Find a matrix A such that 2 A - 3 B + 5 C = 0 , where B = - 2 2 0 3 1 4 and C = 2 0 - 2 7 1 6

We have, 2 A - 3 B + 5 C = O ⇒ 2 A = 3 B - 5 C ⇒ 2 A = 3 - 2 2 0 3 1 4 - 5 2 0 - 2 7 1 6 2 A = - 6 6 0 9 3 12 - 10 0 - 10 35 5 30 2 A = - 16 6 10 - 26 - 2 - 18 ⇒ A = - 8 3 5 - 13 - 1 - 9

If F x = cos x - sin x 0 sin x cos x 0 0 0 1 , then show that F x F y = F x + y

Given that, F x = cos x - sin x 0 sin x cos x 0 0 0 1 To proof : F x F y = F x + y Now, F x F y = cos x - sin x 0 sin x cos x 0 0 0 1 cos y - sin y 0 sin y cos y 0 0 0 1 ⇒ F x F y = cos x cos y - sin x sin y - cos x sin y + sin x cos y 0 sin x cos y + cos x sin y cos x cos y - sin x sin y 0 0 0 1 ⇒ F x F y = cos x + y - sin x + y 0 sin x + y cos x + y 0 0 0 1 . . . . . . . . . . . . . . . 1 ⇒ F x + y = cos x + y - sin x + y 0 sin x + y cos x + y 0 0 0 1 . . . . . . . . . . . . 2 From equation 1 and 2 , F x F y = F x + y Hence, proved.

Biopiracy may be defined as the robbery of indigenous knowledge of nature, naturally-occurring biological resources and genetic materials of a country by the technologically advanced country or organisation for commercial purpose or profit without any permission from or air compensation recognition to the peoples or nations in whose territory the materials were originally developed.

Compute the indicated products. 1 2 3 2 3 4

To find: 1 2 3 2 3 4 Here order of the first matrix is 3 × 1 and the second matrix is 1 × 3 . As here the number of columns in the first matrix is same as number of rows in the second matrix, by using the multiplication principle of matrices we get, 1 2 3 2 3 4 = 1 × 2 1 × 3 1 × 4 2 × 2 2 × 3 2 × 4 3 × 2 3 × 3 3 × 4 = 2 3 4 4 6 8 6 9 12 Hence, 1 2 3 2 3 4 = 2 3 4 4 6 8 6 9 12

Find X and Y , if X + Y = 7 0 2 5 and X - Y = 3 0 0 3

Given: X + Y = 7 0 2 5 ⋯ ⋯ ( 1 ) and X - Y = 3 0 0 3 ⋯ ⋯ ( 2 ) Adding equation ( 1 ) and ( 2 ) , we get X + Y + X - Y = 7 0 2 5 + 3 0 0 3 ⇒ 2 X = 7 + 3 0 + 0 2 + 0 5 + 3 2 X = 10 0 2 8 ⇒ X = 1 2 10 0 2 8 ⇒ X = 10 2 0 2 2 2 8 2 ⇒ X = 5 0 1 4 Putting the value of X in equation ( 1 ) , we get 5 0 1 4 + Y = 7 0 2 5 Y = 7 0 2 5 - 5 0 1 4 ⇒ Y = 7 - 5 0 - 0 2 - 1 5 - 4 ⇒ Y = 2 0 1 1 Therefore, X = 5 0 1 4 and Y = 2 0 1 1 .

If A = cos α sin α - sin α cos α , then verify that A ' A = I

Given: A = cos α sin α - sin α cos α To get transpose interchange rows and columns. ⇒ A ' = cos α - sin α sin α cos α Therefore A ' A = cos α - sin α sin α cos α cos α sin α - sin α cos α = cos 2 α + sin 2 α cos α sin α - cos α sin α cos α sin α - cos α sin α cos 2 α + sin 2 α = 1 0 0 1 = I ∴ A ' A = I Hence, proved

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Which activity does the sale of a patent fall under in the cash flow statement?

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Important Questions on Biotechnology and its Applications

EASY

Biology>Biotechnology>Biotechnology and its Applications>Ethical Issues in Biotechnology

Which one of the following represents a palindromic sequence in DNA?

MEDIUM

Biology>Biotechnology>Biotechnology and its Applications>Ethical Issues in Biotechnology

A

is a square matrix such that

A^{2} = I

, then

(A - I)^{3} + (A + I)^{3} - 7 A

is equal to

EASY

Biology>Biotechnology>Biotechnology and its Applications>Ethical Issues in Biotechnology

Find a matrix

A

such that

2 A - 3 B + 5 C = 0

, where

B = [\begin{array}{r} - 2 & 2 & 0 \\ 3 & 1 & 4 \end{array}]

and

C = [\begin{array}{r} 2 & 0 & - 2 \\ 7 & 1 & 6 \end{array}]

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Biology>Biotechnology>Biotechnology and its Applications>Ethical Issues in Biotechnology

A = [\begin{matrix} \cos α & - \sin α \\ \sin α & \cos α \end{matrix}]

, and

A + A^{'} = I

, then the value of

α

MEDIUM

Biology>Biotechnology>Biotechnology and its Applications>Ethical Issues in Biotechnology

A = [\begin{matrix} 0 \\ 1 \end{matrix} \begin{matrix} - 1 \\ 0 \end{matrix}]

, then which one of the following statements is not correct?

