1

IIT-JEE 2009 Paper 2 Offline

MCQ (Single Correct Answer)

+3

-0

Match the statements/expressions in Column I with the values given in Column II:

Column I | Column II | ||
---|---|---|---|

(A) | The number of solutions of the equation $$x{e^{\sin x}} - \cos x = 0$$ in the interval $$\left( {0,{\pi \over 2}} \right)$$ | (P) | 1 |

(B) | Value(s) of $$k$$ for which the planes $$kx + 4y + z = 0,4x + ky + 2z = 0$$ and $$2x + 2y + z = 0$$ intersect in a straight line | (Q) | 2 |

(C) | Value(s) of $$k$$ for which $$|x - 1| + |x - 2| + |x + 1| + |x + 2| = 4k$$ has integer solution(s) | (R) | 3 |

(D) | If $$y' = y + 1$$ and $$y(0) = 1$$ then value(s) of $$y(\ln 2)$$ | (S) | 4 |

(T) | 5 |

2

IIT-JEE 2009 Paper 1 Offline

MCQ (Single Correct Answer)

+3

-0

Match the statements/expressions in Column I with the open intervals in Column II :

Column I | Column II | ||
---|---|---|---|

(A) | Interval contained in the domain of definition of non-zero solutions of the differential equation $${(x - 3)^2}y' + y = 0$$ | (P) | $$\left( { - {\pi \over 2},{\pi \over 2}} \right)$$ |

(B) | Interval containing the value of the integral $$\int\limits_1^5 {(x - 1)(x - 2)(x - 3)(x - 4)(x - 5)dx} $$ | (Q) | $$\left( {0,{\pi \over 2}} \right)$$ |

(C) | Interval in which at least one of the points of local maximum of $${\cos ^2}x + \sin x$$ lies | (R) | $$\left( {{\pi \over 8},{{5\pi } \over 4}} \right)$$ |

(D) | Interval in which $${\tan ^{ - 1}}(\sin x + \cos x)$$ is increasing | (S) | $$\left( {0,{\pi \over 8}} \right)$$ |

(T) | $$( - \pi ,\pi )$$ |

3

IIT-JEE 2008 Paper 2 Offline

MCQ (Single Correct Answer)

+3

-1

Let a solution $$y=y(x)$$ of the differential equation,

$$x\sqrt {{x^2} - 1} \,\,dy - y\sqrt {{y^2} - 1} \,dx = 0$$ satify $$y\left( 2 \right) = {2 \over {\sqrt 3 }}.$$

$$x\sqrt {{x^2} - 1} \,\,dy - y\sqrt {{y^2} - 1} \,dx = 0$$ satify $$y\left( 2 \right) = {2 \over {\sqrt 3 }}.$$

**STATEMENT-1 :** $$y\left( x \right) = \sec \left( {{{\sec }^{ - 1}}x - {\pi \over 6}} \right)$$ and
**STATEMENT-2 :** $$y\left( x \right)$$ given by $${1 \over y} = {{2\sqrt 3 } \over x} - \sqrt {1 - {1 \over {{x^2}}}} $$

4

IIT-JEE 2008 Paper 2 Offline

MCQ (Single Correct Answer)

+4

-1

Match the Statements/Expressions in Column I with the Statements/Expressions in Column II.

Column I | Column II | ||
---|---|---|---|

(A) | The minimum value of $${{{x^2} + 2x + 4} \over {x + 2}}$$ is | (P) | 0 |

(B) | Let A and B be 3 $$\times$$ 3 matrices of real numbers, where A is symmetric, B is skew-symmetric and (A + B) (A $$-$$ B) = (A $$-$$ B) (A + B). If (AB)$$^t$$ = ($$-1$$)$$^k$$ AB, where (AB)$$^t$$ is the transpose of the matrix AB, then the possible values of k are | (Q) | 1 |

(C) | Let $$a=\log_3\log_3 2$$. An integer k satisfying $$1 < {2^{( - k + 3 - a)}} < 2$$, must be less than | (R) | 2 |

(D) | If $$\sin \theta = \cos \varphi $$, then the possible values of $${1 \over \pi }\left( {\theta + \varphi - {\pi \over 2}} \right)$$ are | (S) | 3 |

Questions Asked from Differential Equations (MCQ (Single Correct Answer))

Number in Brackets after Paper Indicates No. of Questions

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