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JEE MAIN 2022
27-07-2022 - S2
Question
A thin prism of angle 6º and refractive index for yellow light $\left(n_Y\right)$ 1.5 is combined with another prism of angle $5^{\circ}$ and $\mathrm{n}_Y=1.55$. The combination produces no dispersion. The net average deviation $(\delta)$ produced by the combination is $\left(\frac{1}{x}\right)^{\circ}$ . The value of x is …………
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Showing 18 questions
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JEE MainChemistryEasy
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If $y(\theta)=\frac{2 \cos \theta+\cos 2 \theta}{\cos 3 \theta+4 \cos 2 \theta+5 \cos \theta+2}$, then at $\theta=\frac{\pi}{2}, y^{\prime \prime}+y^{\prime}+y$ is equal...
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Let $\alpha \beta \neq 0$ and $...
JEE MainMathematicsEasy
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QJEE Main 20242024
Let $\beta(m, n)=\int_0^1 x^{m-1}(1-x)^{n-1} d x, m, n>0$. If $\int_0^1\left(1-x^{10}\right)^{20} d x=a \times \beta(b, c)$, then $100(a+b+x)$ equals
JEE MainMathematicsEasy
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QJEE Main 20242024
Let ABCD and AEFG be squares of side 4 and 2 units, respectively. The point E is on the line...
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The coefficients $a, b, c$ in the quadratic equation $a x^2+b x+c=0$ are from the set $\{1,2,3,4,5,6\}$. If the probability...
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QJEE Main 20242024
The values of $m, n$, for which the system of equations
$...
JEE MainMathematicsEasy
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Let the set $S=\{2,4,8,16, \ldots, 512\}$ be partitioned into 3 sets $\mathrm{A}, \mathrm{B}, \mathrm{C}$ with equal number of elements such...
JEE MainMathematicsEasy
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QJEE Main 20242024
Let the circle $C_1: x^2+y^2-2(x+y)+1=0$ and $C_2$ be a circle having centre at $(-1,0)$ and radius 2 . If the...
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Let $f, \mathrm{~g}: \mathrm{R} \rightarrow \mathrm{R}$ be defined as : $f(\mathrm{x})=|\mathrm{x}-1|$ and $...
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If the constant term in the expansion of $\left(\frac{\sqrt[5]{3}}{x}+\frac{2 x}{\sqrt[3]{5}}\right)^{12}, x \neq 0$, is $\alpha \times 2^8 \times \sqrt[5]{3}$, then...
JEE MainMathematicsEasy
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QJEE Main 20242024
Let $(\alpha, \beta, \gamma)$ be the point $(8,5,7)$ in the line $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-2}{5}$. Then $\alpha+\beta+\gamma$ is equal to
JEE MainMathematicsEasy
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QJEE Main 20242024
Let $\mathrm{A}(-1,1)$ and $\mathrm{B}(2,3)$ be two points and P be a variable point above the line $A B$ such that...
JEE MainMathematicsEasy
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QJEE Main 20242024
Consider three vectors $\vec{a}, \vec{b}, \vec{c}$. Let $|\vec{a}|=2,|\vec{b}|=3$ and $\overrightarrow{\mathrm{a}}=\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{c}}$. If $\alpha \in\left[0, \frac{\pi}{3}\right]$ is the angle between...
JEE MainMathematicsEasy
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QJEE Main 20242024
Let $\vec{a}=2 \hat{\imath}+5 \hat{\jmath}-\hat{k}, \vec{b}=2 \hat{\imath}-2 \hat{\jmath}+2 \hat{k}$ and $\overrightarrow{\mathrm{c}}$ be three vectors such that $(\vec{c}+\hat{\imath}) \times(\vec{a}+\vec{b}+\hat{\imath})=\vec{a} \times(\vec{c}+\hat{\imath})$. $...
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60 words can be made using all the letters of the word BHBJO, with or without meaning. If these words...
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