JEE Advanced 2007 Paper-2

JEE Advanced 2007 Paper-2 - Question 1

Report

In the experiment to determine the speed of sound using a resonance column,

A

prongs of the tuning fork are kept in a vertical plane

B

prongs of the tuning fork are kept in a horizontal plane

C

in one of the two resonances observed, the length of the resonating air columnis close to the wave length of sound in air

D

in one of the two resonances observed, the length of the resonating air column is close to half of the wave length of sound in air

View Solution

JEE Advanced 2007 Paper-2 - Question 2

Report

A student performs an experiment to determine the Young’s modulus of a wire, exactly 2 m long, by Searle’s method. In a particular reading, the student measures the extension in the length of the wire to be 0.8 mm with an uncertainty of $$\pm 0.05$$ mm at load of exactly 1.0 kg. The student also measures the diameter of the wire to be 0.4 mm with an uncertainty of $$\pm 0.01$$ mm. Take g = 9.8 m/s$$^2$$ (exact). The Young’s modulus obtained from the reading is

A

$$(2.0 \pm 0.3) \times 10^{11} N/m^2$$

B

$$(2.0 \pm 0.2) \times 10^{11} N/m^2$$

C

$$(2.0 \pm 0.1) \times 10^{11} N/m^2$$

D

$$(2.0 \pm 0.05) \times 10^{11} N/m^2$$

View Solution

JEE Advanced 2007 Paper-2 - Question 3

Report

A particle moves in the X-Y plane underthe influence of a force such that its linear momentum is $$\overrightarrow{p}(t) = A\left[\hat{i} \cos (kt) - \hat{j} \sin (kt)\right]$$, where A and k are constants. The angle between the force and the momentum is

A

$$0^\circ$$

B

$$30^\circ$$

C

$$45^\circ$$

D

$$90^\circ$$

View Solution

JEE Advanced 2007 Paper-2 - Question 4

Report

A small object of uniform density rolls up a curved surface with an initial velocity v. It reaches up to a maximum height of $$\frac{3v^2}{4g}$$ with respect to the initial position. The object is

A

ring

B

solid sphere

C

hollow sphere

D

disc

View Solution

JEE Advanced 2007 Paper-2 - Question 5

Report

Water is filled up to a height h in a beaker of radius R as shown in the figure. The density of water is $$\rho$$, the surface tension of water is T and the atmospheric pressure is $$P_0$$. Consider a vertical section ABCD of the water column through a diameter of the beaker. The force on water on one side of this section by water on the other side of this section has magnitude.

A

$$\mid 2P_0Rh + \pi R^2 \rho gh - 2RT \mid$$

B

$$\mid 2P_0Rh + R \rho gh^2 - 2RT \mid$$

C

$$\mid P_0 \pi R^2 + R \rho gh^2 - 2RT \mid$$

D

$$\mid P_0 \pi R^2 + R \rho gh^2 + 2RT \mid$$

View Solution

JEE Advanced 2007 Paper-2 - Question 6

Report

A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as showing the figure. The electric field inside the emptied space is

A

zero everywhere

B

non-zero and uniform

C

non-uniform

D

zero only at its center

View Solution

JEE Advanced 2007 Paper-2 - Question 7

Report

Positive and negative point charges of equal magnitude are kept at $$\left(0, 0, \frac{a}{2}\right)$$ and $$\left(0, 0, \frac{-a}{2}\right)$$, respectively. The work done by the electric field when another positive point charge is moved from (-a, 0, 0) to (0, a, 0) is

A

positive

B

negative

C

zero

D

depends on the path connecting the initial and final positions

View Solution

JEE Advanced 2007 Paper-2 - Question 8

Report

A magnetic field $$\overrightarrow{B} = B_0\hat{j}$$ exists in the region a < x < 2a and $$\overrightarrow{B} = -B_0 \hat{j}$$, in the region 2a < x < 3a, where $$B_0$$ is a positive constant. A positive point charge moving with a velocity $$\overrightarrow{v} = v_0 \hat{i}$$, where $$v_0$$ is a positive constant, enters the magnetic field at x = a. The trajectory of the charge in this region can be like,

