JEE Advanced 2026 Paper 1 Online | JEE Advanced Year Wise Previous Years Questions

JEE Advanced 2026 Paper 1 Online

Numerical

-0

The number of ways to distribute 10 identical red pens and 14 identical blue pens among four persons such that each person gets 6 pens, is ______________.

Your input ____

JEE Advanced 2026 Paper 1 Online

Numerical

-0

Let

$$ \alpha = \left( 1 - 2\cos\left(\frac{\pi}{11}\right) \right) \left( 1 - 2\cos\left(\frac{3\pi}{11}\right) \right) \left( 1 - 2\cos\left(\frac{9\pi}{11}\right) \right) \left( 1 - 2\cos\left(\frac{27\pi}{11}\right) \right) \left( 1 - 2\cos\left(\frac{81\pi}{11}\right) \right). $$

Then the value of $5 - \alpha^2$ is ______________.

Your input ____

JEE Advanced 2026 Paper 1 Online

MCQ (Single Correct Answer)

-1

Match each entry in List-I to the correct entry in List-II and choose the correct option.

List-I	List-II
(P) If $\alpha$ and $\beta$ are the distinct roots of the equation $x^2 + x + 1 = 0$, then the quadratic equation with roots $\frac{1}{(\alpha+1)^{2026}}$ and $\frac{1}{(\beta+1)^{2026}}$ is	(1) $x^2 + x + 1 = 0$
(Q) If $\alpha$ and $\beta$ are the distinct roots of the equation $x^2 + x + 1 = 0$, then the quadratic equation with roots $\frac{1}{(\alpha+1)^{2027}}$ and $\frac{1}{(\beta+1)^{2027}}$ is	(2) $x^2 - x + 1 = 0$
(R) If $\gamma$ and $\delta$ are the distinct roots of the equation $x^2 - x + 1 = 0$, then the value of $\frac{1}{(\gamma-1)^{2026}} + \frac{1}{(\delta-1)^{2026}}$ is	(3) $x^2 + x - 1 = 0$
(S) If $p$ and $r$ are the distinct roots of the equation $x^2 + x - 1 = 0$, then the value of $\frac{1}{(p+1)^3} + \frac{1}{(r+1)^3}$ is	(4) $-1$
	(5) $-4$

(P) $\rightarrow$ (1), (Q) $\rightarrow$ (2), (R) $\rightarrow$ (5), (S) $\rightarrow$ (4)

(P) $\rightarrow$ (3), (Q) $\rightarrow$ (1), (R) $\rightarrow$ (4), (S) $\rightarrow$ (5)

(P) $\rightarrow$ (1), (Q) $\rightarrow$ (2), (R) $\rightarrow$ (4), (S) $\rightarrow$ (5)

(P) $\rightarrow$ (2), (Q) $\rightarrow$ (3), (R) $\rightarrow$ (5), (S) $\rightarrow$ (4)

JEE Advanced 2026 Paper 1 Online

MCQ (Single Correct Answer)

-1

Match each entry in List-I to the correct entry in List-II and choose the correct option.

List-I	List-II
(P) The number of elements in the set $$\left\{x \in [-\pi,\pi] : \sin^6 x + \cos^4 x = 1 \right\}$$	(1) is 1
(Q) The number of elements in the set $$\left\{x \in \left[-\frac{\pi}{2}, \frac{\pi}{2}\right] : \sin^2 x + \cos^6 x = 1 \right\}$$	(2) is 2
(R) The number of elements in the set $$\left\{x \in [-\pi,\pi] : \cos^2\left(\frac{x}{2}\right) - \sin^2 x = \frac{1}{2} \right\}$$	(3) is 3
(S) The number of elements in the set $$\left\{x \in [-2\pi,2\pi] : 6\sin^2\left(\frac{x}{2}\right) - \cos 3x = 3 \right\}$$	(4) is 4 (5) is 5

(P) $\to$ (2), (Q) $\to$ (5), (R) $\to$ (3), (S) $\to$ (4)

(P) $\to$ (5), (Q) $\to$ (3), (R) $\to$ (2), (S) $\to$ (4)

(P) $\to$ (5), (Q) $\to$ (4), (R) $\to$ (1), (S) $\to$ (3)

(P) $\to$ (4), (Q) $\to$ (3), (R) $\to$ (2), (S) $\to$ (5)

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