JEE Main 2026 Question Paper (Jan 21, 2026) (Shift 1)

Question 1

If the coefficient of $x$ in the expansion of $(ax^2 + bx + c)(1 - 2x)^{26}$ is $-56$ and the coefficients of $x^2$ and $x^3$ are both zero, then $a + b + c$ is equal to :

Accepted Answer

1500

Answer

1300

Answer

1403

Answer

1483

Question 2

If $x^2 + x + 1 = 0$, then the value of $\left(x + \frac{1}{x}\right)^4 + \left(x^2 + \frac{1}{x^2}\right)^4 + \left(x^3 + \frac{1}{x^3}\right)^4 + \dots + \left(x^{25} + \frac{1}{x^{25}}\right)^4$ is :

Accepted Answer

175

Answer

128

Answer

145

Answer

162

Question 3

Let $f: \mathbb{R} ightarrow (0, \infty)$ be a twice differentiable function such that $f(3) = 18, f'(3) = 0$ and $f''(3) = 4$. Then $\lim_{x 	o 1} \left( \log_e \left( \frac{f(2+x)}{f(3)} ight)^{\frac{18}{(x-1)^2}} ight)$ is equal to :

Accepted Answer

1

Answer

2

Answer

18

Answer

9

Question 4

Let O be the vertex of the parabola $x^2 = 4y$ and Q be any point on it. Let the locus of the point P, which divides the line segment OQ internally in the ratio 2 : 3 be the conic C. Then the equation of the chord of C, which is bisected at the point (1, 2), is :

Accepted Answer

$5x - y - 3 = 0$

Answer

$5x - 4y + 3 = 0$

Answer

$x - 2y + 3 = 0$

Answer

$4x - 5y + 6 = 0$

Question 5

The value of $\int_{-\pi/6}^{\pi/6} \left( \frac{\pi + 4x^{11}}{1 - \sin(|x| + \pi/6)} \right) dx$ is equal to :

Accepted Answer

$2\pi$

Answer

$8\pi$

Answer

$6\pi$

Answer

$4\pi$