HSC Science (Computer Science) 11th Standard - Maharashtra State Board Question Bank Solutions

Answer the following:

Find the
(i) lengths of the principal axes
(ii) co-ordinates of the foci
(iii) equations of directrices
(iv) length of the latus rectum
(v) Distance between foci
(vi) distance between directrices of the curve

16x² + 25y² = 400

Answer the following:

Find the
(i) lengths of the principal axes
(ii) co-ordinates of the foci
(iii) equations of directrices
(iv) length of the latus rectum
(v) Distance between foci
(vi) distance between directrices of the curve

`x^2/144 - y^2/25` = 1

Answer the following:

Find the
(i) lengths of the principal axes
(ii) co-ordinates of the foci
(iii) equations of directrices
(iv) length of the latus rectum
(v) Distance between foci
(vi) distance between directrices of the curve

x² − y² = 16

Write the conjugates of the following complex number:

3 + i

Write the conjugates of the following complex number:

3 – i

Write the conjugates of the following complex number:

`-sqrt(5) - sqrt(7)"i"`

Write the conjugates of the following complex number:

`-sqrt(-5)`

Write the conjugates of the following complex number:

5i

Write the conjugates of the following complex number:

`sqrt(5) - "i"`

Write the conjugates of the following complex number:

`sqrt(2) + sqrt(3)"i"`

Write the conjugates of the following complex number:

cosθ + i sinθ

Find the value of i⁴⁹ + i⁶⁸ + i⁸⁹ + i¹¹⁰ 

Find the value of i + i² + i³ + i⁴ 

Simplify:

`(i^592 + i^590 + i^588 + i^586 + i^584)/(i^582 + i^580 + i^578 + i^576 + i^574)`

Find the value of 1 + i² + i⁴ + i⁶ + i⁸ + ... + i²⁰

Show that 1 + i¹⁰ + i¹⁰⁰ − i¹⁰⁰⁰ = 0 

Is (1 + i¹⁴ + i¹⁸ + i²²) a real number? Justify your answer

Evaluate: `("i"^37 + 1/"i"^67)`

Prove that `(1 + "i")^4 xx (1 + 1/"i")^4` = 16

Find the value of `("i"^6 + "i"^7 + "i"^8 + "i"^9)/("i"^2 + "i"^3)`