JEE MAIN Mathematics Previous Year Questions (PYQs) – Page 1 of 251
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The region represented by {z = x + iy $ \in $ C : |z| – Re(z) $ \le $ 1} is also given by the inequality :{z = x + iy $ \in $ C : |z| – Re(z) $ \le $ 1}
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Solution
The number of real solutions of the equation, x2 $-$ |x| $-$ 12 = 0 is :
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Solution
Let $\vec{a} = \alpha \hat{i} + \hat{j} - \hat{k}$ and $\vec{b} = 2\hat{i} + \hat{j} - \alpha \hat{k}$, $\alpha > 0$.
If the projection of $\vec{a} \times \vec{b}$ on the vector $-\hat{i} + 2\hat{j} - 2\hat{k}$ is $30$, then $\alpha$ is equal to:
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Solution
The mean and variance of 5 observations are 5 and 8 respectively. If 3 observations are 1, 3, 5, then the sum of cubes of the remaining two observations is :
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Solution
If the system of equations
$x+\big(\sqrt{2}\sin\alpha\big)y+\big(\sqrt{2}\cos\alpha\big)z=0$
$x+(\cos\alpha)y+(\sin\alpha)z=0$
$x+(\sin\alpha)y-(\cos\alpha)z=0$
has a non-trivial solution, then $\alpha\in\left(0,\frac{\pi}{2}\right)$ is equal to:
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Solution
Let $\mathrm{I}(x)=\int \frac{d x}{(x-11)^{\frac{11}{13}}(x+15)^{\frac{15}{13}}}$. If $\mathrm{I}(37)-\mathrm{I}(24)=\frac{1}{4}\left(\frac{1}{\mathrm{~b}^{\frac{1}{13}}}-\frac{1}{\mathrm{c}^{\frac{1}{13}}}\right), \mathrm{b}, \mathrm{c} \in \mathcal{N}$, then $3(\mathrm{~b}+\mathrm{c})$ is equal to
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Let the three sides of a triangle be on the lines $4x-7y+10=0$, $x+y=5$ and $7x+4y=15$. Then the distance of its orthocentre from the orthocentre of the triangle formed by the lines $x=0$, $y=0$ and $x+y=1$ is
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Solution
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
$\displaystyle \lim_{x\to 0}\frac{\sin(\pi \cos^{2}x)}{x^{2}}$ is equal to :
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Solution
Let a , b, c , d and p be any non zero distinct real numbers such that(a2 + b2 + c2)p2 – 2(ab + bc + cd)p + (b2 + c2 + d2) = 0. Then :
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Solution
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