JEE MAIN 2024 Previous Year Questions (PYQs) – Page 4 of 39
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The coefficients $a,b,c$ in the quadratic $ax^{2}+bx+c=0$ are chosen from the set ${1,2,3,4,5,6,7,8}$. The probability that the equation has repeated roots is:
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Solution
If the system
$11x+y+\lambda z=-5,\quad 2x+3y+5z=3,\quad 8x-19y-39z=\mu$
has infinitely many solutions, then $\lambda^{4}-\mu$ equals:
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Solution
The integral $\displaystyle \int_{0}^{\pi/4}\frac{136\sin x}{3\sin x+5\cos x},dx$ is equal to:
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Solution
If $\int_0^1 \frac{1}{\sqrt{3+x}+\sqrt{1+x}}\,dx = a + b\sqrt{2} + c\sqrt{3}$, where $a, b, c$ are rational numbers, then $2a + 3b - 4c$ is equal to:
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Solution
If $\dfrac{1}{\sqrt{1}+\sqrt{2}}+\dfrac{1}{\sqrt{2}+\sqrt{3}}+\cdots+\dfrac{1}{\sqrt{99}+\sqrt{100}}=m$ and $\dfrac{1}{1\cdot 2}+\dfrac{1}{2\cdot 3}+\cdots+\dfrac{1}{99\cdot 100}=n$, then the point $(m,n)$ lies on the line:
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Solution
If $S = \{ z \in \mathbb{C} : |z - i| = |z + i| = |z - 1| \}$, then $n(S)$ is:
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Solution
Let $d$ be the distance of the point of intersection of the lines $\dfrac{x+6}{3}=\dfrac{y}{2}=\dfrac{z+1}{1}$ and $\dfrac{x-7}{4}=\dfrac{y-9}{3}=\dfrac{z-4}{2}$ from the point $(7,8,9)$. Then $d^{2}+6$ is equal to:
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Solution
Let $S=\{1,2,3,\ldots,10\}$. Suppose $M$ is the set of all the subsets of $S$, then the relation
$R=\{(A,B): A\cap B\ne \phi;\ A,B\in M\}$
is:
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Solution
If the function $f(x)=\dfrac{\sin 3x+\alpha\sin x-\beta\cos 3x}{x^{3}},; x\in\mathbb{R},$ is continuous at $x=0$, then $f(0)$ is equal to:
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Solution
If the shortest distance of the parabola $y^2=4x$ from the centre of the circle
$x^2+y^2-4x-16y+64=0$ is $d$, then $d^2$ is equal to:
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Solution
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