JEE Main2025Jan 29, Shift 2

JEE Main 2025 — Jan 29, Shift 2

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

Mathematics

Q1 If the set of all $a \in R$ , for which the equation $2 x^{2} \dots$
Q2If $sin x + sin^{2} x = 1$ , $x \in (0, \frac{π}{2})$ , then $(cos^{12} x + tan^{12} x) + 3 (cos^{10} x + tan^{10} x + cos^{8} x + tan^{8} x) + (cos^{6} x + tan^{6} x)$ is equal to
Q3Let the area enclosed between the curves $∣ y ∣ = 1 - x^{2}$ and $x^{2} + y^{2} = 1$ be $α$ . If $9 α = β π + γ$ ; $β, γ$ are integers, then the value of $∣ β - γ ∣$ equals
Q4 If the domain of the function $lo g_{5} (18 x - \dots$
Q5 Let the function $f (x) = (x^{2} + \dots$
Q6 Let a straight line $L$ pass through the point $P (2, - 1, 3)$ and be perpendicular to the lines $\dots$
Q7 Let $S = N \cup {0}$ . Define a relation $R$ from $\dots$
Q8 Let the line $x + y = 1$ meet the axes of $x$ and $\dots$
Q9If $α x + β y = 109$ is the equation of the chord of the ellipse $\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = 1$ , whose mid point is $(\frac{5}{2}, \frac{1}{2})$ , then $α + β$ is equal to
Q10 If all the words with or without meaning made using all the letters of the word “KANPUR” are arranged as in a dictionary, then the word at $44 0^{th}$ position in this arrangement, is : …
Q11 Let $α, β$ $(α \neq = \dots$
Q12 Let $A = [a_{ij}] \dots$
Q13 Let $P$ be the foot of the perpendicular from the point $(1, 2, 2)$ on the line $L : \dots$
Q14 Let a circle $C$ pass through the points $(4, 2)$ and $(0, 2)$ , and its centre lie on $\dots$
Q15 Let $A = [a_{ij}] \dots$
Q16 Bag 1 contains 4 white balls and 5 black balls, and Bag 2 contains $n$ white balls and 3 black balls. One ball is drawn randomly from Bag 1 and transferred to Bag 2. A ball is then drawn randomly from Bag 2. If the probability, that the ball drawn is white, is $29/45$ , then $n$ is equal to: …
Q17The remainder, when $7^{103}$ is divided by $23$ , is equal to:
Q18Let $f (x) = \int_{0}^{x} t (t^{2} - 9 t + 20) d t$ , $1 \leq x \leq 5$ . If the range of $f$ is $[α, β]$ , then $4 (α + β)$ equals:
Q19 Let $\overset{a}{^}$ be a unit vector perpendicular to the vectors $\overset{\dots}{b}$
Q20 If for the solution curve $y = f (x)$ of the differential equation
Q21If $\int_{0}^{π /4} 24 (sin (4 x - \frac{π}{12}) + [2 sin x]) d x = 2 π + α$ , where $[\cdot]$ denotes the greatest integer function, then $α$ is equal to _________.
Q22If $t \to 0 lim (\int_{0}^{1} (3 x + 5)^{t} d x)^{1/ t} = \frac{α}{5 e} (\frac{8}{5})^{2/3}$ , then $α$ is equal to _______.
Q23 Let $a_{1}, a_{\dots}$
Q24 Let integers $a, b \in [- 3, 3]$ be such that $a +\dots$
Q25 Let $y^{2} = 12 x$ be the parabola and $S\dots$

JEE Main 2025 — Jan 29, Shift 2

Mathematics

Physics

Chemistry

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