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question_answer1)
Directions: (1 - 11) The following questions consist of two statements, one labelled as "Assertion [A] and the other labelled as Reason [R]". You are to examine these two statements carefully and decide if Assertion [A] and Reason [R] are individually true and if so, whether the Reason [R] is the correct explanation for the given Assertion [A]. Select your answer from following options. |
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Assertion [A]: The function \[x+\frac{5}{x},\,\,x\ne 0\] is strictly decreasing |
Reason [R]: For strictly decreasing function\[~f'\left( x \right)<0.\] |
A)
Both A and R are individually true and R is the correct explanation of A. done
clear
B)
Both A and R are individually true and R is not the correct explanation of A. done
clear
C)
'A' is true but 'R' is false done
clear
D)
'A' is false but 'R' is true done
clear
E)
Both A and R are false. done
clear
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question_answer2)
Assertion [A]: The function \[f(x)={{x}^{3}}-12x\] is strictly increasing in\[\left( -\infty ,-2 \right)\cup \left( 2,\text{ }\infty \right)\]. |
Reason [R]: For strictly increasing function \[f'\left( x \right)>0\]. |
A)
Both A and R are individually true and R is the correct explanation of A. done
clear
B)
Both A and R are individually true and R is not the correct explanation of A. done
clear
C)
'A' is true but 'R' is false done
clear
D)
'A' is false but 'R' is true done
clear
E)
Both A and R are false. done
clear
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question_answer3)
Assertion [A]: The function \[f\left( x \right)~={{x}^{2}}+2x+1\] is strictly increasing on (1, 2). |
Reason [R]: The least value of x is 1 in interval (1, 2) |
A)
Both A and R are individually true and R is the correct explanation of A. done
clear
B)
Both A and R are individually true and R is not the correct explanation of A. done
clear
C)
'A' is true but 'R' is false done
clear
D)
'A' is false but 'R' is true done
clear
E)
Both A and R are false. done
clear
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question_answer4)
Assertion [A]: The intervals is which \[f\left( x \right)\text{ }=\text{ }log\text{ }sinx\], \[0\le \text{ }x\text{ }\le \pi \] is increasing is \[\left( 0,\frac{\pi }{2} \right)\]. |
Reason [R]: The function tan x is + ve in first quadrant |
A)
Both A and R are individually true and R is the correct explanation of A. done
clear
B)
Both A and R are individually true and R is not the correct explanation of A. done
clear
C)
'A' is true but 'R' is false done
clear
D)
'A' is false but 'R' is true done
clear
E)
Both A and R are false. done
clear
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question_answer5)
Assertion [A]: The intervals in which\[f(x)=log\,\,cosx,\,\,0\le x\,\,\pi \] is decreasing is \[\left( 0,\frac{\pi }{2} \right)\]. |
Reason [R]: The function \[\tan \,x\] is +ve in 3rd quadrant. |
A)
Both A and R are individually true and R is the correct explanation of A. done
clear
B)
Both A and R are individually true and R is not the correct explanation of A. done
clear
C)
'A' is true but 'R' is false done
clear
D)
'A' is false but 'R' is true done
clear
E)
Both A and R are false. done
clear
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question_answer6)
Assertion [A]: Tangent to the curve \[y={{x}^{2}}-7x+12\] at the points (3, 0) and (4, 0) are at right angles. |
Reason [R]: For perpendicular lines, product of slopes of lines is -1. |
A)
Both A and R are individually true and R is the correct explanation of A. done
clear
B)
Both A and R are individually true and R is not the correct explanation of A. done
clear
C)
'A' is true but 'R' is false done
clear
D)
'A' is false but 'R' is true done
clear
E)
Both A and R are false. done
clear
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question_answer7)
Assertion [A]: The tangent to the curve \[y={{x}^{3}}-{{x}^{2}}-x+2\] at (1, 1) is parallel to the X-axis. |
Reason [R]: The slope of the tangent to the above curve at (1, 1) is zero. |
A)
Both A and R are individually true and R is the correct explanation of A. done
clear
B)
Both A and R are individually true and R is not the correct explanation of A. done
clear
C)
'A' is true but 'R' is false done
clear
D)
'A' is false but 'R' is true done
clear
E)
Both A and R are false. done
clear
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question_answer8)
Assertion [A]: The tangent to curve \[y=4{{x}^{3}}-3x+5\] at \[x\text{ }=\text{ }1\] is perpendicular to the line \[x+9y+3=0.\] |
Reason [R]: Slope of line \[ax+by+c=0\] is |
\[-\frac{Coeff\,.\,of\,x}{Coeff\,.\,of\,y}\] |
A)
Both A and R are individually true and R is the correct explanation of A. done
clear
B)
Both A and R are individually true and R is not the correct explanation of A. done
clear
C)
'A' is true but 'R' is false done
clear
D)
'A' is false but 'R' is true done
clear
E)
Both A and R are false. done
clear
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question_answer9)
Assertion [A]: The local maximum value of |
\[f\left( x \right)={{x}^{3}}-6{{x}^{2}}+9x+15\] at \[x=1\]is 19. |
Reason [R]: For local maximum, \[f''\left( x \right)<0.\] |
A)
Both A and R are individually true and R is the correct explanation of A. done
clear
B)
Both A and R are individually true and R is not the correct explanation of A. done
clear
C)
'A' is true but 'R' is false done
clear
D)
'A' is false but 'R' is true done
clear
E)
Both A and R are false. done
clear
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question_answer10)
Assertion [A]: The point of local maxima of function \[f\left( x \right)={{x}^{3}}-3x+3\text{ }\] is \[x=-1\]. |
Reason [R]: For local minima, \[f''\left( x \right)\text{ }>\text{ }0.\] |
A)
Both A and R are individually true and R is the correct explanation of A. done
clear
B)
Both A and R are individually true and R is not the correct explanation of A. done
clear
C)
'A' is true but 'R' is false done
clear
D)
'A' is false but 'R' is true done
clear
E)
Both A and R are false. done
clear
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question_answer11)
Assertion [A]: Let |
\[f:\text{ }R\to R,\text{ }f\left( x \right)={{x}^{3}}+{{x}^{2}}\text{+3x+ }sin\text{ }x,\text{ f(x)}\]is one-one. |
Reason [R]: f(x) is decreasing function. |
A)
Both A and R are individually true and R is the correct explanation of A. done
clear
B)
Both A and R are individually true and R is not the correct explanation of A. done
clear
C)
'A' is true but 'R' is false done
clear
D)
'A' is false but 'R' is true done
clear
E)
Both A and R are false. done
clear
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