1
JEE Main 2026 (Online) 6th April Evening Shift
Numerical
+4
-1
Change Language

Let $f(x)=\left\{\begin{array}{ll}x^3+8 ; & x<0, \\ x^2-4 ; & x \geq 0,\end{array}\right.$ and $g(x)= \begin{cases}(x-8)^{1 / 3} ; & x<0, \\ (x+4)^{1 / 2} ; & x \geq 0 .\end{cases}$

Then the number of points, where the function $g \circ f$ is discontinuous, is $\_\_\_\_$ .

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2
JEE Main 2026 (Online) 6th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The percentage error in the calculated volume of a sphere, if there is $2 \%$ error in its diameter measurement, is $\_\_\_\_$ .

A

1

B

2

C

6

D

8

3
JEE Main 2026 (Online) 6th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

$$ \text { Match List - I with List - II. } $$

$$
\text { List - I }
$$
$$
\text { List - II }
$$
A. Boltzmann constant I. $$
\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right]
$$
B. Stefan's constant II. $$
\left[\mathrm{M} \mathrm{~L}^2 \mathrm{~T}^{-1}\right]
$$
C. Planck's constant III. $$
\left[\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right]
$$
D. Gravitational constant IV. $$
\left[\mathrm{M} \mathrm{~L}^0 \mathrm{~T}^{-3} \mathrm{~K}^{-4}\right]
$$

Choose the correct answer from the options given below :

A

A-I, B-II, C-III, D-IV

B

A-IV, B-III, C-II, D-I

C

A-III, B-IV, C-II, D-I

D

A-II, B-I, C-IV, D-III

4
JEE Main 2026 (Online) 6th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

A solid sphere $(A)$ of mass $5 m$ and a spherical shell $(B)$ of mass $m$, both having same radius, are placed on a rough surface. When a force of same magnitude is applied tangentially at the highest points of $A$ and $B$, they start rolling without slipping with an acceleration of $a_A$ and $a_B$, respectively. The ratio of $a_A$ and $a_B$ is $\_\_\_\_$ .

A

$$ 5: 21 $$

B

$$ 6: 10 $$

C

$$ 21: 25 $$

D

$$ 1: 5 $$

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