NTA JEE Mains 5th April Shift 1 2026

Let $$A = \{1, 2, 3, 4, 5, 6\}$$. The number of one-one functions $$f: A \to A$$ such that $$f(1) \geq 3$$, $$f(3) \leq 4$$, and $$f(2) + f(3) = 5$$ is :

Two players $$A$$ and $$B$$ play a series of badminton games. The first player, who wins 5 games  first, wins the series. Assuming that no game ends in a draw, the number of ways in which player $$A$$ wins the series is :_____.

If the sum of the coefficients of $$x^7$$ and $$x^{14}$$ in the expansion of $$\left(\frac{1}{x^3} - x^4\right)^n$$, $$x \neq 0$$, is zero, then the value of n is _______ :

If $$\frac{\pi}{4} + \displaystyle\sum_{p=1}^{11} \tan^{-1}\left(\frac{2^{p-1}}{1 + 2^{2p-1}}\right) = \alpha$$, then $$\tan \alpha$$ is equal to :

Let $$y = y(x)$$ be the solution of the differential equation $$x\sin\left(\frac{y}{x}\right)dy = \left(y\sin\left(\frac{y}{x}\right) - x\right)dx$$, $$y(1) = \frac{\pi}{2}$$ and let $$\alpha = \cos\left(\frac{y(e^{12})}{e^{12}}\right)$$. The number of integral values of $$p$$ for which the equation $$x^2 + y^2 - 2px + 2py + \alpha + 2 = 0$$ represents a circle of radius $$r \leq 6$$ is :

In a Vernier calipers, when both jaws touch each other, zero of the Vernier scale is shifted to the right of zero of the main scale and $$7^{th}$$ Vernier division coincides with a main scale reading. If the value of 1 main scale division is 1 mm and there are 10 Vernier scale divisions, then the Vernier caliper has

$$L$$, $$C$$ and $$R$$ represents physical quantities inductance, capacitance and resistance respectively. The dimensional formula $$M L^2 T^{-4} A^{-2}$$ corresponds to _______.

When one moves from a point 16 km below the earth's surface to a point 16 km above the earth's surface. The change in g is approximately $$\alpha$$ %. The value of $$\alpha$$ is _______. (Take radius of the earth = 6400 km.)

Three masses $$m_1 = 4$$ kg, $$m_2 = 4$$ kg and $$m_3 = 6$$ kg are suspended from a fixed smooth frictionless pully as shown in the figure below. The value of $$T_1/T_2$$ is _______. (take $$g = 10$$ m/s$$^2$$)

A wedge Y with mass of 10 kg and all frictionless surfaces and the inclined surface making 37° with horizontal. A block X with mass 2 kg is placed at the highest point of the wedge as shown in figure is at rest. At $$t = 0$$ wedge (Y) is pulled toward right with constant force ($$f$$) of 24 N. Taking the block X at rest at $$t = 0$$, the time taken by it to slide down 8.8 m on the slope, while Y is on the move, is _______ s. (take $$\tan(37°) = 3/4$$ and $$g = 10$$ m/s$$^2$$)