1
JEE Main 2020 (Online) 2nd September Morning Slot
+4
-1
If a function f(x) defined by

$$f\left( x \right) = \left\{ {\matrix{ {a{e^x} + b{e^{ - x}},} & { - 1 \le x < 1} \cr {c{x^2},} & {1 \le x \le 3} \cr {a{x^2} + 2cx,} & {3 < x \le 4} \cr } } \right.$$

be continuous for some $$a$$, b, c $$\in$$ R and f'(0) + f'(2) = e, then the value of of $$a$$ is :
A
$${e \over {{e^2} - 3e - 13}}$$
B
$${1 \over {{e^2} - 3e + 13}}$$
C
$${e \over {{e^2} - 3e + 13}}$$
D
$${e \over {{e^2} + 3e + 13}}$$
2
JEE Main 2020 (Online) 9th January Evening Slot
+4
-1
Let [t] denote the greatest integer $$\le$$ t and $$\mathop {\lim }\limits_{x \to 0} x\left[ {{4 \over x}} \right] = A$$.
Then the function, f(x) = [x2]sin($$\pi$$x) is discontinuous, when x is equal to :
A
$$\sqrt {A + 1}$$
B
$$\sqrt {A + 5}$$
C
$$\sqrt {A + 21}$$
D
$$\sqrt {A}$$
3
JEE Main 2020 (Online) 9th January Morning Slot
+4
-1
Let ƒ be any function continuous on [a, b] and twice differentiable on (a, b). If for all x $$\in$$ (a, b), ƒ'(x) > 0 and ƒ''(x) < 0, then for any c $$\in$$ (a, b), $${{f(c) - f(a)} \over {f(b) - f(c)}}$$ is greater than :
A
1
B
$${{b - c} \over {c - a}}$$
C
$${{b + a} \over {b - a}}$$
D
$${{c - a} \over {b - c}}$$
4
JEE Main 2020 (Online) 9th January Morning Slot
+4
-1
If $$f(x) = \left\{ {\matrix{ {{{\sin (a + 2)x + \sin x} \over x};} & {x < 0} \cr {b\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,;} & {x = 0} \cr {{{{{\left( {x + 3{x^2}} \right)}^{{1 \over 3}}} - {x^{ {1 \over 3}}}} \over {{x^{{4 \over 3}}}}};} & {x > 0} \cr } } \right.$$
is continuous at x = 0, then a + 2b is equal to :
A
0
B
-1
C
-2
D
1
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