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The area bounded by the curve y = cos x, the x-axis and the ordinates x=0 and x=2pi

The area bounded by the curve y = cos x, the x-axis and the ordinated x=0 and x=2 is given by Area bounded = = (since 0 ≤ x < /2... View Article

Let f(x) be a polynomial satisfying limit x tends to infinity [x^2f(x)/(2x^5 + 3)]=6, also f(1)=3, f(3)=7, and f(5)=11, then find the value of [f(6) + 5f(4)]/29.

Given, then, f(x) is a polynomial function of degree 3 [ If the degree of f(x) < 3, the limit will tend to zero. If the degree of f(x)... View Article

What is y = mx + b?

y = mx + b is the Slope-intercept form of the equation of a straight line where, m is the slope of the line with the X-axis and b is the... View Article

What is the range of the greatest integer function?

For the greatest integer function, the domain will be R, i.e. the set of all real numbers. Also, the range of the greatest integer function is Z,... View Article

Find the ratio at which the y-axis divides the line segment joining the points A(-3, -4) and B(1, -2).

Let m : n be the ratio at which the y-axis divides the line segment joining the points A(-3, -4) and B(1, -2).Also, P(0, y) be the point of... View Article

How can we express a general nth degree polynomial using Horner’s method?

We can express a general nth degree polynomial using Horner's method as follows: a0 + a1x + a2x2 + a3x3 + a4x4 + .... + anxn = a0 + x[a1 + x(a2 +... View Article

What is the mixed fraction form of 1210/220?

Given fraction: 1210/220The numerator is greater than the denominator, i.e. 1210 > 220, so it is an improper fraction.Here, 1210 can be... View Article

Is a cubic function always increasing?

Let f(x) be a cubic function. f(x) = ax3 + bx2 + cx + d The derivative of f(x) may be used to determine whether f(x) is increasing or... View Article

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 its sign.... 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 are same, we can add the powers. x + 1 + 5 = 7 x... 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 =... 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.... View Article

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 - 2)j - k are coplanar. 3x+2−x+2=0 2x=−4 x=−2... 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 the seats first. It can be done... 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, we have; an = a + (n - 1)d ............ (1) a... 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 = 15 x = 3 Age of youngest boy = 3x = 3 (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 Value of 10 paise coins = x/10 Value of 50 paise coins = (70 -... 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, then the value of k is 7. As we know, the solution of the... 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 =... 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 to 00C Solution: Let us calculate the difference in temperature for... View Article