JEE Main2026Jan 24, Shift 1

JEE Main 2026 — Jan 24, Shift 1

75 questions with step-by-step solutions. All free.

Mathematics

Q1If the function $f (x) = \frac{e ^{x} ( e ^{t a n x - x} - 1 ) + lo g _{e} ( sec x + tan x ) - x}{tan x - x}$ is Continuous at $x = 0$ , then the value of $f (0)$ is equal to
Q2 Let a circle of radius 4 pass through the origin O, the points $A (- 3 a \dots$
Q3 Let the lines $L_{1} :$
Q4 Let $729, 81, 9, 1, \dots$ be a sequence and $P_{\dots}$
Q5 Let $a = 2 \dots$
Q6If the domain of the function $f (x) = lo g_{(10 x^{2} - 17 x + 7)} (18 x^{2} - 11 x + 1)$ is $(- \infty, a) \cup (b, c) \cup (d, \infty) - {e}$ , then $90 (a + b + c + d + e)$ equals:
Q7 Let each of the two ellipses $E_{1} : \dots$
Q8The value of $\frac{3 csc 2 0 ^{\circ} - sec 2 0 ^{\circ}}{cos 2 0 ^{\circ} cos 4 0 ^{\circ} cos 6 0 ^{\circ} cos 8 0 ^{\circ}}$ is equal to
Q9Let $S = {z \in C : \frac{z - 6 i}{z - 2 i} = 1 and \frac{z - 8 + 2 i}{z + 2 i} = \frac{3}{5}}$ . Then $z \in S \sum ∣ z ∣^{2}$ is equal to
Q10If $cot x = \frac{5}{12}$ for some $x \in (π, \frac{3 π}{2})$ , then $sin 7 x (cos \frac{13 x}{2} + sin \frac{13 x}{2}) + cos 7 x (cos \frac{13 x}{2} - sin \frac{13 x}{2})$ is equal to
Q11Let $f (t) = \int \frac{1 - sin ( lo g _{e} t )}{1 - cos ( lo g _{e} t )} d t$ , $t > 1$ . If $f (e^{π /2}) = - e^{π /2}$ and $f (e^{π /4}) = α e^{π /4}$ , then $α$ equals
Q12Let $R$ be a relation defined on the set ${1, 2, 3, 4} \times {1, 2, 3, 4}$ by $R = {((a, b), (c, d)) : 2 a + 3 b = 3 c + 4 d}$ . Then the number of elements in $R$ is
Q13Let $A (1, 0)$ , $B (2, - 1)$ and $C (\frac{7}{3}, \frac{4}{3})$ be three points. If the equation of the bisector of the angle $A B C$ is $α x + β y = 5$ , then the value of $α^{2} + β^{2}$ is
Q14Let $S = \frac{1}{25 !} + \frac{1}{3 ! 23 !} + \frac{1}{5 ! 21 !} + \dots$ up to 13 terms. If $13 S = \frac{2 ^{k}}{n !}$ , $k \in N$ , then $n + k$ is equal to
Q15Consider an A.P.: $a_{1}, a_{2}, \dots, a_{n}$ ; $a_{1} > 0$ . If $a_{2} - a_{1} = - \frac{3}{4}$ , $a_{n} = \frac{1}{4} a_{1}$ , and $i = 1 \sum n a_{i} = \frac{525}{2}$ , then $i = 1 \sum 17 a_{i}$ is equal to
Q16Let $α, β \in R$ be such that the function $f (x) = {2 α (x^{2} - 2) + 2 β x, x < 1 (α + 3) x + (α - β), x \geq 1$ be differentiable at all $x \in R$ . Then $34 (α + β)$ is equal to
Q17 From a lot containing 10 defective and 90 non-defective bulbs, 8 bulbs are selected one by one with replacement. Then the probability of getting at least 7 defective bulbs is :- …
Q18 The mean and variance of a data of 10 observations are 10 and 2, respectively. If an observations $α$ in this data is replaced by $β$ , then the mean and variance become 10.1 and 1.99, respectively. Then $α + \dots$
Q19 Let $A_{1}$ be the bounded area enclosed by the curves $y = \dots$
Q20The number of the real solutions of the equation : $x ∣ x + 3∣ + ∣ x - 1∣ - 2 = 0$ is
Q21 Let a differentiable function $f$ satisfy the equation $\int_{0}^{36\dots}$
Q22 Let a line $L$ passing through the point $P (1, 1, 1)$ be perpendicular to the lines $\dots$
Q23 The number of numbers greater than 5000, less than 9000 and divisible by 3, that can be formed using the digits $0, 1, 2, 5, 9$ , if the repetition of the digits is allowed, is _____ . …
Q24 Let $(2 α, α)$ be the largest interval in which the function $f (t) = \dots$
Q25 The number of $3 \times 2$ matrices $A$ , which can be formed using the elements of the set ${- 2, - 1 \dots$

Physics

Chemistry

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