SPSC LECTURER MATHEMATICS PAST PAPER 2000 TO TILL DATE
Lecturer Mathematics Past Papers Click here
چار آپشن میں سے کسی ایک پر کلک کرنے سے جواب سرخ ہو جائے گا۔
- Taylor Series of a function
- Leibniz theorem
- Mean value theorem
- None of these
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Explanation
Rolle's Theorem is a special case of the Mean Value Theorem (MVT) where the function has equal values at two endpoints.It ensuring the derivative is zero at some point in the interval.It is derived from MVT by adding the condition .
- Positive Integer
- Negative Integer
- Rational Number
- None of these
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Explanation
Leibniz theorem is also known as the Leibniz rule.It is used for finding the th derivative of a product of two functions.It is defined only when is a positive integer.
- 1/2
- Undefined
- 4
- None of these
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Explanation
To find the third derivative of f(x) = ln(1-x)/e^x, we'll first find the first, second, and third derivatives.
Using the quotient rule and chain rule, we can find the derivatives. After calculating, we get:
f'''(0) = 1/2
So, the third derivative at x = 0 is 1/2.
- 0
- 1
- 1/2
- None of these
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Explanation
Let the quadratic polynomial be f(x) = ax^2 + bx + c.
Given that f'(1) = 1 and f''(1) = 2.
f'(x) = 2ax + b
f''(x) = 2a
f'(1) = 1 => 2a + b = 1
f''(1) = 2 => 2a = 2 => a = 1
Substituting a = 1 in the first equation, we get:
2 + b = 1 => b = -1
Now, f(x) = x^2 - x + c
f(1) = 1^2 - 1 + c = c
f(0) = 0^2 - 0 + c = c
f(1) - f(0) = c - c = 0
- Polite
- Delight
- Hatred
- None of these
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Explanation
ANGUISH means تکلیفDelight means خوشی
- Merciful
- Grief
- Pity
- None of these
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Explanation
Ruthless means بے رحم
Merciful means مہربان
- Whim
- Passion
- Disinclination
- Both B and C
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Explanation
Velleity means خواہش کی کمی
Passion شوق
Passion is a strong and intense emotion, desire, or enthusiasm for something,
The opposite of “Velleity,” which implies a weak desire.
- In rage
- From nowhere
- Campout fast
- None of these
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Explanation
"Out of the blue" means something happening unexpectedly or suddenly.Example: "The news of his promotion came out of the blue."
- Will not cost
- Will not coasting
- Had not cost
- None of these
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Explanation
The correct sentence is: "This watch will not cost very much."اس گھڑی پر بہت زیادہ لاگت نہیں آئے گی۔"Will not cost" is correct because it refers to a future event.
- A former Student of College
- A former Student of U University
- A former Student of School
- All of these
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Explanation
Alumnus refers to a former student of a college, university, or school.The plural form is alumni for males/mixed groups and alumnae for females.