A

B

C

D

View Solution

JEE Advanced 2007 Paper-2 - Question 9

Report

Electrons with de-Broglie wave length $$\lambda$$ fall on the target in an X-ray tube. The cut-off wavelength of the emitted X-rays is

A

$$\lambda_0 = \frac{2mc \lambda^2}{h}$$

B

$$\lambda_0 = \frac{2h}{mc}$$

C

$$\lambda_0 = \frac{2 m^2 c^2 \lambda^3}{h^2}$$

D

$$\lambda_0 = \lambda$$

View Solution

JEE Advanced 2007 Paper-2 - Question 10

Report

STATEMENT-1
If there is no external torque on a body aboutits center of mass, then the velocity of the center of mass remains constant.
because
STATEMENT-2
The linear momentum of an isolated system remains constant.

A

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

B

Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

C

Statement-1 is True, Statement-2 is False

D

Statement-1 is False, Statement-2 is True

View Solution

JEE Advanced 2007 Paper-2 - Question 11

Report

STATEMENT-1
A cloth covers a table. Some dishes are kept on it. The cloth can be pulled out without dislodging the dishes from thetable.
because
STATEMENT-2
For every action there is an equal and opposite reaction.

A

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

B

Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

C

Statement-1 is True, Statement-2 is False

D

Statement-1 is False, Statement-2 is True

View Solution

JEE Advanced 2007 Paper-2 - Question 12

Report

STATEMENT-1
A vertical iron rod has a coil of wire wound over it at the bottom end. An alternating current flows in the coil. The rod goes through a conducting ring as showing the figure. The ring can float at a certain height above the coil.
because
STATEMENT-2
In the above situation, a current is induced in the ring which interacts with the horizontal component of the magnetic field to produce an average force in the upward direction.

A

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

B

Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

C

Statement-1 is True, Statement-2 is False

D

Statement-1 is False, Statement-2 is True

View Solution

JEE Advanced 2007 Paper-2 - Question 13

Report

STATEMENT-1
The total translational kinetic energy of all the molecules of a given massof an ideal gas is 1.5 times the product of its pressure and its volume.
because
STATEMENT-2
The molecules of a gas collide with each other and the velocities of the molecules change dueto thecollision.

A

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

B

Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

C

Statement-1 is True, Statement-2 is False

D

Statement-1 is False, Statement-2 is True

View Solution

JEE Advanced 2007 Paper-2 - Question 14

Report

The speed of sound of the whistle is

A

340 m/s for passengers in A and 310 m/s for passengers in B

B

360 m/s for passengers in A and 310 m/s for passengers in B

C

310 m/s for passengers in A and 360 m/s for passengers in B

D

340 m/s for passengersin both the trains

View Solution

JEE Advanced 2007 Paper-2 - Question 15

Report

The distribution of the sound intensity of the whistle as observed by the passengers in train A is best represented by

A

B

C

D

View Solution

JEE Advanced 2007 Paper-2 - Question 16

Report

The spread of frequency as observed by the passengersin train B is

A

310 Hz

B

330 Hz

C

350 Hz

D

290 Hz

View Solution

JEE Advanced 2007 Paper-2 - Question 17

Report

Light travels as a

A

parallel beam in each medium

B

convergent beam in each medium

C

divergent beam in each medium

D

divergent beam in one medium and convergent beam in the other medium

View Solution

JEE Advanced 2007 Paper-2 - Question 18

Report

The phases of the light wave at c, d, e and f are $$\phi_C, \phi_d, \phi_e$$ and $$\phi_f$$ respectively. It is given that $$\phi_c \neq \phi_f$$.