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Biology>Biotechnology>Biotechnology and its Applications>Ethical Issues in Biotechnology

F (x) = [\begin{matrix} \cos x & - \sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1 \end{matrix}]

, then show that

F (x) F (y) = F (x + y)

EASY

Biology>Biotechnology>Biotechnology and its Applications>Ethical Issues in Biotechnology

A

and

B

are two matrices such that

A B = B, B A = A

then

A^{2} + B^{2} =

MEDIUM

Biology>Biotechnology>Biotechnology and its Applications>Ethical Issues in Biotechnology

Define biopiracy.

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Biology>Biotechnology>Biotechnology and its Applications>Ethical Issues in Biotechnology

If $B$ is a $3 \times 3$ matrix such that $B^{2} = 0$ , then $d e t . [{(I + B)}^{50} - 50 B]$ is equal to :

MEDIUM

Biology>Biotechnology>Biotechnology and its Applications>Ethical Issues in Biotechnology

Let

A = [\begin{matrix} \cos α & - \sin α \\ \sin α & \cos α \end{matrix}], (a \in R)

such that

A^{32} = [\begin{matrix} 0 & - 1 \\ 1 & 0 \end{matrix}] .

Then, a value of

α

is:

EASY

Biology>Biotechnology>Biotechnology and its Applications>Ethical Issues in Biotechnology

Compute the indicated products.

$[\begin{array}{l} 1 \\ 2 \\ 3 \end{array}] [\begin{array}{l} 2 & 3 & 4 \end{array}]$

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Biology>Biotechnology>Biotechnology and its Applications>Ethical Issues in Biotechnology

If the point charge is moved to a distance $d$ from the centre of the square and the side of the square is doubled, explain how the electric flux will be affected.

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EASY

Biology>Biotechnology>Biotechnology and its Applications>Ethical Issues in Biotechnology

Find $X$ and $Y$ , if $X + Y = [\begin{array}{l} 7 & 0 \\ 2 & 5 \end{array}]$ and $X - Y = [\begin{array}{l} 3 & 0 \\ 0 & 3 \end{array}]$

MEDIUM

Biology>Biotechnology>Biotechnology and its Applications>Ethical Issues in Biotechnology

A

is a square matrix such that

A^{2} = A

, then

(I - A)^{3} + A

is equal to

EASY

Biology>Biotechnology>Biotechnology and its Applications>Ethical Issues in Biotechnology

A = [\begin{array}{l} \cos α & \sin α \\ - \sin α & \cos α \end{array}]

, then verify that

A^{'} A = I

EASY

Biology>Biotechnology>Biotechnology and its Applications>Ethical Issues in Biotechnology

A

is a symmetric matrix and

B

is skew- symmetric matrix such that

A + B = [\begin{matrix} 2 & 3 \\ 5 & - 1 \end{matrix}]

, then

A B

is equal to:

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Biology>Biotechnology>Biotechnology and its Applications>Ethical Issues in Biotechnology

If $A = [\begin{matrix} 1 & 2 & 2 \\ 2 & 1 & - 2 \\ a & 2 & b \end{matrix}]$ is a matrix satisfying the equation $A A^{T} = 9 I$ , where $I$ is $3 \times 3$ identity matrix, then the ordered pair $(a, b)$ is equal to

EASY

Biology>Biotechnology>Biotechnology and its Applications>Ethical Issues in Biotechnology

A segment of DNA molecule comprises of 546 nucleotides. How many cytosine nucleotides would be present in it if the number of adenine nucleotides is 96 ?

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Biology>Biotechnology>Biotechnology and its Applications>Ethical Issues in Biotechnology

Direction In each of the following questions, a statement of Assertion (A) is given followed by corresponding statement of Reason (R). Of the statements, mark the correct answer as
Assertion (A): Maintenance of sterile environment is essential for manufacture of biotechnological products.
Reason (R): This is to enable growth of only desired products.

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Biology>Biotechnology>Biotechnology and its Applications>Ethical Issues in Biotechnology

Why is Agrobacterium-mediated genetic transformation described as natural genetic engineering in plants?

Which activity does the sale of a patent fall under in the cash flow statement?

Important Questions on Biotechnology and its Applications

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