JEE Advanced 2022 Paper 1 Online | JEE Advanced Year Wise Previous Years Questions

JEE Advanced 2022 Paper 1 Online

MCQ (More than One Correct Answer)

-2

Consider the equation

$$ \int_{1}^{e} \frac{\left(\log _{\mathrm{e}} x\right)^{1 / 2}}{x\left(a-\left(\log _{\mathrm{e}} x\right)^{3 / 2}\right)^{2}} d x=1, \quad a \in(-\infty, 0) \cup(1, \infty) $$

Which of the following statements is/are TRUE?

No $$a$$ satisfies the above equation

An integer $$a$$ satisfies the above equation

An irrational number $$a$$ satisfies the above equation

More than one $$a$$ satisfy the above equation

JEE Advanced 2022 Paper 1 Online

MCQ (More than One Correct Answer)

-2

Let $$a_{1}, a_{2}, a_{3}, \ldots$$ be an arithmetic progression with $$a_{1}=7$$ and common difference 8. Let $$T_{1}, T_{2}, T_{3}, \ldots$$ be such that $$T_{1}=3$$ and $$T_{n+1}-T_{n}=a_{n}$$ for $$n \geq 1$$. Then, which of the following is/are TRUE ?

$$T_{20}=1604$$

$$\sum\limits_{k=1}^{20} T_{k}=10510$$

$$T_{30}=3454$$

$$\sum\limits_{k=1}^{30} T_{k}=35610$$

JEE Advanced 2022 Paper 1 Online

MCQ (More than One Correct Answer)

-2

Let $$P_{1}$$ and $$P_{2}$$ be two planes given by

$$ \begin{aligned} &P_{1}: 10 x+15 y+12 z-60=0 \\\\ &P_{2}:-2 x+5 y+4 z-20=0 \end{aligned} $$

Which of the following straight lines can be an edge of some tetrahedron whose two faces lie on $$P_{1}$$ and $$P_{2}$$ ?

$$\frac{x-1}{0}=\frac{y-1}{0}=\frac{z-1}{5}$$

$$\frac{x-6}{-5}=\frac{y}{2}=\frac{z}{3}$$

$$\frac{x}{-2}=\frac{y-4}{5}=\frac{z}{4}$$

$$\frac{x}{1}=\frac{y-4}{-2}=\frac{z}{3}$$

JEE Advanced 2022 Paper 1 Online

MCQ (More than One Correct Answer)

-2

Let $$S$$ be the reflection of a point $$Q$$ with respect to the plane given by

$$ \vec{r}=-(t+p) \hat{\imath}+t \hat{\jmath}+(1+p) \hat{k} $$

where $$t, p$$ are real parameters and $$\hat{\imath}, \hat{\jmath}, \hat{k}$$ are the unit vectors along the three positive coordinate axes. If the position vectors of $$Q$$ and $$S$$ are $$10 \hat{\imath}+15 \hat{\jmath}+20 \hat{k}$$ and $$\alpha \hat{\imath}+\beta \hat{\jmath}+\gamma \hat{k}$$ respectively, then which of the following is/are TRUE ?

$$3(\alpha+\beta)=-101$$

$$3(\beta+\gamma)=-71$$

$$3(\gamma+\alpha)=-86$$

$$3(\alpha+\beta+\gamma)=-121$$

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