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If any two adjacent rows or columns of a determinant are interchanged in position, what will be the value of the determinant?

If any two adjacent rows or columns of a determinant are interchanged in position, the value of the determinant changes... View Article

Find the value of x in exponents and powers when the (2)^x+1 x (2)^5 = 2^7.

Given, 2x+1 x 25 = 27 By laws of exponents, we know; am x an = am+n So, if the bases... View Article

A sector of a circle with radius 18 cm has central angle 120°. Find the area of the sector. Use π=3.14

Given, radius, r=18cm, central angle, θ=120° π=3.14 Area of sector = θ/360 × π × r2 = 120/360 × 3.14 × 18 × 18... View Article

The arithmetic operations of addition, subtraction, multiplication, and division help us solve mathematical problems. True or False.

The arithmetic operations of addition, subtraction, multiplication, and division help us solve mathematical problems. The statement is True.

Let a = i + j + k, b = i – j + 2k and c = xi + (x – 2)j – 1k are three vectors. If vector c lies in the plane of a and b, then x equals to: A. 0, B. 1, C. -4, D. -2

Given, a = i + j + k b = i – j + 2k c = xi + (x... View Article

4 gentlemen and 4 ladies take seats at random around a table. The probability that they are sitting alternately is:

Given, 4 gentlemen and 4 ladies take the seats at the random round table. Let us consider, the gentlemen take... View Article

If 73 is the nth term of the arithmetic progression 3, 8, 13, 18…, then ‘n’ is:

Given, 3, 8, 13, 18…, is the A.P. 73 is the nth term of given A.P. By nth term formula,... View Article

The average age of three boys is 15 years and their ages are in proportion 3:5:7. What is the age in years of the youngest boy?

Let the age of three boys be 3x, 5x and 7x. According to given question, (3x+5x+7x)/3 = 15 15x/3 =... View Article

70 coins of 10 paise and 50 paise are mixed in a purse. If the total value of the money in the piggy bank is Rs. 19, find the number of each type of coins in the piggy bank.

Let the number of 10 paise coins = x So, the number of 50 paise coins = 70 – x... View Article

Assertion: if x = 2, y = 1 is a solution of the equation 2x + 3y = k, then the value of k is 7. Reason: the solution of the line will satisfy the equation of the line.

Given, Assertion: if x = 2, y = 1 is a solution of the equation 2x + 3y = k,... View Article

The area of an equilateral triangle having side length equal to √3/4 cm is

Solution: Given side of an equilateral triangle, a = √3/4 cm Area of equilateral triangle = (√3/4)a2 = (√3/4)×(3/16) =... View Article

Find out which of the following shows maximum rise in temperature?

(a) 00 C to 100 C (b) -40 C to 80 C (c) -150 C to -80C (d) -70 C... View Article

If θ is eliminated from the equations x = a cos(θ-α) and y = b cos(θ-β), then (x²/a²) + (y²/b²) – (2xy/ab) cos (α-β) is equal to

(a) sec2(α-β) (b) cosec2(α-β) (c) cos2(-β) (d) sin2 (α-β) Solution: Given x = a cos(θ-α) and y = b cos(θ-β)... View Article

If a pair of variable straight lines x² + 4y²+ α xy =0 (where α is a real parameter) cut the ellipse x²+4y²= 4 at two points A and B, then the locus of the point of intersection of tangents at A and B is

(a) (2x-y)(2x+y) = 0 (b) x2-4y2+8xy = 0 (c) x2-4y2+4xy = 0 (d) (x-2y)(x+2y) = 0 Solution: Let the point... View Article

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