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Solution for Class 11, Mathematics

Question 21

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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Question 22

Views: 5,875

3 tan α tan β = 1

2 cos (α + β) = cos (α - β)

8. Eliminate $θ$ if $tan (θ - α) = a$ and $tan (θ + α) = b$ .
9. Prove that:
(ii) $tan A + tan (6 0^{\circ} + A) + tan (12 0^{\circ} + A) = 3 tan 3 A$
(iii) $\frac{t a n 6 9 ^{\circ} + t a n 6 6 ^{\circ}}{1 - t a n 6 9 ^{\circ} t a n 6 6 ^{\circ}} = - 1$

Topic:

Trigonometry

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Question 23

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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Question 24

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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Question 25

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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Question 26

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 27

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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Question 28

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 29

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 30

Views: 5,800

A, B

then find the locus of

P

. (MARCH-2009, 2006) (TS MAR 15) 1)

O (0, 0), A (6, 0)

B (0, 4)

are three points. If

P

is a point such that the area of

△ POB

is twice the area of

△ PO A

, then find the locus of

P

. ii) Find the equation of locus of the point

Topic:

Coordinate Geometry

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Question 31

Views: 5,291

1.2

Find the length of an arc of a circle which subtends an angle of

10 8^{\circ}

at the centre, if the radius of the circle is 15

cm

Topic:

Vector and 3D

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Question 32

Views: 5,985

The number of solutions of the equation lying in the interval are

0
1
2
3

Topic:

Trigonometry & Logarithm

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Question 33

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 34

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 35

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 36

Views: 5,145

Prove that Cos 15° + sin 15° / cos 15° - sin 15° = √3

Topic:

Trigonometry

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Question 37

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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Question 38

Views: 5,900

tan^{2} θ = 2 tan^{2} ϕ + 1

, then the value of

cos 2 θ + sin^{2} ϕ

1
2
$- 1$
Independent of $ϕ$

Topic:

Trigonometry

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Question 39

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 40

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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