A

$$\phi_c$$ cannot be equal to $$\phi_d$$

B

$$\phi_d$$ can be equal to $$\phi_e$$

C

$$(\phi_d - \phi_f)$$ is equal to $$(\phi_c - \phi_e)$$

D

$$(\phi_d - \phi_c)$$ is not equal to $$(\phi_f - \phi_e)$$

View Solution

JEE Advanced 2007 Paper-2 - Question 19

Report

Speed of light is

A

the same in medium-1 and medium-2

B

larger in medium-1 than in medium-2

C

larger in medium-2 than in medium-1

D

different at b and d

View Solution

JEE Advanced 2007 Paper-2 - Question 20

Report

Column I describes some situations in which a small object moves. Column II describes some characteristics of these motions. Match the situations in Column I with the characteristics in Column II and indicate your answer by darkening appropriate bubbles in the $$4 \times 4$$ matrix given in the ORS.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

JEE Advanced 2007 Paper-2 - Question 21

Report

Two wires each carrying a steady current J are shown in four configurations in Column I. Some of the resulting effects are described in Column II. Match the statements in Column I with the statements in Column II and indicate your answer by darkening appropriate bubbles in the $$4 \times 4$$ matrix given in the ORS.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

JEE Advanced 2007 Paper-2 - Question 22

Report

Column I gives some devices and Column II gives some processes on which the functioning of these devices depend. Match the devices in Column I with the processes in Column II and indicate your answer by darkening appropriate bubbles in the $$4 \times 4$$ matrix given in the ORS.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

JEE Advanced 2007 Paper-2 - Question 23

Report

Consider a titration of potassium dichromate solution with acidified Mohr’s salt solution using diphenylamine as indicator. The number of moles of Mohr’s salt required per mole of dichromate is

A

3

B

4

C

5

D

6

View Solution

JEE Advanced 2007 Paper-2 - Question 24

Report

Among the following metal carbonyls, the C-O bond order is lowest in

A

$$[Mn(CO)_6]^{+}$$

B

$$[Fe(CO)_5]$$

C

$$[Cr(CO)_6]$$

D

$$[V(CO)_6]^{-}$$

View Solution

JEE Advanced 2007 Paper-2 - Question 25

Report

A solution of a metal ion when treated with KI gives a red precipitate which dissolves in excess KI to give a colourless solution. Moreover, the solution of metal ion on treatment with a solution of cobalt(II) thiocyanate gives rise to a deep blue crystalline precipitate. The metal ion is

A

$$Pb^{2+}$$

B

$$Hg^{2+}$$

C

$$Cu^{2+}$$

D

$$Co^{2+}$$

View Solution

JEE Advanced 2007 Paper-2 - Question 26

Report

Cyclohexene on ozonolysis followed by reaction with zinc dust and water gives compound E. Compound E on further treatment with aqueous KOH yields compound F. Compound F is

A

B

C

D

View Solution

JEE Advanced 2007 Paper-2 - Question 27

Report

The numberof stereoisomers obtained by bromination of trans-2-butene is

A

1

B

2

C

3

D

4

View Solution

JEE Advanced 2007 Paper-2 - Question 28

Report

Among the following, the least stable resonance structure is

A

B

C

D

View Solution

JEE Advanced 2007 Paper-2 - Question 29

Report

A positron is emitted from $$_{11}^{23}Na$$. The ratio of the atomic mass and atomic number of the resulting nuclide is

A

$$\frac{22}{10}$$

B

$$\frac{22}{11}$$

C

$$\frac{23}{10}$$

D

$$\frac{23}{12}$$

View Solution

JEE Advanced 2007 Paper-2 - Question 30

Report

For the process $$H_2O(l)$$ (1 bar, 373 K) $$\rightarrow H_2O(g)$$(1 bar, 373 K), the correct set of thermodynamic parameters is

A

$$\triangle G = 0, \triangle S = +ve$$

B

$$\triangle G = 0, \triangle S = -ve$$

C

$$\triangle G = +ve, \triangle S = 0$$

D

$$\triangle G = -ve, \triangle S = +ve$$

View Solution

JEE Advanced 2007 Paper-2 - Question 31

Report

Consider a reaction $$aG + bH \rightarrow$$ Products. When concentration of both the reactants G and is doubled, the rate increases by eight times. However, when concentration of G is doubled keeping the concentration of H fixed, the rate is doubled. The overall order of the reaction is

A

0

B

1

C

2

D

3

View Solution

JEE Advanced 2007 Paper-2 - Question 32

Report

STATEMENT-1: Alkali metals dissolve in liquid ammoniato give blue solutions.
because
STATEMENT-2: Alkali metals in liquid ammonia give solvated species of the type $$[M(NH_3)_n]^{+}$$ (M = alkali metals).

