by the sum of its digits, the quotient is 7. If 27 is subtracted from the number, the digits interchange their places, find the number Ans: Let’s consider X and Y are the digits of the given number. Hence the given number is 10 X

A number consists of two digits. Where the number is divided by the sum of its digits, Read More »

Q) Solve for x and y: = -1; = 3 Ans: Let’s take the equations one by one: = -1 3X + 4 Y = – 6 ………. (i) Similarly, = 3 We can write this as: = 3 3X – Y = 9 ….. (ii) By solving equations (i) and (ii), we get: X =

Solve for x and y : x / 2 + 2y / 3 = − 1; x − y / 3 = 3 Read More »

Q) In figure, PQ is a tangent from an external point P to a circle with centre O and OP cuts the circle at T and QOR is adiameter. If ∠POR = 130° and S is a point on the circle, find ∠1 +∠2 Ans: In the given diagram, it is given that: ∠ POR

In figure, PQ is a tangent from an external point P to a circle with centre O Read More »

Q) In Fig. AD bisects ∠A, AB = 12 cm, AC = 20 cm and BD = 5 cm, determine CD. Ans: ∵ AD bisects ∠ A We know that, according to the angle bisector theorem, the angle bisector of a triangle divides the opposite side into two parts that are proportional to the other

In Fig. AD bisects ∠A, AB = 12 cm, AC = 20 cm and BD = 5 cm, determine CD. Read More »