1
NDA Mathematics 16 April 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the following for the next three (03) items that follow :
Let f(x) = Pex + Qe2x + Re3x where P, Q, R are real numbers. Further f(0) = 6, f'(ln 3) = 282 and $\int_0^{\ln 2} f(x) d x=11$
‘What is the value of Q ?
2
NDA Mathematics 16 April 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the following for the next three (03) items that follow :
Let f(x) = Pex + Qe2x + Re3x where P, Q, R are real numbers. Further f(0) = 6, f'(ln 3) = 282 and $\int_0^{\ln 2} f(x) d x=11$
What is the value of R ?
3
NDA Mathematics 16 April 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the following for the next three (03) items that follow :
Let $I_1=\int_0^\pi \frac{x}{1+\cos ^2 x} d x$ and
$I_2=\int_0^\pi \frac{1}{1+\sin ^2 x} d x $
What is the value of $\frac{I_1+I_2}{I_1-I_2} $ ?
4
NDA Mathematics 16 April 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the following for the next three (03) items that follow :
Let $I_1=\int_0^\pi \frac{x}{1+\cos ^2 x} d x$ and
$I_2=\int_0^\pi \frac{1}{1+\sin ^2 x} d x $
What is the value of $8 I_1^2$
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