JEE MAIN 2024 Previous Year Questions (PYQs) – Page 39 of 39
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Let the point, on the line passing through the points $P(1,-2,3)$ and $Q(5,-4,7)$,
farther from the origin and at a distance of $9$ units from the point $P$, be $(\alpha,\beta,\gamma)$.
Then $\alpha^2+\beta^2+\gamma^2$ is equal to:
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Solution
The vertices of a triangle are $A(-1,3)$, $B(-2,2)$ and $C(3,-1)$.
A new triangle is formed by shifting the sides of the triangle by one unit inwards.
Then the equation of the side of the new triangle nearest to the origin is:
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Solution
Three urns $A$, $B$ and $C$ contain $(7\text{ red}, 5\text{ black})$, $(5\text{ red}, 7\text{ black})$ and $(6\text{ red}, 6\text{ black})$ balls, respectively.
One of the urns is selected at random and a ball is drawn from it.
If the ball drawn is black, then the probability that it is drawn from urn $A$ is:
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Solution
If the solution $y = y(x)$ of the differential equation
$(x^{4}+2x^{3}+3x^{2}+2x+2)\,dy-(2x^{2}+2x+3)\,dx=0$
satisfies $y(-1)=-\dfrac{\pi}{4}$, then $y(0)$ is equal to:
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Solution
Let the first three terms $2,\,p,\,q$ with $q\ne 2$ of a G.P. be respectively the $7^{\text{th}},\,8^{\text{th}}$ and $13^{\text{th}}$ terms of an A.P.
If the $5^{\text{th}}$ term of the G.P. is the $n^{\text{th}}$ term of the A.P., then $n$ is equal to:
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Solution
The sum of all rational terms in the expansion of $\left(2^{\frac15}+5^{\frac13}\right)^{15}$ is equal to:
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Solution
If $2$ and $6$ are roots of the equation $ax^{2}+bx+1=0$, then the quadratic equation whose roots are $\dfrac{1}{2a+b}$ and $\dfrac{1}{6a+b}$ is:
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Solution
If the center and radius of the circle $\left|\dfrac{z-2}{z-3}\right|=2$ are respectively $(\alpha,\beta)$ and $\gamma$, then $3(\alpha+\beta+\gamma)$ is equal to:
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Solution
Let the sum of the maximum and the minimum values of the function
$f(x)=\dfrac{2x^{2}-3x+8}{2x^{2}+3x+8}$ be $\dfrac{m}{n}$, where $\gcd(m,n)=1$.
Then $m+n$ is equal to:
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Solution
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