Mathematics MCQS for class 12 with Answers Chapter 3

? ax dx =

a^x lna +c

lna/a^x + c

l/aⁿlna + c

ax/lna + c

The conditions through which the orbitrary constants involving in the differential equation can be determined is called

1/2 (ln Sin x)²+ c

n-initial value conditions

Final value condition

none

?sec2 x/ tan  dx + ?cosec²x/cotx dx =

in tan x + c

In cot x + c

2 in cot x + c

2 in tan x + c

? Tan(ax+b)dx= _________

1/b ln |Sec(ax+b)| + c

1/a ln |Sec(ax+b)| + c

1/a Cos(ax+b) + c

ln |Sec(ax+b)| + c

?lnx dx= ______________

ln x + x + c

ln |Sec x+ Tan x| + c

x lnx + x + c

xln x + c

?e^x [Cos x -sin x] dx =

1/a e^ax+b+ c

e^x tanx + c

e^x Sin + c

e^ax sinx + c

1/b ln|ax-b| + c

1/b ln|ax+b| + c

3

(ax+b)/b+c

? Sec x dx= _________

ln |Sec x+ Cot x| + c

Sin x – x Cos x + c

ln |Sin x+ Cot x| + c

ln |Tan x+ Cosec x| + c

If

Derivative

Integrand

Differential

Integral

If ²?₁ (3x² +2x – k) dx = 12 then k =

0

1

-1

y = ce^-x