1

JEE Advanced 2018 Paper 2 Offline

MCQ (Single Correct Answer)

+3

-1

Let $${E_1} = \left\{ {x \in R:x \ne 1\,and\,{x \over {x - 1}} > 0} \right\}$$ and

$${E_2} = \left\{ \matrix{ x \in {E_1}:{\sin ^{ - 1}}\left( {{{\log }_e}\left( {{x \over {x - 1}}} \right)} \right) \hfill \cr is\,a\,real\,number \hfill \cr} \right\}$$

(Here, the inverse trigonometric function $${\sin ^{ - 1}}$$ x assumes values in $$\left[ { - {\pi \over 2},{\pi \over 2}} \right]$$.).

Let f : E

The correct option is :

$${E_2} = \left\{ \matrix{ x \in {E_1}:{\sin ^{ - 1}}\left( {{{\log }_e}\left( {{x \over {x - 1}}} \right)} \right) \hfill \cr is\,a\,real\,number \hfill \cr} \right\}$$

(Here, the inverse trigonometric function $${\sin ^{ - 1}}$$ x assumes values in $$\left[ { - {\pi \over 2},{\pi \over 2}} \right]$$.).

Let f : E

_{1}$$ \to $$ R be the function defined by f(x) = $${{{\log }_e}\left( {{x \over {x - 1}}} \right)}$$ and g : E_{2}$$ \to $$ R be the function defined by g(x) = $${\sin ^{ - 1}}\left( {{{\log }_e}\left( {{x \over {x - 1}}} \right)} \right)$$.LIST-I | LIST-II |
---|---|

P. The range of $f$ is | 1. $\left( -\infty, \frac{1}{1-e} \right] \cup \left[ \frac{e}{e-1}, \infty \right)$ |

Q. The range of $g$ contains | 2. $(0, 1)$ |

R. The domain of $f$ contains | 3. $\left[ -\frac{1}{2}, \frac{1}{2} \right]$ |

S. The domain of $g$ is | 4. $(-\infty, 0) \cup (0, \infty)$ |

5. $\left( -\infty, \frac{e}{e-1} \right)$ | |

6. $(-\infty, 0) \cup \left( \frac{1}{2}, \frac{e}{e-1} \right]$ |

2

JEE Advanced 2018 Paper 2 Offline

MCQ (Single Correct Answer)

+3

-1

In a high school, a committee has to be formed from a group of 6 boys M

(i) Let $$\alpha $$

(ii) Let $$\alpha $$

i) Let $$\alpha $$

(iv) Let $$\alpha $$

The correct option is

_{1}, M_{2}, M_{3}, M_{4}, M_{5}, M_{6}and 5 girls G_{1}, G_{2}, G_{3}, G_{4}, G_{5}.(i) Let $$\alpha $$

_{1}be the total number of ways in which the committee can be formed such that the committee has 5 members, having exactly 3 boys and 2 girls.(ii) Let $$\alpha $$

_{2}be the total number of ways in which the committee can be formed such that the committee has at least 2 members, and having an equal number of boys and girls.i) Let $$\alpha $$

_{3}be the total number of ways in which the committee can be formed such that the committee has 5 members, at least 2 of them being girls.(iv) Let $$\alpha $$

_{4}be the total number of ways in which the committee can be formed such that the committee has 4 members, having at least 2 girls such that both M_{1}and G_{1}are NOT in the committee together.LIST-I | LIST-II |
---|---|

P. The value of $\alpha_1$ is | 1. 136 |

Q. The value of $\alpha_2$ is | 2. 189 |

R. The value of $\alpha_3$ is | 3. 192 |

S. The value of $\alpha_4$ is | 4. 200 |

5. 381 | |

6. 461 |

3

JEE Advanced 2018 Paper 2 Offline

MCQ (Single Correct Answer)

+3

-1

Let $$H:{{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$, where a > b > 0, be a hyperbola in the XY-plane whose conjugate axis LM subtends an angle of 60$$^\circ $$ at one of its vertices N. Let the area of the $$\Delta $$LMN be $$4\sqrt 3 $$.

List - I | List - II | ||
---|---|---|---|

P. | The length of the conjugate axis of H is | 1. | 8 |

Q. | The eccentricity of H is | 2. | $${4 \over {\sqrt 3 }}$$ |

R. | The distance between the foci of H is | 3. | $${2 \over {\sqrt 3 }}$$ |

S. | The length of the latus rectum of H is | 4. | 4 |

4

JEE Advanced 2018 Paper 2 Offline

MCQ (Single Correct Answer)

+3

-1

Let $${f_1}:R \to R,\,{f_2}:\left( { - {\pi \over 2},{\pi \over 2}} \right) \to R,\,{f_3}:( - 1,{e^{\pi /2}} - 2) \to R$$ and $${f_4}:R \to R$$ be functions defined by

(i) $${f_1}(x) = \sin (\sqrt {1 - {e^{ - {x^2}}}} )$$,

(ii) $${f_2}(x) = \left\{ \matrix{ {{|\sin x|} \over {\tan { - ^1}x}}if\,x \ne 0,\,where \hfill \cr 1\,if\,x = 0 \hfill \cr} \right.$$

the inverse trigonometric function tan

(iii) $${f_3}(x) = [\sin ({\log _e}(x + 2))]$$, where for $$t \in R,\,[t]$$ denotes the greatest integer less than or equal to t,

(iv) $${f_4}(x) = \left\{ \matrix{ {x^2}\sin \left( {{1 \over x}} \right)\,if\,x \ne 0 \hfill \cr 0\,if\,x = 0 \hfill \cr} \right.$$

(i) $${f_1}(x) = \sin (\sqrt {1 - {e^{ - {x^2}}}} )$$,

(ii) $${f_2}(x) = \left\{ \matrix{ {{|\sin x|} \over {\tan { - ^1}x}}if\,x \ne 0,\,where \hfill \cr 1\,if\,x = 0 \hfill \cr} \right.$$

the inverse trigonometric function tan

^{$$-$$1}x assumes values in $$\left( { - {\pi \over 2},{\pi \over 2}} \right)$$,(iii) $${f_3}(x) = [\sin ({\log _e}(x + 2))]$$, where for $$t \in R,\,[t]$$ denotes the greatest integer less than or equal to t,

(iv) $${f_4}(x) = \left\{ \matrix{ {x^2}\sin \left( {{1 \over x}} \right)\,if\,x \ne 0 \hfill \cr 0\,if\,x = 0 \hfill \cr} \right.$$

LIST-I | LIST-II |
---|---|

P. The function $$ f_1 $$ is | 1. NOT continuous at $$ x = 0 $$ |

Q. The function $$ f_2 $$ is | 2. continuous at $$ x = 0 $$ and NOT differentiable at $$ x = 0 $$ |

R. The function $$ f_3 $$ is | 3. differentiable at $$ x = 0 $$ and its derivative is NOT continuous at $$ x = 0 $$ |

S. The function $$ f_4 $$ is | 4. differentiable at $$ x = 0 $$ and its derivative is continuous at $$ x = 0 $$ |

Paper analysis

Total Questions

Chemistry

18

Mathematics

18

Physics

18

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