Find the quotient of the identity function by the modulus function

Show that the function f : R ⟶ R given by f(x) = cos x for all x ∈ R is neither one-one nor onto.

Which of the following sets are finite and which are infinite?
Set of concentric circles in a plane.

Write a description of each shaded area. Use symbols U, A, B, C, U, ∩, ' and \ as necessary.

Draw venn diagram of three sets A, B and C which illustrates the following:
A ∩ B ∩ C

Solve the equation x^2/3 + x^1/3 - 2 = 0.

Solve \(\sqrt [ 8 ]{{{x}\over{x+3}} } -\sqrt{{{x+3}\over{x}}}=2.\)

Find the value of log₂ \(\left({{\sqrt [ 3 ]{4 } }\over{4^2\sqrt{8}}} \right).\)

Simplify: \(\frac{cos(90°+\theta)sec(-\theta)tan(180°-\theta)}{sec(360°-\theta)sin(180°+\theta)cot(90°+\theta)}\)

Prove that sin (A+B) sin (A - B) = cos²B - cos²A.

If \(tan\alpha=\frac{1}{3}\ and\ tan \beta=\frac{1}{7}\) show that \(2\alpha+\beta=\frac{\pi}{4}.\)

Prove that n!(n + 2) = n! + (n + 1)!

How many 3-digit numbers more than 600 can be formed using the digits 2, 3, 4, 6, 7?

If 9P₅ + 5.9P₄ = 10P_r , find r.

If the letter of the word 'RACHIT' are arranged in all possible ways as listed in dictionary, then what is the rank of the word 'RACHIT'?

How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7 if no digit is repeated?

Out of 18 points in a plane, no three are in the same line except five points which are collinear. Find the number of lines that can be formed joining the points.

if n is an odd positive integer, prove that the Co-efficients of the middle terms in the expansion equal

Prove that in the expansion of (1+x)ⁿ, the Co-efficient of terms equidistant from the beginning and from the end are equal

Find 3 numbers in AP where sum is 15 and sum of their reciprocals is \(\frac{71}{105}.\)

Find \(\sum_{1}^{\infty}{\frac{1}{(k+1)(k+2)}}\).

Sum up to n terms the series: 
7 + 77 + 777 + 7777 + ...

The line 2x - y = 5 turns about the point on it, whose ordinate and abscissae are equal, through an angle of 45° in the anti-clockwise direction. find the equation of the line in the new position.

Find matrix C if \(A=\left[ \begin{matrix} 3 & 7 \\ 2 & 5 \end{matrix} \right] ,B=\left[ \begin{matrix} -3 & 2 \\ 4 & -1 \end{matrix} \right] \) and 5C + 2B = A.

If x = \(a\sec ^{ 3 }{ \theta }\) and \(y=a\tan ^{ 3 }{ \theta }\) find \(\frac { dy }{ dx }\) at \(\theta =\frac { \pi }{ 3 }\)