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Calculus - Mathematics Questions asked by Filo students

Views: 5,167

2 Consider the relation

R = 1

{(x, y) ∣ x - y = 0} \subset R \times R

R

. Which of the following is/are true?

R

is a transitive relation.

R

R

is not an equivalence relation.

R

is a reflexive relation.

R

is a symmetric relation.

Topic:

Calculus

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Views: 5,928

The value of integral

\int e^{x} (\frac{x - 2}{( x - 1 ) ^{2}}) d x

{" $f r a c e^{x} x - 1 + C$ "," $f r a c e^{x} (x - 1)^{2} + C$ "," $f r a c 2 e^{x} (x - 1)^{2} + C$ "," $f r a c e^{x} + 1 x - 1 + C$ "}

Topic:

Calculus

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Views: 5,431

The value of integral

\int \frac{d x}{2 + c o s 2 x}

{" $t a n^{- 1} l e f t (f r a c t an x s q r t 3 r i g h t) + C$ "," $f r a c 13 t a n^{- 1} l e f t (f r a c t an x 3 r i g h t) + C$ "," $co t^{- 1} l e f t (f r a c t an x s q r t 3 r i g h t) + C$ "," $f r a c 1 s q r t 3 t a n^{- 1} l e f t (f r a c t an x s q r t 3 r i g h t) + C$ "}

Topic:

Calculus

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Views: 6,075

f : D ⟶ R

is a ) function defined by

f (x) =

\frac{x ^{2} - 16}{x + 4}

D \subset Z

A

be the set of integers which are not in the domain of

f

, then find the cardinality of the set

A

Topic:

Calculus

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Views: 5,337

6 Consider the set

S = {a ∣ a \in

N, a \leq 36}

R_{1}

R_{2}

be relations from

S

S

R_{1} = {(x, y) ∣ x, y \in S, y = 3 x}

R_{2} = {(x, y) ∣ x, y \in S, y = x^{2}}

. Find the cardinality of the set

R_{1} \ (R_{1} \cap

R_{2}

Topic:

Calculus

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Views: 5,892

7 In a Zoo, there are 6 Bengal ) white tigers and 8 Bengal royal tigers. Out of these tigers, 5 are males and 10 are either Bengal royal tigers or males. Find the number of female Bengal white tigers in the Zoo.

Topic:

Calculus

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Views: 5,528

8 Consider the following sets, )

A = {x ∣ x \in N}

B = {x ∣ - 5 < x < 105, x \in R}

C = {x ∣ x

is a rational number,

10 <

x \leq 80}

Find the cardinality of the set

(A -

\cap B

Topic:

Calculus

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Views: 5,445

progression 2, 6,

10 \dots ..86

3 x, x + 2

and 8 are three consecutive terms of an A.P., find its Fourth term. 17. The 1st term of an A.P. is

- 24

Topic:

Calculus

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Views: 5,542

(1 + ω) (1 + ω^{2}) (1 + ω^{4}) (1 + ω^{5}) = 1

(1 + ω) (1 + ω^{2}) (1 + ω^{4}) (1 + ω^{8}) = 1

(2 + ω + ω^{2})^{3} + (1 + ω - ω^{2})^{8} - (1 - 3 ω + ω^{2})^{4} = 1

(1 - ω + ω^{2}) (1 - ω^{2} + ω^{4}) (1 - ω^{4} + ω^{8}) (1 - ω^{8} + ω^{16}) = 16

(a + b + c) (a + bω + c ω^{2}) (a + b ω^{2} + g ω) = a^{3} + b^{3} + c^{3} - 3 ab c

ω

be an imaginary cube root of urfty, show that

Topic:

Calculus

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Question 10

Views: 5,184

26. The 4th term of an A.P. is three times the

1 st

term and the 7th term is 1 more than two times the 3rd term. Find the first term and common difference of the progression.

Topic:

Calculus

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Question 11

Views: 5,462

Qucstion No:49(b) 1. Find the sum to

n -

terms of the series

1^{3} + (1^{2} + 2^{2}) + (1^{2} + 2^{2} + 3^{2}) +

Topic:

Calculus

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Question 12

Views: 5,245

Using the sum formula We have

S_{10} = 2

Hence, the number of ancestors

p

9.5.3 Geometric Mean (G.M.) ] and

b

ab

Topic:

Calculus

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Question 13

Views: 5,122

Ex. A dice is rolled 3 times, top-most face is considered as outcome then find the number of outcome such that : (i) 5 appears atleast once. (ii) All 3 outcomes are different. (iii) Exactly 2 outcomes are same. (getifing a doublet)

Topic:

Calculus

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Question 14

Views: 5,670

find the sum of all two digit no. which is divided by 4 yields 1 as remanded

Topic:

Calculus

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Question 15

Views: 5,103

, Il Airtel < Back A4 Differentiation (22-01-2022) Part A : Differentiate following with respect to

x

$\frac{1}{x}$
$x$
$x^{3/2}$
$\frac{1}{x}$
$e^{3}$
$3 x^{3/2}$

Topic:

Calculus

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Question 16

Views: 5,033

2 x-y-3 z &=9 \\ x y z &=6 \\ x-y z &=2 \end{aligned} \]

Topic:

Calculus

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Question 17

Views: 5,366

- 12 x > 30

x

is a natural number (ii)

x

Topic:

Calculus

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Question 18

Views: 5,602

The order of a set

A

is 3 and that of a set

B

is 2 . What is the number of relations from

A

B

? [NDA 2010 (I)]

4
6
32
64

Topic:

Calculus

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Question 19

Views: 5,228

Ex:- Find the Range of

a) f (x) = x^{2} + 2 x + 4

Topic:

Calculus

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Question 20

Views: 5,187

Using the property of squares that helps you calculate

(n + 1)^{2} - n^{2}

, find the values of the following.

$1 9^{2} - 1 8^{2}$
$11 0^{2} - 10 9^{2}$
$6 3^{2} - 6 2^{2}$
$240 1^{2} - 240 0^{2}$

Topic:

Calculus

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