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Resolve a³ – b³ + c³ + 3abc into factors.

The given expression can be rewritten as... View Article

One centimetre is equal to

1 cm = 10 mm... View Article

For what value of k, are the roots of the quadratic equation (k + 4) x² + (k + 1) x + 1 = 0 equal?

The roots of the quadratic equation are found as follows.... View Article

The value of ∫e^2x (2 sin 3x + 3 cos 3x)dx is

Answer: The value of is e2xsin3x + c.... View Article

Find the LCM of 4, 5 and 6.

4 = 2 × 2 5 = 5 6 = 2 × 3 LCM (4, 5, 6) = 2 × 2 × 3 × 5 = 4 × 3 × 5 = 12 × 5 = 60... View Article

What is the radius of the circumcircle of a triangle whose sides are 30 cm, 36 cm and 30 cm?

Dimension of triangle is given by... View Article

The difference between the sum of prime numbers from 21 to 30 and the sum of composite from 21 to 30 is divisible by which of the following numbers? A) 3 B) 7 C) 151 D) 17

The sum of prime numbers from 21 to 30 = 23 + 29 = 52 The sum of composite numbers from 21 to 30 = 21 + 22 + 24 + 25 + 26 + 27 + 28 + 30 = 203... View Article

If θ is an acute angle and sin θ = cos θ. The value of 2 tan² θ + sin² θ – 1 is

sin θ = cos θ sin θ / cos θ = cos θ / cos θ [dividing both sides by cos θ] tan... View Article

Say true or false: The diagonals of a square are perpendicular.

The given statement is true. The diagonals of a square are perpendicular.... View Article

Determine the degree of the following polynomials: 2x – 1.

The highest power of x is 1, hence the degree of the polynomial 2x - 1 is 1.... View Article

Robin purchased an old car for ₹73500. He spent ₹10300 on repairs and paid ₹2600 for its insurance. Then he sold it to a mechanic for ₹84240. What was his percentage gain or loss? Hint: overheads = ₹ 10300 + ₹ 2600 = ₹ 12900

Actual price of old car = purchase price + overheads = 73500 + 12900 = 86400 Cost price = ₹ 86400 Selling price = ₹... View Article

Find the square of 85.

We have to find the square of 85. To find the square of number, multiply the number by itself. So square of 85 = 85 × 85 = 7225 The square... View Article

Prove that tan 225° cot 405° + tan 765° cot 675° = 0.

tan 225° cot 405° + tan 765° cot 675° = tan (90° × 2 + 45°) cot (90° × 4 + 45°) + tan (90°... View Article

Using distributivity of multiplication over the addition of whole numbers, find the following product: 736 × 103

736 × 103 = 736 × (100 + 3) By using distributivity of multiplication over the addition of whole numbers = (736 × 100) +... View Article

The number of six-digit numbers that can be formed from the digits 1, 2, 3, 4, 5, 6 and 7 so that digits do not repeat and the terminal digits are even is

The first position can be occupied in 3 ways, the last place in 2 ways and the remaining places can be filled in 5P4 ways = 120 ways The... View Article

A person invests Rs. 5,000 for two years at a certain rate of interest compounded annually. At the end of one year, this sum amounts to Rs. 5,600. Calculate : (i) the rate of interest per year. (ii) the amount at the end of the second year.

Principal (P) = Rs. 5000 Time = 2 Years Amount at the end of one year = Rs. 5600 Interest for the first year = A - P = Rs. 5600 - 5000 = Rs. 600... View Article

Find the percentage increase in the area of a triangle if each side is doubled.

Semi-perimeter of the triangle... View Article

Which Of The Following Polymers Occur Naturally (A) Protein And Pvc (B) Starch And Nylon (C) Proteins And Nylon (D) Starch And Cellulose

The correct answer is (D) Starch And Cellulose. Starch, cellulose and proteins are purely polymeric or naturally occurring polymers composed in... View Article

What Is The Symbol Of Switch In On Position Is

The switch symbol in the ON position is represented by two small circled connected by a straight line. When a switch is on, it completes the... View Article

What Happens When White Light Passes Through A Glass Prism

When white light passes through a glass prism, the light gets dispersed and there is a formation of a seven colours spectrum. The seven colours... View Article