Consider two sets $A$ and $B$, each containing three numbers in A.P. Let the sum and the product of the elements of $A$ be $36$ and $p$ respectively and the sum and the product of the elements of $B$ be $36$ and $q$ respectively. Let $d$ and $D$ be the common differences of the A.P.s in $A$ and $B$ respectively such that $D=d+3$, $d>0$. If $\dfrac{p+q}{p-q}=\dfrac{19}{5}$, then $p-q$ is equal to:
Previous 10 Questions — JEE Main 2025 (4 April Evening Shift)
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Let $f(x)+2f!\left(\frac{1}{x}\right)=x^{2}+5$ and $2g(x)-3g!\left(\frac{1}{x}\right)=x$, $x>0$. If $\alpha=\displaysty…
Topic: JEE Main 2025 (4 April Evening Shift)
The axis of a parabola is the line $y=x$ and its vertex and focus are in the first quadrant at distances $\sqrt{2}$ and…
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The sum of the infinite series $\cot^{-1}\left(\dfrac{7}{4}\right)+\cot^{-1}\left(\dfrac{19}{4}\right)+\cot^{-1}\left(\…
Topic: JEE Main 2025 (4 April Evening Shift)
Let $A$ be the point of intersection of the lines $L_{1}:\ \dfrac{x-7}{1}=\dfrac{y-5}{0}=\dfrac{z-3}{-1}$ and $L_{2}:\ …
Topic: JEE Main 2025 (4 April Evening Shift)
If $1^{2}\cdot{^{15}C_{1}}+2^{2}\cdot{^{15}C_{2}}+3^{2}\cdot{^{15}C_{3}}+\cdots+15^{2}\cdot{^{15}C_{15}}=2^{m}\cdot3^{n…
Topic: JEE Main 2025 (4 April Evening Shift)
Let the product of $\omega_1=(8+i)\sin\theta+(7+4i)\cos\theta$ and $\omega_2=(1+8i)\sin\theta+(4+7i)\cos\theta$ be $\al…
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A line passing through the point $A(-2,0)$ touches the parabola $P: y^2=x-2$ at the point $B$ in the first quadrant. Th…
Topic: JEE Main 2025 (4 April Evening Shift)
The centre of a circle $C$ is at the centre of the ellipse $E:\ \dfrac{x^{2}}{a^{2}}+\dfrac{y^{2}}{b^{2}}=1,\ a>b$. Let…
Topic: JEE Main 2025 (4 April Evening Shift)
Let for two distinct values of $p$ the lines $y=x+p$ touch the ellipse $E:\ \dfrac{x^{2}}{4^{2}}+\dfrac{y^{2}}{3^{2}}=1…
Topic: JEE Main 2025 (4 April Evening Shift)
If the sum of the first $20$ terms of the series $\dfrac{4\cdot1}{4+3\cdot1^{2}+1^{4}}+\dfrac{4\cdot2}{4+3\cdot2^{2}+2^…
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Next 10 Questions — JEE Main 2025 (4 April Evening Shift)
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Let the values of $p$, for which the shortest distance between the lines
$\dfrac{x+1}{3}=\dfrac{y}{4}=\dfrac{z}{5}$ and…
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Let $f$ be a differentiable function on $\mathbb{R}$ such that $f(2)=1,\ f'(2)=4$.
Let $\displaystyle \lim_{x\to 0}\big…
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