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Solution for Class 12, Mathematics

Views: 5,442

π - sec^{- 1} (x), ∣ x ∣ > 1

, is equal to :

$sec^{- 1} (x)$
$cosec^{- 1} (- x)$
$sec^{- 1} (- x)$
$cosec^{- 1} (x)$ ::

Topic:

Calculus

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Views: 5,117

set of all integers in

Z

which are related to 2 . Thus,

A_{1} = [0]

A_{1} = {3 r ∣ . A_{1} = {3 r + 1]

A_{3} = {3 r + 2]

r \in Z

. Example 6 Let

R

be the relation defined in the set

A = {1, 2, 3, 4, 5, 6, 7}

R = {(a, b)

a

b

are either odd or even

}

R

is an equivalence relation. Further, show that all the elements of the subset

{1, 3, 5, 7}

are related to each other and all the elements of the subset

{2, 4, 6}

are related to each other, but no element of the subset

(1, 3, 5, 7}

is related to any element of the subset

{2, 4, 6}

Topic:

Algebra

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Views: 5,792

∣ a ∣ b + ∣ b ∣ a

is perpendicular to

∣ a ∣ b - ∣ b ∣ a

, for any iw vectors

a

b

a \cdot a = 0

a \cdot b = 0

, then what can be concluded about the vector

b

a, b, c

are unit vectors such that

a + b + c = 0

, find the value of

a \cdot b + b \cdot c + c \cdot a

14. If either vector

a = 0

b = 0

a \cdot b = 0

. But the converse need not be true. Justify your answer with an example.

Topic:

Calculus

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Views: 5,144

12. Express the matrix

A = ⎣ ⎡ 271 43 - 2 - 6 54 ⎦ ⎤

as the sum of a symmetric and skew-symmetric matrix. All india 2015C

Topic:

Calculus

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Views: 5,052

3 - 1 21] [1 - 1 0211]

solve the equation for

x, y, z

t

2 [x y z t] + 3 [10 - 1 2] = 3 [3456]

x [23] + y [- 1 1] = [105]

, find the values of

x

y

3 [x z y w] = [x - 1 6 2 w] + [4 z + w x + y 3]

, find the values of

x, y, z

w

Topic:

Algebra

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Views: 5,524

Paragraph for Questions 3 and 4 Consider an equation

(x - a) (x - b) (x - c) + (x - 1) (x^{2} + x + 1) = 0

whose roots are

α, β, γ

. 3. Sum of roots of the equation

2 (x - α) (x - β) (x - γ) - (x - a) (x - b) (x - c) = 0

, is - 4. The roots of equation

2 (x - α) (x - β) (x - γ) + 1 - x^{3} = 0

p, q, r

\frac{p + q + r}{a + b + c} =

Topic:

Algebra

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Views: 6,008

Using Cofactors of elements of third column, evaluate

Δ = ∣ ∣ 111 x y z yz z x x y ∣ ∣

∣ ∣ a_{11} a_{12} a_{13} ∣ ∣

Topic:

Calculus

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Views: 5,506

cos (A + B) sin (C - D) = cos (A - B) sin (C + D)

tan A tan B tan C + tan D = 0

x cos θ = y cos (θ + \frac{2 π}{3}) = z cos (θ + \frac{4 π}{3})

x y + yz + z x = 0

m sin θ = n sin (θ + 2 α)

tan (θ + α) cot α = \frac{m + n}{m - n}

. [NCERT EXEMPLA (i)

2 sin 8 x cos 4 x

2 sin 2 x cos 3 x

2 cos 10 x cos 2 x

Topic:

Trigonometry

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Views: 5,385

The value of determinant

∣ ∣ 111 b c c a ab a (b + c) b (c + a) c (a + b) ∣ ∣

1
$- 1$
0
None of these.

Topic:

Coordinate Geometry

View 7 solutions

Question 10

Views: 5,171

lim_{x \to α} f (x)

exist, then the true set of values of

α

{k}

denotes the fractional part of

k

Q

be the set of all ratise numbers.]

$(- 1, 1)$
$(- 1, 0]$
$(0, 1)$
$[0, 1)$

Topic:

Calculus

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Question 11

Views: 5,989

f (x) = x^{3}

is continuous as well as differenti ble at

x = 3

Topic:

Calculus

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Question 12

Views: 5,075

The number of real solution of the equation

{" $f r a c t a n^{- 1} s q r t x^{2} - 3 x + 7 ∣ + f r a c co s^{- 1} s q r t 4 x^{2} - x + 3 Do w na rro w = p i$ is $f r a c zer$ "," $t a n^{- 1}$ (tre)","Ist quad Ist quad"," $l e f t (0, f r a c p i 2 r i g h t) + l e f t (0, f r a c p i 2 r i g h t) e q u i v (0, p i)$ "}

Topic:

Trigonometry

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Question 13

Views: 5,960

ABC share profit and losses in the profit and 1/2,1/3,16 recipe dear balance shift as on 31 March 2019 is as follows

Topic:

Calculus

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Question 14

Views: 5,347

In Argand diagram all the complex numbers z satisfying

∣ z - 4 i ∣ + ∣ z + 4 i ∣ = 10

straight line
circle
ellipse
parabola

Topic:

Calculus

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Question 15

Views: 5,323

A had purchased a cycle few years back. He carries out repairs of Rs. 1000 and then sells it to B at a profit of

10%

. B caries out repairs of Rs. 1000 and then later sells it to

C

10%

. C also carries out repairs of Rs. 1000 and then later sells it to

D

10%

D

paid Rs. 7634 , what did the cycle cost to

A

, when he had purchased the cycle few years back?

{"A 2400","B $q u a d 3000$ ","C 3600","D 4000"}

Topic:

Algebra

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Question 16

Views: 5,885

the logarithm of two numbers is independent of their common base."

\frac{m}{b}

a > 0, a \neq = 1, b > 0, b \neq = 1

Topic:

Algebra

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Question 17

Views: 5,484

Show that the matrix

A = ⎣ ⎡ 1 - 1 5 - 1 21 513 ⎦ ⎤

is a symmetric matrix. Show that the matrix

A = ⎣ ⎡ 0 - 1 1 10 - 1 - 1 10 ⎦ ⎤

is a skew symmetric matrix.

Topic:

Vector and 3D

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Question 18

Views: 5,531

2 & 0 & 1 \\ 2 & 1 & 3 \\ 1 & -1 & 0 \end{array}\right] \]

Topic:

Algebra

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Question 19

Views: 5,124

\frac{π}{12}

What is the area of the region bounded by

x - ∣ y ∣ = 0

x - 2 = 0

2 = 2

Topic:

Coordinate Geometry

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Question 20

Views: 5,300

Find the remainder when

x^{3} + 3 x^{2} + 3 x + 1

$x + 1$
$x - \frac{1}{2}$
$x$
$x + π$
$5 + 2 x$

Topic:

Algebra

View 9 solutions

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