1
AP EAPCET 2022 - 4th July Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $$\int \frac{1+\sqrt{\tan x}}{\sin 2 x} d x=A \log \tan x+B \tan x+C$$, then $$4 A-2 B=$$

A
$$-$$1
B
2
C
1
D
$$-$$2
2
AP EAPCET 2022 - 4th July Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$\int \frac{1+\tan x \tan (x+a)}{\tan x \tan (x+a)} d x=$$

A
$$\tan a(\log (\sec (x+a))+\log \sec x+C$$
B
$$\cot a(\log |\sin x|-\log |\sin (x+a)|)+C$$
C
$$\tan a\left(\log \left(\frac{\cos x}{\sin (x+a)}\right)\right)+C$$
D
$$\cot a\left(\log \frac{\sin (x+a)}{\cos (x+a)}\right)+C$$
3
AP EAPCET 2022 - 4th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

Assertion (A) If $$I_n=\int \cot ^n x d x$$, then $$I_6+I_4=\frac{-\cot ^5 x}{5}$$

Reason (R) $$\int \cot ^n x d x=\frac{-\cot ^{n-1} x}{n} -\int \cot ^{n-2} x d x$$

A
A is false, R is false
B
A is true, R is true
C
A is true, R is false
D
A is false, R is true
4
AP EAPCET 2022 - 4th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $$I_n=\int \tan ^n x d x$$, and $$I_0+I_1+2 I_2+2 I_3+2 I_4 +I_5+I_6=\sum_\limits{k=1}^n \frac{\tan ^k x}{k}$$, then $$n=$$

A
6
B
5
C
4
D
3
AP EAPCET Subjects
EXAM MAP