NTA JEE Mains 24th Jan 2026 Shift 2

If f(x) satisfies the relation $$f(x)=e^{x}+\int_{0}^{1}\left(y+xe^{x}\right)f(y)dy,$$ then e + f(0) is equal to ______.

Let (h, k) lie on the circle $$C: x^{2}+y^{2}=4$$ and the point (2h + l , 3k + 2) lie on an ellipse with eccentricity e. Then the value of $$\frac{5}{e^{2}}$$ is equal to __________.

The number of elements in the set $$\left\{x \in [0,180^{\circ}]:\tan (x+100^{\circ}) = \tan (x+50^{\circ}) \tan x \tan(x-50^{\circ})\right\}$$ is ___________.

Let S be a set of 5 elements and P(S) denote the power set of S. Let E be an event of choosing an ordered pair (A, B) from the set P(S) x P(S) such that $$A\cap B=\phi.$$ If
the probability of the event E is $$\frac{3^{p}}{2^{q}}$$, where p,q $$\in$$ N, then p + q is equal to __________

Let z = (1 + i) (1 + 2i) (1 + 3i) .... (l + ni), where i = $$\sqrt{-1}$$. If $$|z|^{2}$$ = 44200, then n is equal to __

In the Young's double slit experiment the intensity produced by each one of the individual slits is $$I_{o}.$$ The distance between two slits is 2 mm . The distance of
screen from slits is 10 m. The wavelength of light is $$6000_A^\circ$$. The intensity of light on the screen in front of one of the slits is __________.

When a light of a given wavelength falls on a metallic surface the stopping potential for photoelectrons is 3.2 V. If a second light having wavelength twice of first light is used, the stopping potential drops to 0. 7 V. The wavelength of first light is ___ m.
$$(h= 6.63\times10^{-34}J.s,e=1.6\times10^{-19}C,c=3\times10^{8}m/s)$$

A cubical block of density $$\rho_{b}= 600kg/m^{3}$$ floats in a liquid of density $$\rho_{e}= 900kg/m^{3}$$. If the height of block is H = 8.0 cm then height of the submerged part is ________ cm.

The binding energy for the following nuclear reactions are expressed in MeV.
$$ _{2}He^{3}+ _{0}n^{1} \rightarrow {}_{2}He^{4}+20$$ MeV
$$ _{2}He^{4}+ _{0}n^{1} \rightarrow {}_{2}He^{5}-0.9$$ MeV
If $$X_{3}$$, $$X_{4}$$, $$X_{5}$$ denote the stability of $${}_{2}He^{3}, {}_{2}He^{4}$$ and $${}_{2}He^{5},$$ respectively, then the correct order is :

Identify the correct truth table of the given logic circuit.