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A chord of a circle of radius 10 cm subtends a right angle at the centre, then the area of the minor segment is (a) 78.5 (b) 28.5 (c) 50 (d) 128.5

Correct answer: (b) 28.5Solution:Let O be the centre of the circle.OA = OB = radius Given,OA = OB = 10 cmCentral angle = θ = 90°Area of... View Article

ABCD is a rectangle, AC and BD are diagonals. Prove that diagonals are equal.

Given: Rectangle ABCD such that AC and BD are diagonals. To prove: AC = BD Proof: We know that the opposite sides of rectangle are equal. AB... View Article

What are the points on the x-axis whose perpendicular distance from the line x/3 + y/4 = 1 is 4 units?

Given equation of line: x/3 + y/4 = 14x + 3y = 124x + 3y - 12 = 0And the point on the x-axis will be (x, 0).We know that the distance of a point... View Article

If three different coins are tossed together, what is the probability of getting two heads?

Three different coins are tossed together.Total outcomes = {(HHH), (THH), (HTH), (HHT), (TTT), (TTH), (THT), (HTT)}i.e. n(S) = 8Let E be the... View Article

Find the sets A and B if A/B = {1, 5, 7, 8}, B/A = {2, 10} and A ∩ B = {3, 6, 9}. Are they unique?

Given,A/B = {1, 5, 7, 8}B/A = {2, 10}A ∩ B = {3, 6, 9}Thus, A = (A/B) U (A ∩ B)= {1, 5, 7, 8} U {3, 6, 9}= {1, 3, 5, 6, 7, 8, 9}B = (B/A)... View Article

In the given figure, ∆OBA ~ ∆ODC, ∠BOC = 125° and ∠CDO = 70°. Find teh value of ∠OAB.

Figure: Solution:Given,∆OBA ~ ∆ODC Thus, ∠ODC = ∠OBA = 70° {corresponding angles of similar triangles)AOC is a straight line.∠AOB... View Article

Find the derivative of (3x^2 + 5)sin x.

Let y = (3x2 + 5)sin x Differentiating with respect to x on both sides, dy/dx = (d/dx) [(3x2 + 5) sin x] Using the product rule of... View Article

In triangle ABC, prove that cos(A/2) + cos(B/2) + cos(C/2) = 4. cos(π – A)/4. cos(π – B)/4. cos(π – C)/4.

In triangle ABC,A + B + C = πFrom this we can write the following:π - A = B + Cπ - B = A + Cπ - C = A + BNow, consider the RHS,=... View Article

ABC is an equilateral triangle with each side of length 2p. If AD ⊥ BC, find the value of AD.

Given,ABC is an equilateral triangle with each side of length 2p.That means, AB = BC = CA = 2pAlso, AD ⊥ BCAs we know, in an equilateral... View Article

Prove that (sin θ – cos θ + 1)/(sin θ + cos θ – 1) = 1/(sec θ – tan θ).

LHS = (sin θ - cos θ + 1)/(sin θ + cos θ - 1) Dividing the numerator and denominator by cos θ, = [(sin θ/cos θ) - (cos θ/cos θ) + (1/cos θ)] /... View Article

An exterior angle is drawn to a triangle; if this exterior angle is acute, then what type of a triangle will be formed?

We know that,The exterior angle is equal to the sum of interior opposite angles of a triangle.Also, the sum of all angles of a triangle = 180∘In... View Article

Find the number of sides of a regular polygon if each of its interior angles measure 120°.

Let n be the number of sides of a regular polygon.Each interior angle = 120°We know that,Measure of each interior angle of a regular polygon... View Article

Find the value of (sin 30° + cos 30°) – (sin 60° + cos 60°).

Using the trigonometric table, sin 30° = 1/2 cos 30° = √3/2 sin 60° = √3/2 cos 60° = 1/2 (sin 30° + cos 30°) - (sin 60° + cos 60°) = [(1/2) +... View Article

In the division method, the divisor is 5 times the quotient and twice the remainder. If the remainder is 15, then find the dividend.

Let p be the quotient.Divisor = 5pGiven that the remainder = 15According to the given,Divisor = 2 × Remainder5p = 2 × 155p = 30p =... View Article

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Archives

A chord of a circle of radius 10 cm subtends a right angle at the centre, then the area of the minor segment is (a) 78.5 (b) 28.5 (c) 50 (d) 128.5

ABCD is a rectangle, AC and BD are diagonals. Prove that diagonals are equal.

What are the points on the x-axis whose perpendicular distance from the line x/3 + y/4 = 1 is 4 units?

If three different coins are tossed together, what is the probability of getting two heads?

Find the sets A and B if A/B = {1, 5, 7, 8}, B/A = {2, 10} and A ∩ B = {3, 6, 9}. Are they unique?

In the given figure, ∆OBA ~ ∆ODC, ∠BOC = 125° and ∠CDO = 70°. Find teh value of ∠OAB.

Find the derivative of (3x^2 + 5)sin x.

In triangle ABC, prove that cos(A/2) + cos(B/2) + cos(C/2) = 4. cos(π – A)/4. cos(π – B)/4. cos(π – C)/4.

ABC is an equilateral triangle with each side of length 2p. If AD ⊥ BC, find the value of AD.

Prove that (sin θ – cos θ + 1)/(sin θ + cos θ – 1) = 1/(sec θ – tan θ).

An exterior angle is drawn to a triangle; if this exterior angle is acute, then what type of a triangle will be formed?

Find the number of sides of a regular polygon if each of its interior angles measure 120°.

Find the value of (sin 30° + cos 30°) – (sin 60° + cos 60°).

In the division method, the divisor is 5 times the quotient and twice the remainder. If the remainder is 15, then find the dividend.

If the median of the data arranged in ascending order is 63, find the value of x.

Evaluate using properties: 724 × (-56) + (-724) × 44

Find the number of triangles in the given figure.

One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting a king of red colour.

A can do a piece of work in 10 days, B in 15 days. How many days together they will take to complete the same work?

What will be the HCF of two consecutive odd numbers?

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