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Math Short Questions

Math Short Questions

Math Short Questions

Prove that Z + Z is real.

2. If Z = a + ί b then prove that Z – Z is imaginary.

3. If Z = a + ί b then prove that z. z = |Z|2

4. Prove that Z = z iff Z is real.

5. Find the multiplication Inverse of 2 + 3 ί.

__ __

6. Express (4 + √-3) (3 + √-3 in the form of a + bi.

__

7. Express √3 + ί in polar form.

8. Express 1 – ί in polar form.

9. Factorize a

10. (Factorize) 7×2

11. Simplify (1, -2) / (3, 4).

__

12. Show that √3 is an irrational number.

13. Prove that (Z1 / Z2) = Z1 / Z2 , For all Z ε C.

.

2

+ 9 b2

.

+ 7y2

A set has …………… objects.

(a) Identical (b) Not well-defixed

(c) Distinct (d) None

2. B = {x│ x Є N Λ 1 ≤ x ≤ 10}

(a) The descriptive method (b) The tabular method

(c) Set-builder notation (d) None of these

3. The set {1, 2, 3} and {2, 1, 3} are ……………….

(a) Equal (b) Equivalent

(c) Different (d) Equal and Equalent

4. A Singleton set has……………….

(a) One element (b) No element

(c) Two element (d) None of these

5. If every element of a set A is an element of set B then ………………

(a) A B (b) A b (c) B A (d) None

6. If B is a super set of A then ………….

(a) A B (b) B A (c) B A (d) None

7. A is an improper subset of B when A B and…………….

(a) A = B (b) A – B = U (c) A ∩ B = Φ (d) None

8. If A = { } then P (A) = ……………………

(a) Empty set (b) {0} (c) {Φ} (d) None

9. If n(s) = m, then nP(s) =…………………..

(a) 2 m

10. A UB is defined as …………………….

(a) {x / x Є A v x Є B} (b) {x / x Є A Λ x Є B}

(c) {x / x Є A Λ x Є B} (d) None

11. A∩B is defined as………………

(a) {x / x Є A v x Є B} (b) {x / x Є A ^ X Є B}

(c) {x / x Є A ^ x Є B} (d) None

12. The complement of a set A is defined as ……………..

(a) A/

(c) A/

13. A U Φ =………………………….

(b) 2 m-1

(c) 2 m+1

= {x / x Є U ^ x Є A} (b) A/

= {x / x Є U v x Є A} (d) None

(a) A (b) Φ (c) u (d) None

14. A ∩ Φ =…………………………………

(a) A (b) Φ (c) A/

15. A – Φ =…………………..

(a) A (b) Φ (c) A/

16. (AUB)/

= ………………………………….

(a) A/ UB/

17. If AxB = BxA then …………….

(a) A = B (b) A∩B = Φ (c) A = B (d) None

18. The function f : A ‡ B is A into B function when …………….

(a) Ran f = B (b) Ran f ≠ B (c) Ran f = A (d) None

19. Which one is linear function?

(a) {(x, y) | y = mx + c} (b) {(x, y) | y = mx

(c) {(x, y) | y

20. Which one is quadratic function?

(a) {(x, y) | y = mx + c} (b) {(x, y) | y

(c) {(x, y) | y = ax

(b) A/ UB (c) A/∩B

/

(d) A∩B

2

+ c}

2

= mx + c} (d) None

2

= mx +c

2

+ bx + c} (d) None

Write down the power set of A = {9, 10} possible subsets of A are Φ,

{9}, {10}, {9, 10} so power set of A = {Φ}, {9}, {10}, {9, 10}

2. If A = {1, 2, 3, 4,} B = {4, 5, 6} then verify the Commutation

property of union.

3. If v = {(x, y) | x

function.

4. r = {(x, y) | y = 2x + 3}then show that r and r

5. Why (N, +) is not a group.

6. State and prove associative property of union and intersection.

7. For any sets A, B ,C Prove that

(i) AU(B∩C) = (AUB) ∩ (AUC)

(ii) A∩(BUC) = (A∩B) U (A∩C)

8. Let A,B are the subsets of a universal set X then prove that

(i) (AUB)C

(ii) (A∩B)C

9. Define a group. Is Z the set integer is a group under multiplication.

10. Show that set {1, w, w

11. Does the set { 1, -1 } posses the closure property w.r.t

(i) Addition (ii) multiplication

2

2

= 9 , | x | ≤ 3, | y| ≤ 3|} show that r is not a

+ y

-1

are functions.

= AC

∩ BC

= AC

U BC

 

 

2

} where w

3

=1 is a group under multiplication.

Trivial solution of homogeneous linear equation is

(a) (1, 0, 0) (b) (0, 1, 0) (c) (0, 0, 1) (d) (0,0,0)

2. For non-trivial solution |A| is ……………

(a) |A| > 0 (b) |A| < 0 (c) |A| = 0 (d) None

3. For trivial solution |A| is……………..

(a) |A| > 0 (b) |A| < 0 (c) |A| = 0 (d) None

4. System o linear equations is Inconsistent if ………

(a) System has no solution (b) System has many solution

(c) System has unique solution (d) None

5. Minimum number of equation for any system of equations

(a) 2 (b) 3 (c) 4 (d) 10

6. The matrix A is Hermitian when (A)t

(a) A (b) – A (c) At

7. The square matrix A is skew-Hermitian when ( A )t

(a) A (b) – A (c) A (d) – A

8. The square matrix A is skew – Symmetric when At

(a) 0 (b) A (c) – A (d) None

= ……………

(d) A

=……………

= …………

Math Short Questions

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