Please select a subject first
Advertisements
Advertisements
Is the given relation a function? Give reasons for your answer.
h = {(4, 6), (3, 9), (– 11, 6), (3, 11)}
Concept: undefined >> undefined
Is the given relation a function? Give reasons for your answer.
f = {(x, x) | x is a real number}
Concept: undefined >> undefined
Advertisements
Is the given relation a function? Give reasons for your answer.
g = `"n", 1/"n" |"n"` is a positive integer
Concept: undefined >> undefined
Is the given relation a function? Give reasons for your answer.
s = {(n, n2) | n is a positive integer}
Concept: undefined >> undefined
Is the given relation a function? Give reasons for your answer.
t = {(x, 3) | x is a real number
Concept: undefined >> undefined
Let n(A) = m, and n(B) = n. Then the total number of non-empty relations that can be defined from A to B is ______.
Concept: undefined >> undefined
Define the sequence a1, a2, a3 ... as follows:
a1 = 2, an = 5 an–1, for all natural numbers n ≥ 2.
Write the first four terms of the sequence.
Concept: undefined >> undefined
If P(n) : “2.42n+1 + 33n+1 is divisible by λ for all n ∈ N” is true, then the value of λ is ______.
Concept: undefined >> undefined
If P(n): “49n + 16n + k is divisible by 64 for n ∈ N” is true, then the least negative integral value of k is ______.
Concept: undefined >> undefined
If z1 and z2 both satisfy `z + barz = 2|z - 1|` arg`(z_1 - z_2) = pi/4`, then find `"Im" (z_1 + z_2)`.
Concept: undefined >> undefined
State true or false for the following:
If a complex number coincides with its conjugate, then the number must lie on imaginary axis.
Concept: undefined >> undefined
Match the statements of column A and B.
| Column A | Column B |
| (a) The value of 1 + i2 + i4 + i6 + ... i20 is | (i) purely imaginary complex number |
| (b) The value of `i^(-1097)` is | (ii) purely real complex number |
| (c) Conjugate of 1 + i lies in | (iii) second quadrant |
| (d) `(1 + 2i)/(1 - i)` lies in | (iv) Fourth quadrant |
| (e) If a, b, c ∈ R and b2 – 4ac < 0, then the roots of the equation ax2 + bx + c = 0 are non real (complex) and |
(v) may not occur in conjugate pairs |
| (f) If a, b, c ∈ R and b2 – 4ac > 0, and b2 – 4ac is a perfect square, then the roots of the equation ax2 + bx + c = 0 |
(vi) may occur in conjugate pairs |
Concept: undefined >> undefined
If `((1 - i)/(1 + i))^100` = a + ib, then find (a, b).
Concept: undefined >> undefined
If a = cosθ + isinθ, find the value of `(1 + "a")/(1 - "a")`.
Concept: undefined >> undefined
State True or False for the following:
The order relation is defined on the set of complex numbers.
Concept: undefined >> undefined
State True or False for the following:
2 is not a complex number.
Concept: undefined >> undefined
Match the statements of Column A and Column B.
| Column A | Column B |
| (a) The polar form of `i + sqrt(3)` is | (i) Perpendicular bisector of segment joining (–2, 0) and (2, 0). |
| (b) The amplitude of `-1 + sqrt(-3)` is | (ii) On or outside the circle having centre at (0, –4) and radius 3. |
| (c) If |z + 2| = |z − 2|, then locus of z is | (iii) `(2pi)/3` |
| (d) If |z + 2i| = |z − 2i|, then locus of z is | (iv) Perpendicular bisector of segment joining (0, –2) and (0, 2). |
| (e) Region represented by |z + 4i| ≥ 3 is | (v) `2(cos pi/6 + i sin pi/6)` |
| (f) Region represented by |z + 4| ≤ 3 is | (vi) On or inside the circle having centre (–4, 0) and radius 3 units. |
| (g) Conjugate of `(1 + 2i)/(1 - i)` lies in | (vii) First quadrant |
| (h) Reciprocal of 1 – i lies in | (viii) Third quadrant |
Concept: undefined >> undefined
The real value of θ for which the expression `(1 + i cos theta)/(1 - 2i cos theta)` is a real number is ______.
Concept: undefined >> undefined
In a class, there are 27 boys and 14 girls. The teacher wants to select 1 boy and 1 girl to represent the class for a function. In how many ways can the teacher make this selection?
Concept: undefined >> undefined
How many numbers are there between 99 and 1000 having 7 in the units place?
Concept: undefined >> undefined