A

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

B

Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

C

Statement-1 is True, Statement-2 is False

D

Statement-1 is False, Statement-2 is True

View Solution

JEE Advanced 2007 Paper-2 - Question 33

Report

STATEMENT-1: Glucose gives a reddish-brown precipitate with Fehling’s solution.
because
STATEMENT-2: Reaction of glucose with Fehling’s solution gives CuO and gluconic acid.

A

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

B

Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

C

Statement-1 is True, Statement-2 is False

D

Statement-1 is False, Statement-2 is True

View Solution

JEE Advanced 2007 Paper-2 - Question 34

Report

STATEMENT-1: Molecules that are not superimposable on their mirror images are chiral.
because
STATEMENT-2: All chiral molecules have chiral centres.

A

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

B

Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

C

Statement-1 is True, Statement-2 is False

D

Statement-1 is False, Statement-2 is True

View Solution

JEE Advanced 2007 Paper-2 - Question 35

Report

STATEMENT-1: Band gap in germanium is small.
because
STATEMENT-2: The energy spread of each germanium atomic energy level is infinitesimally small.

A

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

B

Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

C

Statement-1 is True, Statement-2 is False

D

Statement-1 is False, Statement-2 is True

View Solution

JEE Advanced 2007 Paper-2 - Question 36

Report

Among the following, identify the correct statement.

A

Chloride ion is oxidised by $$O_2$$

B

$$Fe^{2+}$$ is oxidised by iodine

C

Iodide ion is oxidised by chlorine

D

$$Mn^{2+}$$ is oxidised by chlorine

View Solution

JEE Advanced 2007 Paper-2 - Question 37

Report

While $$Fe^{3+}$$ is stable, $$Mn^{3+}$$ is not stable in acid solution because

A

$$O_2$$ oxidises $$Mn^{2+}$$ to $$Mn^{3+}$$

B

$$O_2$$ oxidises both $$Mn^{2+}$$ to $$Mn^{3+}$$ and $$Fe^{2+}$$ to $$Fe^{3+}$$

C

$$Fe^{3+}$$ oxidises $$H_2O$$ to $$O_2$$

D

$$Mn^{3+}$$ oxidises $$H_2O$$ to $$O_2$$

View Solution

JEE Advanced 2007 Paper-2 - Question 38

Report

Sodium fusion extract, obtained from aniline, on treatment with iron(II) sulphate and $$H_2SO_4$$ in presence of air gives a Prussian blue precipitate. The blue colour is due to the formation of

A

$$Fe_4[Fe(CN)_6]_3$$

B

$$Fe_3[Fe(CN)_6]_2$$

C

$$Fe_4[Fe(CN)_6]_2$$

D

$$Fe_3[Fe(CN)_6]_3$$

View Solution

JEE Advanced 2007 Paper-2 - Question 39

Report

Which one of the following reagents is used in the above reaction?

A

$$aq.NaOH + CH_3Cl$$

B

$$aq.NaOH + CH_2Cl_2$$

C

$$aq.NaOH + CHCl_3$$

D

$$aq.NaOH + CCl_4$$

View Solution

JEE Advanced 2007 Paper-2 - Question 40

Report

The electrophile in this reaction is

A

$$:CHCl$$

B

$$^{+}CHCl_2$$

C

$$:CCl_2$$

D

$$.CCl_3$$

View Solution

JEE Advanced 2007 Paper-2 - Question 41

Report

The structure of the intermediate I is

A

B

C

D

View Solution

JEE Advanced 2007 Paper-2 - Question 42

Report

Match the reactions in Column I with nature of the reactions/type of the products in Column II. Indicate your answer by darkening the appropriate bubbles of the $$4 \times 4$$ matrix given in the ORS.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

