FSc Math Material

Orthogonal Matrices and their examples

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Orthogonal Matrices and their examples A square matrix A over R fot which [katex]A^T=A^{-1}[/katex], or equivalently [katex]AA^T=A^TA=I[/katex], is called an orthogonal matrix . Clearly, an orthogonal matrix is non singular. Earn Money online without investment Earn Money online from home without investment Therorem: The following conditions for a square matrix A are equivalent: Example of … Read more

Integration Multiple choice questions with their answers

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Integration Multiple choice questions with their answers consist of 100+ Multiple Choice Questions. Prepare these mcqs for Fsc, ECAT and other examinations. These mcqs are very helpful for preparing NTS and PPSC exams. The mcqs were uploaded on daily basis so keep visiting this website. ONCE the material is completely uploaded then Explanation of each mcqs and videos will be provided very soon.
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Q.1   Differential of y is denoted as

(a)        dy ‘

(b)      \frac{dy}{dx}

(c)     dy

(d)     dx

(Lahore board,2007)

c

Q.2 Differential of x is denoted as

(a)        1

(b)      \frac{dx}{dy}

(c)     dy

(d)     dx

c

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Differenciation Multiple choice questions

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Differenciation Multiple choice questions consist of 50+ Multiple Choice Questions. Prepare these mcqs for Fsc, ECAT and other examinations. These mcqs are very helpful for preparing NTS and PPSC exams. The mcqs were uploaded on daily basis so keep visiting this website. ONCE the material is completely uploaded then Explanation of each mcqs and videos will be provided very soon.
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Q.1    \lim_{\delta x \rightarrow 0} \frac{f(a+\delta x)-f(a)}{\delta x} =

(a)     f ‘ (x)

(b)     f ‘ (a)

(c)     f ‘ (2)

(d)     f ‘ ( 0)

Check Answer
b

Q.2  \lim_{\delta x \rightarrow 0} \frac{f(x+\delta x)-f(x)}{\delta x} =

(a)     0

(b)     f ‘ (x)

(c)     f ‘ (2)

(d)     Not defined

Check Answer
b

Q.3 \lim_{\delta x \rightarrow 0} \frac{f(0+\delta x)-f(0)}{\delta x} =

(a)     f ‘ (x)

(b)     f ‘ (a)

(c)     f ‘ (2)

(d)     f ‘ ( 0)

Check Answer
d

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Function and Limits Mcqs with answers

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Function and Limits Mcqs with answers consist of 50+ Multiple Choice Questions. This paragraph seems to be a topic list of multiple-choice questions (MCQs) related to the concept of functions and limits. It is likely to be useful for students studying mathematics, particularly calculus. The questions appear to have answers provided, which may make it a helpful study aid.

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1. A function f: Y ➝ X defined by f(x) = c for all x ∈ X, c ∈ Y, has a domain equal to
A. {c}
B.  R
C.  R-{c}
D.  X
(Gujranwala Board 2007)

X

2. If y is expressed in terms of a variable x as y = f(x), then y is called

A. Explicit function
B. Implicit function
C. Linear function
D. Identity function
(Lahore Board 2005)

Explicit function

3. If f: X ➝ Y is a function then y ∈ Y is called

A. Explicit function
B. Implicit function
C. Linear function
D. Identity function
(Lahore Board 2006)

Explicit function

4. x² + y² = 4 is

A. Function
B. Not function
C. Ellipse
D. Line
(Lahore Board 2007)