Let f:R➝R be defined by f(x) = 1 - |x|. Then the range of f is

The number of roots of (x + 3)⁴+ (x + 5)⁴ = 16 is

If tan40⁰ = λ, then \(\frac { tan{ 140 }^{ 0 }-tan{ 130 }^{ 0 } }{ 1+tan{ 140 }^{ 0 }.tan{ 130 }^{ 0 } } \) =

In a \(\triangle\) ABC, C = 90° then the value of sin A + sin B - 2\(\sqrt{2} cos{A\over2}cos {B\over 2}is\) _______________

If P_r stands for ^r P_r then the sum of the series 1+ P₁ + 2P₂ + 3P₃ +...+ nP_n is

The HM of two positive numbers whose AM and GM are 16, 8 respectively is

1 - 2x + 3x² - 4x³ + ..., Ixl< 1 is ______________

If a vertex of a square is at the origin and its one side lies along the line 4x + 3y - 20 = 0, then the area of the square is

If(1, 3) (2,1) (9, 4) are collinear then a is ______________

State whether the following sets are finite or infinite.
{x \(\in \) N : x is an even prime number}

Solve (2x + 1)²- (3x + 2)² = 0

Show that \(\frac { (cos\theta -cos3\theta )(sin8\theta +sin2\theta ) }{ (sin5\theta -sin\theta )(cos4\theta -cos6\theta ) } =1\)

Prove that \(\sin { 4\alpha } =4\tan { \alpha } \frac { 1-\tan ^{ 2 }{ \alpha } }{ { \left( 1+\tan ^{ 2 }{ \alpha } \right) }^{ 2 } } \)

Find sin15°, cos15° and tan15°. Hence evaluate cot75° + tan75°.

Find the values of \(sin(-\frac{11\pi}{3})\).

How many two-digit numbers can be formed using 1, 2, 3, 4, 5 without repetition of digits?

Suppose 8 people enter an event in a swimming meet. In how many ways could the gold, silver and bronze prizes be awarded?

A Mathematics club has 15 members. In that 8 are girls. 6 of the members are to be selected for a competition and half of them should be girls. How many ways of these selections are possible?

In the binomial expansion of (a+b)ⁿ the coefficients of the 4^th and 13^th terms are equal to each other, find n.

By taking suitable sets A, B, C, verify the following results:
(A\(\times\) B)\(\cap \)(B\(\times\)A) = (A\(\cap \)B) \(\times\) (B\(\cap \)A)

Compare and contrast the graph y = x² - 1, y = 4(x² - 1) and y = (4x)² = 1.

Find the real roots of x⁴ = 16

Find the principal value of sec^-1\(\left( -\sqrt { 2 } \right) \)

Show that sin 12^o sin 48^o sin 54^o = \(\frac{1}{8}\)

A polygon has 90 diagonals. Find the number of its sides?

Write the first 4 terms of the logarithmic series of log (1 + 4x). Find the intervals on which the expansions are valid

Check the following functions for one-to-oneness and ontoness.
(i) \(f:N\rightarrow N\) defined by f(n) = n².
(ii) \(f: \mathbb{R} \rightarrow \mathbb{R}\) defined by f(n) = n².

Express each of the following as a product.
sin 50^o + sin 40^o