JEE Advanced 2007 Paper-2 - Question 43

Report

Match the compounds/ions in Column I with their properties/reactions in Column II. Indicate your answer by darkening the appropriate bubbles of the $$4 \times 4$$ matrix given in the ORS.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

JEE Advanced 2007 Paper-2 - Question 44

Report

Match the crystal system/unit cells mentioned in Column I with their characteristic features mentioned in Column II. Indicate your answer by darkening the appropriate bubbles of the $$4 \times 4$$ matrix given in the ORS.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

JEE Advanced 2007 Paper-2 - Question 45

Report

Let O(0, 0), P(3, 4), Q(6, 0) be the vertices of the triangle OPQ. The point R inside the triangle OPQ is such that the triangles OPR, PQR, OQR are of equal area. The coordinates of R are

A

$$\left(\frac{4}{3}, 3\right)$$

B

$$\left(3, \frac{2}{3}\right)$$

C

$$\left(3, \frac{4}{3}\right)$$

D

$$\left(\frac{4}{3}, \frac{2}{3}\right)$$

View Solution

JEE Advanced 2007 Paper-2 - Question 46

Report

If $$\mid z \mid = 1$$ and $$z \neq \pm 1$$, then all the values of $$\frac{z}{1 - z^2}$$ lie on

A

a line not passing through the origin

B

$$\mid z \mid = \sqrt{2}$$

C

the x-axis

D

the y-axis

View Solution

JEE Advanced 2007 Paper-2 - Question 47

Report

Let $$E^c$$ denote the complement of an event E. Let E, F, G be pairwise independent events with $$P(G) > 0$$ and $$P(E \cap F \cap G) = 0$$. Then $$P(E^c \cap F^c \mid G)$$ equals

A

$$P(E^c) + P(F^c)$$

B

$$P(E^c) - P(F^c)$$

C

$$P(E^c) - P(F)$$

D

$$P(E) - P(F^c)$$

View Solution

JEE Advanced 2007 Paper-2 - Question 48

Report

$$\frac{d^2x}{dy^2}$$ equals

A

$$\left(\frac{d^2y}{dx^2}\right)^{-1}$$

B

$$-\left(\frac{d^2y}{dx^2}\right)^{-1}\left(\frac{dy}{dx}\right)^{-3}$$

C

$$\left(\frac{d^2y}{dx^2}\right)\left(\frac{dy}{dx}\right)^{-2}$$

D

$$-\left(\frac{d^2y}{dx^2}\right)\left(\frac{dy}{dx}\right)^{-3}$$

View Solution

JEE Advanced 2007 Paper-2 - Question 49

Report

The differential equation $$\frac{dy}{dx} = \frac{\sqrt{1 - y^2}}{y}$$ determines a family of circles with

A

variable radii and a fixed centre at (0, 1)

B

variable radii and a fixed centre at (0, -1)

C

fixed radius 1 and variable centres along the x-axis

D

fixed radius 1 and variable centres along the y-axis

View Solution

JEE Advanced 2007 Paper-2 - Question 50

Report

Let $$\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}$$ be unit vectors such that $$\overrightarrow{a} + \overrightarrow{b} + \overrightarrow{c} = \overrightarrow{0}$$. Which one of the following is correct?

A

$$\overrightarrow{a} \times \overrightarrow{b} = \overrightarrow{b} \times \overrightarrow{c} = \overrightarrow{c} \times \overrightarrow{a} = \overrightarrow{0}$$

B

$$\overrightarrow{a} \times \overrightarrow{b} = \overrightarrow{b} \times \overrightarrow{c} = \overrightarrow{c} \times \overrightarrow{a} \neq \overrightarrow{0}$$

C

$$\overrightarrow{a} \times \overrightarrow{b} = \overrightarrow{b} \times \overrightarrow{c} = \overrightarrow{a} \times \overrightarrow{c} \neq \overrightarrow{0}$$

D

$$\overrightarrow{a} \times \overrightarrow{b}, \overrightarrow{b} \times \overrightarrow{c}, \overrightarrow{c} \times \overrightarrow{a}$$ are mutually perpendicular

