1
WB JEE 2023
+1
-0.25

$$\mathop {\lim }\limits_{x \to \infty } \left\{ {x - \root n \of {(x - {a_1})(x - {a_2})\,...\,(x - {a_n})} } \right\}$$ where $${a_1},{a_2},\,...,\,{a_n}$$ are positive rational numbers. The limit

A
does not exist
B
is $${{{a_1} + {a_2}\, + \,...\,{a_n}} \over n}$$
C
is $$\root n \of {{a_1}{a_2}\,...\,{a_n}}$$
D
is $${n \over {{a_1} + {a_2}\, + \,...\,{a_n}}}$$
2
WB JEE 2023
+1
-0.25

Let $$f:[1,3] \to R$$ be continuous and be derivable in (1, 3) and $$f'(x) = {[f(x)]^2} + 4\forall x \in (1,3)$$. Then

A
$$f(3) - f(1) = 5$$ holds
B
$$f(3) - f(1) = 5$$ does not hold
C
$$f(3) - f(1) = 3$$ holds
D
$$f(3) - f(1) = 4$$ holds
3
WB JEE 2023
+1
-0.25

f(x) is a differentiable function and given $$f'(2) = 6$$ and $$f'(1) = 4$$, then $$L = \mathop {\lim }\limits_{h \to 0} {{f(2 + 2h + {h^2}) - f(2)} \over {f(1 + h - {h^2}) - f(1)}}$$

A
does not exist
B
equal to $$-3$$
C
equal to 3
D
equal to 3/2
4
WB JEE 2023
+1
-0.25

Let $$f(x) = \left\{ {\matrix{ {x + 1,} & { - 1 \le x \le 0} \cr { - x,} & {0 < x \le 1} \cr } } \right.$$

A
f(x) is discontinuous in [$$-1,1$$] and so has no maximum value or minimum value in [$$-1,1$$].
B
f(x) is continuous in [$$-1,1$$] and so has maximum value and minimum value.
C
f(x) is discontinuous in [$$-1,1$$] but still has the maximum and minimum value.
D
f(x) is bounded in [$$-1,1$$] and does not attain maximum or minimum value.
WB JEE Subjects
Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Coordinate Geometry
Calculus
EXAM MAP
Joint Entrance Examination