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JEE Advanced 2022 Question Paper & Answers

The official JEE Advanced 2022 question papers, with the official answer key. Attempt as a real timed exam (with negative marking) or switch to practice mode for instant per-question answers and explanations.

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Official PYQ

JEE Advanced 2022 - Paper 1

180 Mins 177 Marks
53Questions
177Max Marks

Sample questions from JEE Advanced 2022 - Paper 1

1Considering only the principal values of the inverse trigonometric functions, the value of 32cos⁡−122+π2+14sin⁡−122π2+π2+tan⁡−12π\dfrac32\cos^{-1}\sqrt{\dfrac{2}{2+\pi^2}}+\dfrac14\sin^{-1}\dfrac{2\sqrt2\pi}{2+\pi^2}+\tan^{-1}\dfrac{\sqrt2}{\pi} is ______.
Answer: 2.35-2.37
2Let α\alpha be a positive real number. Let f:R→Rf:\mathbb{R}\to\mathbb{R} and g:(α,∞)→Rg:(\alpha,\infty)\to\mathbb{R} be the functions defined by f(x)=sin⁡(πx12)andg(x)=2log⁡e(x−α)log⁡e(ex−eα).f(x)=\sin\left(\dfrac{\pi x}{12}\right)\quad\text{and}\quad g(x)=\dfrac{2\log_e(\sqrt x-\sqrt\alpha)}{\log_e(e^{\sqrt x}-e^{\sqrt\alpha})}. Then the value of lim⁡x→α+f(g(x))\displaystyle\lim_{x\to\alpha^+}f(g(x)) is ______.
Answer: 0.49-0.51
3In a study about a pandemic, data of 900 persons was collected. It was found that 190 persons had symptom of fever,
220 persons had symptom of cough,
220 persons had symptom of breathing problem,
330 persons had symptom of fever or cough or both,
350 persons had symptom of cough or breathing problem or both,
340 persons had symptom of fever or breathing problem or both,
30 persons had all three symptoms (fever, cough and breathing problem). If a person is chosen randomly from these 900 persons, then the probability that the person has at most one symptom is ______.
Answer: 0.79-0.81
4Let zz be a complex number with non-zero imaginary part. If 2+3z+4z22−3z+4z2\dfrac{2+3z+4z^2}{2-3z+4z^2} is a real number, then the value of ∣z∣2|z|^2 is ______.
Answer: 0.49-0.51
5Let zˉ\bar z denote the complex conjugate of a complex number zz and let i=−1i=\sqrt{-1}. In the set of complex numbers, the number of distinct roots of the equation zˉ−z2=i(zˉ+z2)\bar z-z^2=i(\bar z+z^2) is ______.
Answer: 4-4

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Official PYQ

JEE Advanced 2022 - Paper 2

180 Mins 173 Marks
52Questions
173Max Marks

Sample questions from JEE Advanced 2022 - Paper 2

1Let α\alpha and β\beta be real numbers such that −π4<β<0<α<π4-\dfrac{\pi}{4}<\beta<0<\alpha<\dfrac{\pi}{4}. If sin⁡(α+β)=13\sin(\alpha+\beta)=\dfrac13 and cos⁡(α−β)=23\cos(\alpha-\beta)=\dfrac23, then the greatest integer less than or equal to (sin⁡αcos⁡β+cos⁡βsin⁡α+cos⁡αsin⁡β+sin⁡βcos⁡α)2\left(\dfrac{\sin\alpha}{\cos\beta}+\dfrac{\cos\beta}{\sin\alpha}+\dfrac{\cos\alpha}{\sin\beta}+\dfrac{\sin\beta}{\cos\alpha}\right)^2 is ______.
Answer: 1
2If y(x)y(x) is the solution of the differential equation x dy−(y2−4y) dx=0for x>0,y(1)=2,x\,dy-(y^2-4y)\,dx=0\quad\text{for }x>0,\qquad y(1)=2, and the slope of the curve y=y(x)y=y(x) is never zero, then the value of 10 y(2)10\,y(\sqrt2) is ______.
Answer: 8
3The greatest integer less than or equal to ∫12log⁡2(x3+1) dx+∫1log⁡29(2x−1)1/3 dx\int_1^2\log_2(x^3+1)\,dx+\int_1^{\log_29}(2^x-1)^{1/3}\,dx is ______.
Answer: 5
4The product of all positive real values of xx satisfying the equation x(16(log⁡5x)3−68log⁡5x)=5−16x^{\left(16(\log_5x)^3-68\log_5x\right)}=5^{-16} is ______.
Answer: 1
5If β=lim⁡x→0ex3−(1−x3)1/3+((1−x2)1/2−1)sin⁡xxsin⁡2x,\beta=\lim_{x\to0}\dfrac{e^{x^3}-(1-x^3)^{1/3}+\left((1-x^2)^{1/2}-1\right)\sin x}{x\sin^2x}, then the value of 6β6\beta is ______.
Answer: 5

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