JEE MAIN 2019 Previous Year Questions (PYQs) – Page 1 of 34
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If the angle of intersection at a point where two circles with radii $5\text{ cm}$ and $12\text{ cm}$ intersect is $90^\circ$, then the length (in cm) of their common chord is:
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Solution
The number of values of $\theta \in (0, \pi)$ for which the system of linear equations
$x + 3y + 7z = 0$
$-x + 4y + 7z = 0$
$(\sin 3\theta)x + (\cos 2\theta)y + 2z = 0$
has a non-trivial solution, is -
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Solution
The coefficient of $x^{18}$ in the product
$(1+x)(1-x)^{10}(1+x+x^{2})^{9}$ is:
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Solution
The curve amongst the family of curves represented by the differential equation
$(x^2 - y^2)dx + 2xy\,dy = 0$
which passes through $(1, 1)$ is :
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Solution
If $m$ is the minimum value of $k$ for which the function $f(x)=x\sqrt{kx-x^{2}}$ is increasing in the interval $[0,3]$ and $M$ is the maximum value of $f$ in $[0,3]$ when $k=m$, then the ordered pair $(m,M)$ is equal to:
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Solution
Let $z = \left(\dfrac{\sqrt{3}}{2} + \dfrac{i}{2}\right)^5 + \left(\dfrac{\sqrt{3}}{2} - \dfrac{i}{2}\right)^5.$
If $R(z)$ and $I(z)$ respectively denote the real and imaginary parts of $z$, then :
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Solution
Let $A, B$ and $C$ be sets such that $\varnothing \ne A\cap B \subseteq C$. Which of the following statements is not true?
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Solution
The positive value of $\lambda$ for which the coefficient of $x^2$ in the expression
$x^2 \left( \sqrt{x} + \dfrac{\lambda}{x^2} \right)^{10}$ is $720$, is –
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Solution
If the area (in sq. units) bounded by the parabola $y^{2}=4\lambda x$ and the line $y=\lambda x,\ \lambda>0$, is $\dfrac{1}{9}$, then $\lambda$ is equal to:
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Solution
The value of $\lambda$ such that the sum of the squares of the roots of the quadratic equation
$x^2 + (3 - \lambda)x + 2 = \lambda$
has the least value, is –
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Solution
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