Other Maths · JEE Main previous year questions

2018 5 questions

1. Q32018 · 16 Apr 2018 · Shift 1

   The least positive integer n for which ${\left(\frac{1+i\sqrt{3}}{1-i\sqrt{3}}\right)}^n=1$, is :

   1. A.2
   2. B.3
   3. C.5
   4. D.6
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   Answer: B

2. Q42018 · 16 Apr 2018 · Shift 1

   Let $\text{A}=\left[\begin{array}{ccc}1& 0& 0\\ 1& 1& 0\\ 1& 1& 1\end{array}\right]$ and $\text{B}={\text{A}}^{20}$. Then the sum of the elements of the first column of B is :

   1. A.210
   2. B.211
   3. C.231
   4. D.251
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   Answer: C

3. Q102018 · 16 Apr 2018 · Shift 1

   If $x=\sqrt{2^{{\text{cosec}}^{-1}t}}$ and $y=\sqrt{2^{{\sec }^{-1}t}}$ $(|t|\ge 1)$, then $\frac{dy}{dx}$ is equal to :

   1. A.$\frac{y}{x}$
   2. B.$\frac{x}{y}$
   3. C.$-\frac{y}{x}$
   4. D.$-\frac{x}{y}$
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   Answer: C

4. Q32018 · 8 Apr 2018 · Shift 1

   If $\left|\begin{array}{ccc}x-4& 2x& 2x\\ 2x& x-4& 2x\\ 2x& 2x& x-4\end{array}\right|=(A+Bx)(x-A{)}^2$ then the ordered pair (A, B) is equal to :

   1. A.$(4,5)$
   2. B.$(-4,-5)$
   3. C.$(-4,3)$
   4. D.$(-4,5)$
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   Answer: D

5. Q52018 · 8 Apr 2018 · Shift 1

   Let $\mathrm{S}=\{x\in \mathrm{R}:x\ge 0$ and $2|\sqrt{x}-3|+\sqrt{x}(\sqrt{x}-6)+6=0\}$. Then S

   1. A.contains exactly four elements
   2. B.is an empty set
   3. C.contains exactly one element
   4. D.contains exactly two elements
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   Answer: D