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Algebra - Mathematics Questions asked by Filo students

Views: 5,981

Find the domain and range of real values function fx=2/3-x²

Topic:

Algebra

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Views: 5,730

A \cup B = {a, b_{1} c} .

A

B

are two sets such that

A CB

A \cup B

Topic:

Algebra

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Views: 5,986

3 A = {1, 2, 3, 5, 5

B = {4, 6, 9}

. Define a relation

R

A

B

R = {(x, y)

: the difference between

x

y

x \in A

y \in B}

R

in roaster form.

R = ξ (x, y) :=

Topic:

Algebra

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Views: 5,090

The polar form of complex number

\frac{1 - 1}{c o s \frac{π}{3} + i s i n \frac{π}{3}}

2 (cos \frac{5 π}{12} + i sin \frac{5 π}{12})

2 (cos \frac{5 π}{12} - i sin \frac{5 π}{12})

2 (- cos \frac{5 π}{12} + i sin \frac{5 π}{12})

2 (- cos \frac{5 π}{12} - i sin \frac{5 π}{12})

x

y

for which the equation

(x^{4} + 2 x i) - (3 x^{2} + y i) = (3 - 5

Topic:

Algebra

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Views: 5,521

lo g_{10} (\frac{1}{2 ^{x} + x - 1}) = x (lo g_{10} 5 - 1)

x =

4
3
2
1

Topic:

Algebra

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Views: 5,207

n (A) = x & n (B) = y

max {x, y} \leq n (A \cup B) \leq x + y

. 15. In a group of 100 students, 60 like to play Cri

Topic:

Algebra

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Views: 5,722

roster form. 4. The Fig2.7 shows a relationship between the sets

P

Q

. Write this relation (i) in set-builder form (ii) roster form. What is its domain and range?

Topic:

Algebra

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Views: 5,440

[JEE (Advanced)-2021, Paper-2] 33. Consider

M

r = \frac{1025}{513}

k

be the number of all those circles

C_{n}

that are inside

M

l

be the maximum possible umber of circles among these

k

circles such that no two circles intersect. Then :

$k + 2 l = 22$
$2 k + l = 26$
$2 k + 3 l = 34$
$3 k + 2 l = 40$

Topic:

Algebra

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Views: 5,909

M

r = \frac{( 2 ^{199} - 1 ) 2}{2 ^{198}}

. The number of all those circles

D_{n}

that are inside

M

198
199
200
201

Topic:

Algebra

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Question 10

Views: 5,940

JEE Main 12 th Jan - 12019 Q5. Let

S = {1, 2, 3, \dots, 100}

. The number of non-empty subsets

A

S

such that the product of elements in

A

2^{100} - 1

2^{50} (2^{50} - 1)

2^{50} - 1

2^{50} + 1

Topic:

Algebra

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Question 11

Views: 5,863

\frac{a ^{n} + b ^{n}}{a ^{n - 1} + b ^{n - 1}}

is the G.M.'s between

a

b

, then find the value of

n

Topic:

Algebra

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Question 12

Views: 5,959

R

is the sut of Real number. and

Q

is the set of rational number., them what

R - Q

Topic:

Algebra

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Question 13

Views: 5,731

A = {1, 2, 3, 4, 6}

R

be the relation on

A

{(a, b) : a, b \in A, b

is exactly divisible by

a}

R

in roster form (ii) Find the domain of

R

(iii) Find the range of

R

Topic:

Algebra

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Question 14

Views: 5,604

3_{2 n + 2}^{2 n - 8 n - 9}

is divisible by 8 . 23.

4 1^{n} - 1 4^{n}

is a multiple of 27 . 24.

(2 n + 7) < (n + 3)^{2}

Topic:

Algebra

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Question 15

Views: 5,407

the number line. 8. Given

x \in {1, 2, 3, 4, 5, 6, 7, 9}

x - 3 < 2 x - 1

. 9. List the solution set of the inequation

\frac{1}{2} + 8 x > 5 x - \frac{3}{2}, x \in Z

. 110. List the solution set of

11 - 2 x \geq \frac{9 - 3 x}{+} + \frac{3}{3}

Topic:

Algebra

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Question 16

Views: 5,567

(a) lo g_{1} 32 - 5 (b) lo g_{2} 4 = 4 (c) lo g_{0} 0, 01 = - 2

lo g_{+ 7} 1728 = x

x

. 4. Find the logarithms of the following numbers to the base 2 :

1
2
4
8

Topic:

Algebra

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Question 17

Views: 5,303

{x : \frac{x - 1}{x - 3} = 4, x \in R}

in roster form is

{" $(a) l e f t - f r a c 113 r i g h t$ "," $(b) l e f t - f r a c 123 r i g h t$ "," $(c) l e f t - f r a c 133 r i g h t (d) l e f t - f r a c 143 r i g h t$ ","Page $1/8$ "}

Topic:

Algebra

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Question 18

Views: 5,875

\frac{2}{x} + \frac{3}{y} + \frac{10}{z} = 4, \frac{4}{x} - \frac{6}{y} + \frac{5}{z} = 1

\frac{6}{x} + \frac{9}{y} - \frac{20}{z} = 2

A = ⎣ ⎡ 347 2 - 1 3 12 - 3 ⎦ ⎤

A^{- 1}

and with its help solve the system of equations

3 x + 2 y + z = 6, 4 x - y + 2 z = 5

7 x + 3 y - 3 z = 7

B = ⎣ ⎡ 2 - 4 2 22 - 1 - 4 - 4 5 ⎦ ⎤

A = ⎣ ⎡ 120 - 1 31 042 ⎦ ⎤

A B

and with its help solve the system of equations

y + 2 z = 7, x - y = 3

2 x + 3 y + 4 z = 17

Topic:

Algebra

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Question 19

Views: 5,701

5.5

A sequence of integers

a_{1} + a_{2} + \dots + a_{n}

a_{n + 2} = a_{n + 1}

- a_{n}

n \geq 1

. Suppose the sum of first 999 terms is 1003 and the sum of the first 1003 terms is

- 999

. Find the sum of the first 2002 terms.

Topic:

Algebra

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Question 20

Views: 5,594

x^{4} + 3 x^{2} - a = 0 is

8. The value of

\frac{- D}{a}

D = b^{2} - 4 a c

a x^{2} + b x + c = 0

a, b, c \in R - {0}

y = a x^{2} + b x + c

∣ y - 3∣ \leq 0

have exactly one intersection point is 9. If

a + b + c = - 46

α_{1}, α_{2}

α_{3}

x^{3} + a x^{2} + b x + c = 0

are integers and greater than 2 then

Topic:

Algebra

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