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If (150)^x = 7, then x is equal to:

The given expression is... View Article

ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA. Prove that ∠ABD = ∠BAC.

Answer: A quadrilateral can be defined as a plane figure having 4 sides. There are mainly 6 types of quadrilaterals which are: Trapezium... View Article

Evaluate using suitable identities: (52)².

The algebraic equations which are valid for all values of variables in them are called algebraic identities. Using the... View Article

Limit from x to 0 of [1 – cos (1 – cos x)] / x⁴ =

The given limit is as follows.... View Article

Find the common factors of 12x, 36.

12x = 2 × 2 × 3 × x 36 = 2 × 2 × 3 × 3 Common factor = 2 × 3 = 6... View Article

Which constant must be added and subtracted to solve the quadratic equation 9x² + (3 / 4) x + 2 = 0 by the method of completing the square?

The given expression is... View Article

Solve the equation 3 (2p -1 ) = 5 – (3p – 2).

The given equation is... View Article

Find the perpendicular distance from the origin of the line joining the points (cos θ, sin θ) and (cosφ, sinφ).

Let A = (cos θ, sin θ) and B = (cosφ, sinφ) be the given points.... View Article

Define coaxial circles and deduce their equation in the simplest form.

A family of circles, out of which every pair have the same radical axis, are called co-axial circles. Equation of coaxial circles in simplest... View Article

f (x) = x cosx. Find f′ (π).

Consider the given function.... View Article

Write the following statement in the form of the equation: One-fourth of m is 3 more than 7.

One-fourth of m is m / 4.... View Article

Give reason: A square can be thought of as a special rhombus.

All sides of a rhombus and a square are the same. A rhombus with each angle as a right angle becomes a square. Hence, a square can be... View Article

Write the following rational numbers in ascending order: (1 / 3), (- 2 / 9), (- 4 / 3).

The given rational numbers are... View Article

Integral of x²e^x dx

On applying integrating by parts,... View Article

From a point in the interior of an equilateral triangle, perpendiculars are drawn on

From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides.... View Article

Find all the solutions of 4 cos² xsinx – 2 sin² x = 3 sinx.

The given expression can be written as... View Article

A rectangular plot is given for constructing a house, having a measurement of 40m long and 15m in the front. According to the laws, a minimum of 3m wide space should be left in the front and back each and 2m wide space on each of the other sides. Find the largest area where the house can be constructed.

Length of rectangular plot = 40m Width = 15m By keeping 3m wide space both in front and back The length becomes = 40 - 3 - 3 =... View Article

A sum of money lent out at simple interest amounts to Rs 720 after 2 years and to Rs 1020 after a further period of 5 years. What is the sum?

Simple interest for 2 years = Rs. 720. Simple interest for 7 years = Rs. 1020 Simple interest for 5 years = Rs. 1020 - Rs. 720 = Rs. 300.... View Article

By actual division find the quotient and the remainder when (x⁴ + 1) is divided by (x – 1).

The division is as follows.... View Article

If sin α + sin β = a and cos α + cos β = b, then prove that cos (α − β) = [a² + b² – 2] / 2.

On squaring sin α + sin β = a and cos α + cos β = b and adding them,... View Article

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