JEE Main2026Apr 2, Shift 1

JEE Main 2026 — Apr 2, Shift 1

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

Mathematics

Q1 Let $α, α + 2$ , $α \in \dots$
Q2Let $x$ and $y$ be real numbers such that $50 (\frac{2 x}{1 + 3 i} - \frac{y}{1 - 2 i}) = 31 + 17 i$ , $i = - 1$ . Then the value of $10 (x - 3 y)$ is :
Q3Let $α, β \in R$ be such that the system of linear equations $x + 2 y + z = 5$ $2 x + y + α z = 5$ $8 x + 4 y + β z = 18$ has no solution. Then $\frac{β}{α}$ is equal to :
Q4 Let $A = [12 1 α \dots$
Q5 Let $A$ be the set of first $101$ terms of an A.P., whose first term is $1$ and the common difference is $5$ and let $B$ be the set of first $\dots$
Q6The number of seven-digit numbers, that can be formed by using the digits $1, 2, 3, 5$ and $7$ such that each digit is used at least once, is :
Q7The number of elements in the set $S = {(r, k) : k \in Z and^{36} C_{r + 1} = \frac{6 \cdot ^{35} C _{r}}{k ^{2} - 3}}$ , is
Q8If the mean of the data above is $21$ , then $k$ is one of the roots of the equation :
Q9Let the mid points of the sides of a triangle $A B C$ be $(\frac{5}{2}, 7)$ , $(\frac{5}{2}, 3)$ and $(4, 5)$ . If its incentre is $(h, k)$ , then $3 h + k$ is equal to :
Q10Let an ellipse $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1$ , $a < b$ , pass through the point $(4, 3)$ and have eccentricity $\frac{5}{3}$ . Then the length of its latus rectum is :
Q11If $sin (\frac{π}{18}) sin (\frac{5 π}{18}) sin (\frac{7 π}{18}) = K$ , then the value of $sin (\frac{10 K π}{3})$ is :
Q12Let $S = {x \in [- π, π] : sin x (sin x + cos x) = a, a \in Z}$ . Then $n (S)$ is equal to :
Q13If the point of intersection of the lines $\frac{x + 1}{3} = \frac{y - a}{5} = \frac{z - b + 1}{7}$ and $\frac{x - 2}{1} = \frac{y - b}{4} = \frac{z - 2 a}{7}$ lies on $x y$ -plane, then the value of $a + b$ is :
Q14If $a$ and $b$ are two vectors such that $∣ a ∣ = 2$ and $∣ b ∣ = 3$ , then the maximum value of $3∣3 a + 2 b ∣ + 4∣3 a - 2 b ∣$ is :
Q15 Let a line $L$ passing through the point $(1, 1, 1)$ be perpendicular to both the vectors $2 \dots$
Q16If $x \to 2 lim \frac{sin ( x ^{3} - 5 x ^{2} + a x + b )}{( x - 1 - 1 ) lo g _{e} ( x - 1 )} = m$ , then $a + b + m$ is equal to :
Q17If the curve $y = f (x)$ passes through the point $(1, e)$ and satisfies the differential equation $d y = y (2 + lo g_{e} x) d x$ , $x > 0$ , then $f (e)$ is equal to :
Q18The number of critical points of the function $f (x) = ⎩ ⎨ ⎧ \frac{sin x}{x}, x \neq = 0 1, x = 0$ in the interval $(- 2 π, 2 π)$ is equal to :
Q19Let $[\cdot]$ denote the greatest integer function. Then the value of $\int_{0}^{3} (\frac{e ^{x} + e ^{- x}}{[ x ]!}) d x$ is :
Q20 Let $y = y (x)$ be the solution curve of the differential equation $(1 + \dots$
Q21If the domain of the function $f (x) = lo g_{(0.6)} (\frac{2 x - 5}{x ^{2} - 4})$ is $(- \infty, a] \cup {b} \cup [c, d) \cup (e, \infty)$ , then the value of $a + b + c + d + e$ is __________.
Q22If $k = 1 \sum n a_{k} = 6 n^{3}$ , then $k = 1 \sum 6 (\frac{a _{k + 1} - a _{k}}{36})^{2}$ is equal to ____.
Q23Let $a, b, c \in {1, 2, 3, 4}$ . If the probability that $a x^{2} + 22 b x + c > 0$ for all $x \in R$ , is $\frac{m}{n}$ , $g cd (m, n) = 1$ , then $m + n$ is equal to _______.
Q24 Let a circle $C$ have its centre in the first quadrant, intersect the coordinate axes at exactly three points and cut off equal intercepts from the coordinate axes. If the length of the chord of $C$ on the line $x + \dots$
Q25If $α = \int_{0}^{23} lo g_{2} (x^{2} + 4) d x + \int_{2}^{4} 2^{x} - 4 d x$ , then $α^{2}$ is equal to ________.

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