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How much water a pump of 2kW can raise in one minute to a height of 10 m. Take g = 10 m/s2?

Answer: Given, Power of the motor pump = 2 kW = 2000 W Time (t)= 60 sec Height (h) = 10 m g = 10 m/s2 As we know, Power (P) =... View Article

Factorize : a⁶ – b⁶ (a) (b – a) (a + b) (a³ + ab + b³) (a² – ab + b²) (b) (a – b) (a + b) (a² + ab + b²) (a² – ab + b²) (c) (a + b) (a + b) (a² + ab + b²) (2a² – ab + b²) (d) (a + b) (a – b) (a² + ab + b² (a³ – ab + b³)

Given a6 - b6 This can be written as below = (a2)3 - (b2)3 Using the formula: (a3 - b3) = (a - b) (a2 + ab + b2) = (a2 - b2) [(a2)2 + a2b2 +... View Article

Using the formula, tan 2A = 2 tan A / 1 – tan²A, find the value of tan 60⁰, it being given that tan 30⁰ = 1/√3

Put A = 300 2A = 600 tan 600 = 2 tan 300 / (1 - tan2 300) Given tan 300 = 1/√3 = (2 x 1/√3)/{1 - (1/√3)2} = (2 x 1/√3) /... View Article

Check whether the given equation is quadratic equation x² – 2x = (-2)(3-x)

Given x2 - 2x = (-2) (3 - x) By using the formula for (a+b)2 = a2 + 2ab + b2 ⇒ x2 - 2x = -6 + 2x We get, ⇒ x2 - 4x + 6 = 0 Since, the... View Article

At a cricket test match 2/7 of the spectators were in a covered place while 15000 were in open. Find the total number of spectators

Given Fraction of spectators covered = 2/7 Fraction left = 1 - 2/7 We get, = 5/7 Number of spectators in open = 15000 As per the question, Number... View Article

Two poles of equal height are standing opposite to each other on the either side of the roads, which is 80 m wide. From a point P between them on the road , the angle of elevation of the top of a pole is 60°and the angle of depression from the top of another pole at point P is 30°. Find the heights of the poles and distances of the point P from the poles.

Let us consider AC and BD as the two poles of the same height h m Given AB = 80 m Let AP = x m Hence, PB = (80 - x) m In △APC, tan 300 = AC/AP... View Article

The larger of two supplementary angles exceeds the smaller by 18 degrees. Find the angles.

Let the larger angle = x<sup>0</sup> and smaller angle = y<sup>0</sup> We know that the sum of two supplementary pair of... View Article

Write the successor of: (a) 2440701 (b) 100199 (c) 1099999 (d) 2345670

The successors are (a) 2440701 + 1 = 2440702 (b) 100199 + 1 = 100200 (c) 1099999 + 1 = 1100000 (d) 2345670 + 1 = 2345671... View Article

Define a reflexive relation

In relation and functions, a reflexive relation is the one in which every element maps to itself. For example, consider a set A = {1, 2,}. Now,... View Article

The difference between two numbers is 26 and one number is three times the other. Find them?

Let the two numbers be x and y respectively, such that y > x. According to the question, y = 3x... View Article

4522 is not divided by

To find the numbers by which 4522 is not divisible let us first find the factors of 4522. Each number is divided by all the factors of that... View Article

Factorise 3x square – x – 4

Given polynomial = 3x2 - x - 4 This can be written as, = 3x2 + 3x - 4x - 4 = 3x (x + 1) - 4 (x + 1) = (3x - 4) (x + 1) Therefore, 3x2 - x - 4 =... View Article

The arithmetic mean of 1, 2, 3 … n is (a) (n-1)/2 (b) (n+1)/2 (c) n/2 (d) n

We know sum of first n natural numbers, (1+2+3+…n) = n(n+1)/2 Arithmetic mean of first n natural numbers = (1+2+3+…n)/n = n(n+1)/2n... View Article

Solve the following mentioned question (-7)-(-5)

Let us consider x = (-7)-(-5) x = -7 + 5 We get, x = -2... View Article

Prove that the sum of a rational number and an irrational number is always irrational

Let us consider a is a rational number and b is an irrational number Then ab is irrational Example: a = 2 and b = √3 ab = 2√3... View Article

Define signum function draw its graph and find its domain and range

Answer: The real function f : P → P defined by is called the signum function or sign function.(gives the sign of real number) Domain of f... View Article

If two tangents inclined at an angle of 60⁰, are drawn to a circle of radius 3 cm, the length of each tangent is equal to: (a) 3 (b) 6 (c) (3/2)√3 (d) 3√3

The tangent to any circle is perpendicular to the radius of the circle at point of contact. Let two Tangents originate from point A and touch the... View Article