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The difference between two positive integers is 30. The ratio of these integers is 2:5. Find the integers.

Solution: Given that the ratio of the integers is 2:5. Let 2x be the first integer and 5x be the second integer. The difference between two... View Article

Period of cos x is

(a) 2π (b) π (c) π/4 (d) none of these Solution: The period of cos x is 2π. The period of a periodic function is the interval of... View Article

Factorise 1 + 2ab – (a² + b²)

Solution: 1 + 2ab - (a2 + b2) = 1 - (a2 + b2 - 2ab) = 1 - (a - b)2 = (1 - (a-b))(1 + (a-b)) = (1 - a + b)(1 + a - b)... View Article

State whether the statement given is true or false. Zero is the smallest rational number.

Solution: A number that can be expressed in the form p/q where q is not equal to zero is called a rational number. Rational numbers consist of... View Article

Find the cube of 21.

Solution: The cube of a number means a number multiplied by itself three times. So we multiply 21 by itself 3 times. 213 = 21×21×21... View Article

Find 1% of 1 hour.

Solution: 1 hour = 60 min = 3600 sec 1% of 3600 = (1/100)3600 = 36 sec So 1% of 1 hour is 36 seconds.... View Article

How many vertices does an angle have?

Solution: An angle can be defined as the figure formed by two rays meeting at a common endpoint. The point where the arms of the angle meet is... View Article

In a division sum, we have dividend = 199, quotient = 16 and remainder = 7. The divisor is

(a) 11 (b) 12 (c) 23 (d) none of these Solution: We know dividend = (Divisor × Quotient) + remainder Given dividend = 199 quotient =... View Article

The total number of injective mappings from a set with m elements to a set with n elements, m ≤ n, is

(a) mn (b) nm (c) n!/(n-m)! (d) n! Solution: Let A= {a1, a2 ...am} B = {b1, b2 ...bn} m ≤ n Given f: A → B is injective... View Article

A shopkeeper purchased 200 bulbs for Rs.10 each. However, 5 bulbs were fused and put them into scrap. The remaining were sold at Rs.12 each. Find the gain or loss percent.

Solution: The cost price of 200 bulbs = 200×10 = Rs. 2000 5 bulbs were fused. Remaining 195 bulbs are there. The remaining were... View Article

A dealer sells a toy for Rs. 24 and gains as much percent as the cost price of the toy. Find the cost price of the toy.

Solution: Given selling price, SP = Rs. 24 Dealer gains as much percent as the cost price of the article. Let cost price be x. So gain %... View Article

Prove that : sin 2x + 2 sin 4x + sin 6x = 4 cos²x sin 4x

Solution: LHS = sin 2x + 2 sin 4x + sin 6x = (sin 6x + sin 2x) + 2 sin 4x …(i) We know sin A + sin B = 2 sin (A+B)/2 cos (A-B)/2 (i)... View Article

If the area of a rectangle is equal to the area of a square and the length of the rectangle is equal to the perimeter of the square, then the breadth of the rectangle is

(a) side/2 (b) side2/2 (c) side/4 (d) side/3 Solution: Let l be length and b be the breadth of the rectangle. Area of rectangle = l×b... View Article

If G be the centroid of a triangle ABC, prove that AB²+ BC² + AC² = 3(GA² + GB² + GC²).

Solution: Let A (x1, y1), B(x2, y2), and C(x3, y3) be the vertices of ∆ABC. Without the loss of Generality, assume the centroid of the... View Article

Find the condition for the line x cos α + y sin α = p to be a tangent to the ellipse x²/a²+y²/b²= 1

Solution: Given equation of line is x cos α + y sin α = p => y sin α = -x cos α + p => y = -x (cos α/sin... View Article

A shopkeeper sells 25 articles at Rs.45 per article after giving 10% discount and earns 50% profit. If the discount is not given the profit gained is

(a) 60% (b) 66% (c) (d) none of these Solution: Selling price = Rs. 45 Let marked price be x. So 90% x = 45 => 90x/100 = 45 => x =... View Article

In the question below is given a group of letters followed by four combinations of digits/symbols numbered (a), (b), (c), and (d)

You have to find out which of the combinations correctly represents the group of letters based on the coding system and mark the number of that... View Article