1
NDA Mathematics 3 September 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Consider the following for the next items that follow:

Let $\displaystyle I=\int_{-2 \pi}^{2 \pi} \frac{\sin ^4 x+\cos ^4 x}{1+3^x} d x$

What is $\displaystyle \int_0^\pi\left(\sin ^4 x+\cos ^4 x\right) d x$ equal to?
A
$\frac{3 \pi}{8}$
B
$\frac{3 \pi}{4}$
C
$\frac{3 \pi}{2}$
D
3π 
2
NDA Mathematics 3 September 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Consider the following for the next items that follow:

Let $\displaystyle I=\int_{-2 \pi}^{2 \pi} \frac{\sin ^4 x+\cos ^4 x}{1+3^x} d x$

What is I equal to?
A
0
B
$\frac{3 \pi}{4}$
C
$\frac{3 \pi}{2}$
D
3π 
3
NDA Mathematics 3 September 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Consider the following for the next items that follow:

Let $f(x)=\left\{\begin{array}{cc} a x(x+1)+b, & x<1 \\ x-1, & 1 \leq x \leq 2 \end{array}\right.$

If the function f(x) is differentiable at x = 1, then what is the value of (a + b)?
A
$-\frac{1}{3}$
B
-1
C
0
D
1
4
NDA Mathematics 3 September 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Consider the following for the next items that follow:

Let $f(x)=\left\{\begin{array}{cc} a x(x+1)+b, & x<1 \\ x-1, & 1 \leq x \leq 2 \end{array}\right.$

What is $\displaystyle \lim _{x \rightarrow 0} $ f(x) equal to ?
A
$- \frac{1}{3} $
B
$-\frac{2}{3}$
C
0
D
1
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