1
JEE Main 2019 (Online) 9th January Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If   $$f\left( x \right) = \int {{{5{x^8} + 7{x^6}} \over {{{\left( {{x^2} + 1 + 2{x^7}} \right)}^2}}}} \,dx,\,\left( {x \ge 0} \right),$$

$$f\left( 0 \right) = 0,$$    then the value of $$f(1)$$ is :
A
$$ - $$ $${1 \over 2}$$
B
$$ - $$ $${1 \over 4}$$
C
$${1 \over 2}$$
D
$${1 \over 4}$$
2
JEE Main 2019 (Online) 9th January Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
A data consists of n observations : x1, x2, . . . . . . ., xn.    

If     $$\sum\limits_{i = 1}^n {{{\left( {{x_i} + 1} \right)}^2}} = 9n$$    and

$$\sum\limits_{i = 1}^n {{{\left( {{x_i} - 1} \right)}^2}} = 5n,$$

then the standard deviation of this data is :
A
2
B
$$\sqrt 5 $$
C
5
D
$$\sqrt 7 $$
3
JEE Main 2019 (Online) 9th January Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Let f be a differentiable function from

R to R such that $$\left| {f\left( x \right) - f\left( y \right)} \right| \le 2{\left| {x - y} \right|^{{3 \over 2}}},$$   

for all  $$x,y \in $$ R.

If   $$f\left( 0 \right) = 1$$  

then   $$\int\limits_0^1 {{f^2}} \left( x \right)dx$$  is equal to :
A
1
B
2
C
$${1 \over 2}$$
D
0
4
JEE Main 2019 (Online) 9th January Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If   x $$=$$ 3 tan t and y $$=$$ 3 sec t, then the value of $${{{d^2}y} \over {d{x^2}}}$$ at t $$ = {\pi \over 4},$$ is :
A
$${1 \over {3\sqrt 2 }}$$
B
$${1 \over {6\sqrt 2 }}$$
C
$${3 \over {2\sqrt 2 }}$$
D
$${1 \over 6}$$
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