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3D Geometry - Mathematics Questions asked by Filo students

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a-b-c & 2 a & 2 a \\ 2 b & b-c-a & 2 b \\ 2 c & 2 c & c-a-b \end{array}\right|(a+b+c)^{3} \]

Topic:

Vector and 3D

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Views: 5,396

Express each of the complex number given in the Exercises 1 to

10 i

a + ib

(5 i) (- \frac{3}{5} i)

i^{9} + i^{19}

i^{- 39}

Topic:

Vector and 3D

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Views: 5,696

(a) i The smallest positive integer n for which (\frac{1 + i}{1 - i})^{n} = 1, is (b) i - 1 (c) - i (d) 0^{(1998, 2 M)}

(1980, 2 M)

(c) 12 (d) None of these ctive Question II or more than one correct option) Let

a, b, x

y

be real numbers such that

a - b = 1

Topic:

Vector & 3D

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Views: 5,199

= \frac{3 + 6 2 i}{1 + 2} = \frac{3 ( 1 + 2 2 i )}{3} = 1 + 22 i

i^{- 35} = \frac{1}{i ^{35}} = \frac{1}{( i ^{2} ) ^{17} i} = \frac{1}{- i} \times \frac{i}{i} = \frac{i}{- i ^{2}} = i

of the complex number given in the Exercise 2.

i^{9} + i^{19}

i^{- 39}

Topic:

Vector and 3D

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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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Views: 5,186

(v) Three consecutive vertices of a triangle

ABC

A (6, - 2, 4), B (2, 4, - 8)

C (- 2, 2, 4)

. Find the co-ordinates of centroid.

Topic:

Vector and 3D

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Views: 5,140

(7) Pind the Variance and stam dred devicition for the folloving elulat

Topic:

Vector and 3D

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Views: 5,650

Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set A multiply B each having at least three elements is

Topic:

Vector and 3D

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Views: 5,616

Find the multiplicative inve Exercises 11 to

13.

4 - 3 i

14. Express the following ex

Topic:

Vector and 3D

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Question 10

Views: 5,221

(4

marks, 8 min.) 1. Find the va ue of

C D

x

n

the adjoinng fgure, where

O

is the oentre of semiorcle:

Topic:

Vector and 3D

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Question 11

Views: 6,035

△ A BC

A, B, C

are in A.P., then prove that

2 cos \frac{A - C}{2} = \frac{a + c}{a ^{2} + c ^{2} - a c}

. (v) If in a triangle

A BC, ∠ C = 6 0^{\circ}

, then prove that

\frac{1}{a + c} + \frac{1}{b + c} = \frac{3}{a + b + c}

. (vi) Triangle

ABC

BC = 1

AC = 2

. Find the maximum possible value of ang

Topic:

Vector and 3D

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Question 12

Views: 5,989

am- impo (2.) find the circumcentre of the die where sides are

3 x - y - 5 = 0, x + 2 y - 4 = 0

5 x + 3 y + 1 - 0

Topic:

Vector and 3D

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Question 13

Views: 5,541

n=2 \text { वर्ष } \\ A=6615 \text { रू० } \end{array} \]

Topic:

Vector and 3D

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Question 14

Views: 5,316

5. List all the elements of each of the following sets: (i)

A = {x : x \in Z

- \frac{1}{2} < x < \frac{7}{2}}

B = {x : x \in Z

x^{2} \leq 4}

C = {x : x = 2 n, n \in N

n \leq 5}

Topic:

Vector and 3D

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Question 15

Views: 5,893

α, β (α - β \neq = 2 n π, n \in I)

are different values of

θ

satisfying the equation

5 cos θ - 12 sin θ = 11

. If the value of

sin (α + β) = - \frac{5 k}{169}

, then find the value of

k

x \in (π, \frac{3 π}{2})

4 cos^{2} (\frac{π}{4} - \frac{x}{2}) + 4 sin^{4} x + sin^{2} 2 x

is always equal to

Topic:

Vector and 3D

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Question 16

Views: 5,575

The radius of a circle is

9 cm

. Find the length of an arc of this circle which cuts off a chord of length, equal to length of radius.

Topic:

Vector and 3D

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Question 17

Views: 5,768

The angles of a quadrilateral are in A.P. and the greatest angle is double the least. Find angles of the quadrilateral in radian.

Topic:

Vector and 3D

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Question 18

Views: 5,704

8. Find the domain and range of the functior 9. Convert

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

in to polar form.

Topic:

Vector and 3D

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Question 19

Views: 5,806

Q.4 Express the following angles in degree, minute and second. i)

(183.7)^{\circ}

(245.33)^{0}

(\frac{1}{5})^{c}

△ ABC

m ∠ A = \frac{7 π ^{c}}{36}

m ∠ B = 12 0^{\circ}

m ∠ C

in degree and radian. Q.6 Two angles of a triangle are

\frac{5 π ^{c}}{9}

\frac{5 π ^{c}}{18}

. Find the degree and radian measure of third angle.

Topic:

Vector and 3D

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Question 20

Views: 5,535

In the given figure, which vectors are (provided vertices A, B, C, D, E, F are all fixed) :

Parallel
Equal
Coinitial
Parallel but not equal.

Topic:

Vector and 3D

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