Differential Calculus jee mains questions | JEE Main Maths Quadratic Equations Previous Year Question

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Topic Question Set

Q 71 :

Let $y = y (x)$ be a differentiable function in the interval $(0, \infty)$ such that $y (1) = 2$ , and $\lim_{t \to x} (\frac{t^{2} y (x) - x^{2} y (t)}{x - t}) = 3$ for each $x > 0$ . Then $2 y (2)$ is equal to [2026]

23
27
18
12

1

2

3

4

(1)

Q 72 :

Let $[t]$ denote the greatest integer less than or equal to $t$ . If the function

$f (x) =$ ${\begin{matrix} b^{2} \sin (\frac{π}{2} [\frac{π}{2} (\cos x + \sin x) \cos x]), & x < 0 \\ \frac{\sin x - \frac{1}{2} \sin 2 x}{x^{3}}, & x > 0 \\ a, & x = 0 \end{matrix}$

is continuous at $x = 0$ , then $a^{2} + b^{2}$ is equal to [2026]

$\frac{9}{16}$
$\frac{1}{2}$
$\frac{5}{8}$
$\frac{3}{4}$

1

2

3

4

(4)

Q 73 :

If $f (x) = {\begin{matrix} \frac{a | x | + x^{2} - 2 (\sin | x | (\cos | x |)}{x} & , x \neq 0 \\ b & , x = 0 \end{matrix}$

is continuous at x=0, then a+b is equal to [2026]

0
4
2
1

1

2

3

4

(3)

Q 74 :

Let $[\cdot]$ denote the greatest integer function, and let $f (x) = \min {\sqrt{2 x}, x^{2}} .$ Let $S = {x \in (- 2, 2) : the function g (x) = | x | [x^{2}] is discontinuous at x} .$ Then $\sum_{x \in S} f (x)$ equals: [2026]

$\sqrt{6} - 2 \sqrt{2}$
$1 - \sqrt{2}$
$2 - \sqrt{2}$
$2 \sqrt{6} - 3 \sqrt{2}$

1

2

3

4

(2)

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