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Find the square root of the surd 9 + 2 √14.

The given surd is 9 + 2 √14.... View Article

Factorise the following: (x² + y² – z²)² – 4x²y².

The given expression is... View Article

25% of the total mangoes which are rotten is 1,250. Find the total number of mangoes in the basket. Also, find the number of good mangoes.

Assume the total number of mangoes to be x.(25x / 100) = 1250x = [1250 * 100] / 25 x = 5000 mangoesTotal number of mangoes in the basket =... View Article

A rectangular sheet of paper is 12 (1 / 2) cm long and 10 (2 / 3) cm wide. Find the perimeter.

Length of the rectangle = 12 (1 / 2) cmBreadth of the rectangle = 10 (2 / 3) cmPerimeter of a rectangle = 2 (length + breadth)... View Article

The maximum number of points of intersection of five lines and four circles is

The point of intersection of two circles is at two distinct points. The point of intersection of two straight lines is at one point.The point of... View Article

Angle between y² = x and x² = y at the origin is

The slope of the tangent to the parabola x2 = y is given by2x = dy / dx(dy / dx)(x, y) = 0 = 0θ = 90The slope of the tangent to the... View Article

Using divisibility tests, determine the following number is divisible by 11 10000001.

The sum of the digits at even places is 1.The sum of the digits at odd places is 1.Difference between the sum of the digits at the even and odd... View Article

The most general solution of tan θ = 1 and cos theta = – 1 / √2 is

tan θ = 1 and cos theta = - 1 / √2... View Article

Find the derivative of cos √x with respect to x using the first principle.

f (x) = cos √x... View Article

The graph of y = log x cuts

y = logb x x = byThe graph cuts the x-axis at x = 1.... View Article

A room is 6 m long, 5 m broad and 4 m in height. If all its walls are to be covered with paper 50 cm wide, the length of the paper is

The room is in the shape of a cuboid.Area of cuboid = 2bh + 2hl= (2 × 20) + (2 × 24)= 88 square metre Area of paper = lb= l ×... View Article

Show that 107 is of the form 4q + 3 for any integer q.

107 = 4 * 26 + 3This is of the form a = bq + r.... View Article

A rectangle measures 40 cm at its length and 20 cm at its width. Find the ratio of the length to the width.

Length of the rectangle = 40 cmWidth of the rectangle = 20 cmLength / Width = 40 / 20= 2 / 1= 2 : 1... View Article

log (70 / 33) + log (22 / 135) – log (7 / 18)

log (70 / 33) + log (22 / 135) - log (7 / 18)= log (70 / 33) * (22 / 135) - log (7 / 18) (Since , log a + log b = log (ab))= log ((70 * 22) / (33... View Article

If 3y = y + 2, calculate the value of 2y.

The given equation is... View Article

A number from 1 to 11 is chosen at random. What is the probability of choosing an odd number?

The numbers from 1 to 11 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11. The probability of choosing an odd number = (odd number) / (total number)= 6 / 11... View Article

If cos θ + cos 2θ + cos 3θ = 0, then the general value of θ is:

cos θ + cos 2θ + cos 3θ = 0... View Article

If 79 ⊕ 86 = 6897 then the value of 53 ⊕ 47 =

79 ⊕ 86 = 689753 ⊕ 47 = 7435... View Article

Two adjacent angles of a parallelogram are equal. What is the measure of each angle?

The adjacent angles of a parallelogram are equal.The sum of adjacent angles of parallelogram = 180. Assume the adjacent angles to be x and... View Article

(√11 – √7) / (√11 + √7) = a – √77 b. Find a and b.

On rationalizing the LHS,... View Article