The function f:[0,2π]➝[-1,1] defined by f(x) = sin x is

If the function f:[-3,3]➝S defined by f(x) = x² is onto, then S is

Let X = {1, 2, 3, 4}, Y = {a, b, c, d} and f = {(1, a), (4, b), (2, c), (3, d), (2, d)}. Then f is

If A = {(x,y) : y = e^x, x∈R} and B = {(x,y) : y = e^-x, x ∈ R} then n(A∩B) is

If A = {(x,y) : y = sin x, x ∈ R} and B = {(x,y) : y = cos x, x ∈ R} then A∩B contains

Let R be the set of all real numbers. Consider the following subsets of the plane R x R: S = {(x, y) : y =x + 1 and 0 < x < 2} and T = {(x,y) : x - y is an integer} Then which of the following is true?

Let A and B be subsets of the universal set N, the set of natural numbers. Then A^'∪[(A⋂B)∪B^'] is

For non-empty sets A and B, if A ⊂ B then (A \(\times\)B) ⋂ (B \(\times\)A) is equal to

The number of relations on a set containing 3 elements is

Let R be the universal relation on a set X with more than one element. Then R is

The value of log_a b log_b c log_c a is

If 8 and 2 are the roots of x²+ ax + c = 0 and 3, 3 are the roots of x² + dx + b = 0; then the roots of the equation x²+ ax + b = 0 are

If a and b are the real roots of the equation x²- kx + c = 0, then the distance between the points (a, 0) and (b, 0) is

If  \(\frac { kx }{ (x+2)(x-1) } =\frac { 2 }{ x+2 } +\frac { 1 }{ x-1 } \), then the value of k is

If \(\alpha\) and \(\beta\) are the roots of 2x² - 3x - 4 = 0 find the value of \(\alpha^2+\beta^2\)

If \(\alpha\) and \(\beta\) are the roots of 2x² + 4x + 5 = 0 the equation where roots are 2\(\alpha\) and 2\(\beta\) is ___________

Solve 3x² + 5x - 2≤0

If \(\frac{1}{\sqrt{3}\times\sqrt{2}}=\sqrt{3}+a\) then a is ___________

If \(\pi <2\theta <\frac { 3\pi }{ 2 } \), then \(\sqrt { 2+\sqrt { 2+2cos4\theta } } \) equals to

Which of the following is not true?

If A = { 0, 1, 2, 3, 4, 5, 6, 7 } is a set. Then,

Try to write the following intervals in symbolic form:
(i) \(\{x:x\in R,-2\le x \le 0 \},\) 
(ii) \(\{ x:x\in R, 0\)
(iii) \(\{ x:x \in R, -8\le -2 \}\)
(iv) \(\{x:x\in R, -5\le x \le 9 \}\)

Find two irrational numbers such that their sum is a rational number. Can you find two irrational numbers whose product is a rational number

Find a positive number small than \(\frac { 1 }{ { 2 }^{ 1000 } } \). Justify.

A fighter jet has to hit a small target by flying a horizontal distance. When the target is sighted, the pilot measures the angle of depression to be 30⁰. If after 100 km, the target has an angle of depression of 60⁰, how far is the target from the fighter jet at that instant?

A plane is 1 km from one landmark and 2 km from another. From the planes point of view the land between them subtends an angle of 45⁰. How far apart are the land marks?

Show that cos² A + cos² B - 2 cos A cos B cos (A + B) = sin² (A + B)

If \(\cos { \left( \alpha -\beta \right) } +\cos { \left( \beta -\gamma \right) } +\cos { \left( \gamma -\alpha \right) } =\frac { -3 }{ 2 } \) then prove that \(\cos { \alpha } +\cos { \beta } +\cos { \gamma } =\sin { \alpha } +\sin { \beta } +\sin { \gamma } =0\)

Find the pairs of equal sets from the following sets. A = {0}, B = {x : x > 15 and x < 5}, C = {x : x - 5 = 0}, D = {x : x² = 25}, E = {x : x is an integral positive root of the equation x² - 2x - 15 = 0}.

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

If one root of the equation 3x²+ kx - 81= 0 is the square of the other then find k

If one root of the equation 2x²- ax + 64 = 0 is twice that of the other then find the value of a

Prove that sin (270° - \(\theta\)) sin (90° - \(\theta\)) - cos (270° - \(\theta\)) cos (90° + \(\theta\)) + 1 = 0.

Prove that: cos 24° + cos 55° + cos 125° + cos 204° + cos 300°\(=\frac{1}{2}\)

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

If (n+2)! = 60(n-1)! find n.

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

Show that the sequence where log a,\(log\frac { { a }^{ 2 } }{ b^{ 1 } } log\frac { { a }^{ 2 } }{ { b }^{ 2 } } \)  ..is an A.P

Let A = {a, b, c, d}, B = {a, c, e}, C = {a, e}.
Show that A ∩ (B ∩ C) = (A ∩ B) ∩ C

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

There are 5 teachers and 20 students. Out of them a committee of 2 teachers and 3 students is to be formed. Find the number of ways in which this can be done. Further find in how many of these committees
(i) a particular teacher is included?
(ii) a particular student is excluded?

Show that the sum of (m + n)^th and (m - n)^th term of an A.P is equal to twice the m^th term.

A man repays an amount of Rs. 3250 by paying Rs. 20 in the first month and then increases the payment by Rs.15 per month. How long will it take him to clear the amount?

Find the equation of a straight line parallel to 2x + 3y = 10 and which is such that the sum of its intercepts on the axes is 15.