The sum of all the elements in the range of$ f(x) = \text{Sgn}(\sin x) + \text{Sgn}(\cos x) + \text{Sgn}(\tan x) + \text{Sgn}(\cot x),; x \ne \frac{n\pi}{2},; n \in \mathbb{Z} $
where $ \text{Sgn}(t) = \begin{cases} 1, & \text{if } t > 0 \ -1, & \text{if } t < 0 \end{cases} $ is
Previous 10 Questions — JEE Main 2026 (28 January Evening Shift)
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Let $ y = y(x) $ be the solution of the differential equation$ x \frac{dy}{dx} - y = x^2 \cot x,; x \in (0,\pi) $.If $ …
Topic: JEE Main 2026 (28 January Evening Shift)
Let $ [\cdot] $ denote the greatest integer function. Then$ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \left( \frac{12(3 + […
Topic: JEE Main 2026 (28 January Evening Shift)
Let the circle $ x^2 + y^2 = 4 $ intersect $ x $-axis at the points $ A(a, 0),; a > 0 $ and $ B(b, 0) $. Let $ P(2\c…
Topic: JEE Main 2026 (28 January Evening Shift)
Let $ P_1 : y = 4x^2 $ and $ P_2 : y = x^2 + 27 $ be two parabolas. If the area of the bounded region enclosed between …
Topic: JEE Main 2026 (28 January Evening Shift)
Let the ellipse $ E: \frac{x^2}{144} + \frac{y^2}{169} = 1 $ and the hyperbola$ H: \frac{x^2}{16} - \frac{y^2}{\lambda^…
Topic: JEE Main 2026 (28 January Evening Shift)
An ellipse has center at $ (1,-2) $, one focus at $ (3,-2) $ and one vertex at $ (5,-2) $. Then the length of its latus…
Topic: JEE Main 2026 (28 January Evening Shift)
Given below are two statements :Statement I : The function $ f : \mathbb{R} \rightarrow \mathbb{R} $ defined by$ f(x) =…
Topic: JEE Main 2026 (28 January Evening Shift)
Let the arithmetic mean of $ \frac{1}{a} $ and $ \frac{1}{b} $ be $ \frac{5}{16},; a > 2 $.If $ \alpha $ is such tha…
Topic: JEE Main 2026 (28 January Evening Shift)
Considering the principal values of inverse trigonometric functions, the value of the expression
$ \tan \left( 2\sin^{-…
Topic: JEE Main 2026 (28 January Evening Shift)
Let $ f(x) = \lim_{\theta \to 0} \left( \frac{\cos \pi x - x^{(\theta)} \sin(x-1)}{1 + x^{(\theta)} (x - 1)} \right),; …
Topic: JEE Main 2026 (28 January Evening Shift)
Next 10 Questions — JEE Main 2026 (28 January Evening Shift)
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Let $ Q(a, b, c) $ be the image of the point $ P(3, 2, 1) $ in the line$ \frac{x - 1}{1} = \frac{y}{2} = \frac{z - 1}{1…
Topic: JEE Main 2026 (28 January Evening Shift)
Let $ P $ be a point in the plane of the vector$ \overrightarrow{AB} = 3\hat{i} + \hat{j} - \hat{k} $ and $ \overrighta…
Topic: JEE Main 2026 (28 January Evening Shift)
Let
$ A = { z \in \mathbb{C} : |z - 2| \le 4 } $
and
$ B = { z \in \mathbb{C} : |z - 2| + |z + 2| = 5 } $.
Then the…
Topic: JEE Main 2026 (28 January Evening Shift)
Let $ f(x) = \int \frac{dx}{x^{2/3} + 2x^{1/2}} $ be such that $ f(0) = -26 + 24\log_e 2 $. If $ f(1) = a + b\log_e 3 $…
Topic: JEE Main 2026 (28 January Evening Shift)
$ \frac{6}{3^{26}} + \frac{10.1}{3^{25}} + \frac{10.2}{3^{24}} + \frac{10.2^2}{3^{23}} + \ldots + \frac{10.2^{24}}{3} $…
Topic: JEE Main 2026 (28 January Evening Shift)
$ \sum_{r=1}^{25} \frac{r}{r^2 + r + 1} = \frac{p}{q} $, where $ p $ and $ q $ are integers such that $ \gcd(p, q) = 1 …
Topic: JEE Main 2026 (28 January Evening Shift)
Three persons enter in a lift at the ground floor. The lift will go upto $ 10^{th} $ floor. The number of ways, in whic…
Topic: JEE Main 2026 (28 January Evening Shift)
Let $ f $ be a differentiable function satisfying
$ f(x) = 1 - 2x + e^{-x} \int_0^x e^t f(t),dt,; x \in \mathbb{R} $
…
Topic: JEE Main 2026 (28 January Evening Shift)
If the distance of the point $ P(43, \alpha, \beta) $ from the line
$ \vec{r} = 4\hat{i} - \hat{k} + \mu(2\hat{i} + 3\…
Topic: JEE Main 2026 (28 January Evening Shift)
Let $ A = \left[ \matrix{ 3 & -4 \cr 1 & -1 } \right] $ and $ B $ be two matrices such that
$ A^{100} = 100B + I $. The…
Topic: JEE Main 2026 (28 January Evening Shift)