View Solution

JEE Advanced 2007 Paper-2 - Question 51

Report

Let ABCD be a quadrilateral with area 18, with side AB parallel to the side CD and AB =2CD. Let AD be perpendicular to AB and CD. If a circle is drawn inside the quadrilateral ABCD touchingall the sides, then its radius is

A

3

B

2

C

$$\frac{3}{2}$$

D

1

View Solution

JEE Advanced 2007 Paper-2 - Question 52

Report

Lat $$f(x) = \frac{x}{\left(1 + x^n\right)^{\frac{1}{n}}}$$ for $$n \geq 2$$ and $$g(x) = \underbrace{(f\circ f \circ ... \circ f)(x)}_{f occurs n times}$$. Then $$\int x^{n-2}g(x)dx$$ equals

A

$$\frac{1}{n(n-1)}\left(1 + nx^n\right)^{1-\frac{1}{n}}+K$$

B

$$\frac{1}{n-1}\left(1 + nx^n\right)^{1-\frac{1}{n}}+K$$

C

$$\frac{1}{n(n+1)}\left(1 + nx^n\right)^{1+\frac{1}{n}}+K$$

D

$$\frac{1}{n+1}\left(1 + nx^n\right)^{1+\frac{1}{n}}+K$$

View Solution

JEE Advanced 2007 Paper-2 - Question 53

Report

The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN is

A

360

B

192

C

96

D

48

View Solution

JEE Advanced 2007 Paper-2 - Question 54

Report

Consider the planes $$3x - 6y - 2z = 15$$ and $$2x + y - 2z = 5$$.
STATEMENT-1: The parametric equations of the line of intersection of the given planes are $$x = 3 + 14t, y = 1 + 2t, z = 15t.
because
STATEMENT-2: The vector $$14\hat{i} + 2 \hat{j} + 15 \hat{k}$$ is parallel to the line ofintersection of given planes.

A

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

B

Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

C

Statement-1 is True, Statement-2 is False

D

Statement-1 is False, Statement-2 is True

View Solution

JEE Advanced 2007 Paper-2 - Question 55

Report

STATEMENT-1: The curve $$y = \frac{-x^2}{2} + x + 1$$ is symmetric with respect to the line x = 1.
because
STATEMENT-2: A parabola is symmetric aboutits axis.

A

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

B

Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

C

Statement-1 is True, Statement-2 is False

D

Statement-1 is False, Statement-2 is True

View Solution

JEE Advanced 2007 Paper-2 - Question 56

Report

Let $$f(x) = 2 + \cos x$$ for all real x.
STATEMENT-1: For each real t, there exists a point c in $$[t, t + \pi]$$ such that $$f'(c) = 0.$$
because
STATEMENT-2: $$f(t) = f(t + 2\pi)$$ for each real t.

A

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

B

Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

C

Statement-1 is True, Statement-2 is False

D

Statement-1 is False, Statement-2 is True

View Solution

JEE Advanced 2007 Paper-2 - Question 57

Report

Lines $$L_1 : y - x = 0$$ and $$L_2 : 2x + y = 0$$ intersect the line $$L_3 : y + 2 = 0$$ at P and Q, respectively. The bisector of the acute angle between $$L_1$$ and $$L_2$$ intersects $$L_3$$ at R.
STATEMENT-1: The ratio PR : RQ equals $$2\sqrt{2} : \sqrt{5}.$$
because
STATEMENT-2: In any triangle, bisector of an angle divides the triangle into two similar triangles.

A

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

B

Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

C

Statement-1 is True, Statement-2 is False

D

Statement-1 is False, Statement-2 is True

View Solution

JEE Advanced 2007 Paper-2 - Question 58

Report

Which one of the folowing statements is correct?

A

$$G_1 > G_2 > G_3 > ....$$

B

$$G_1 < G_2 < G_3 < ....$$

C

$$G_1 = G_2 = G_3 = ....$$

D

$$G_1 < G_3 < G_5 < ....$$ and $$G_2 > G_4 > G_6 > ....$$

View Solution

JEE Advanced 2007 Paper-2 - Question 59

Report

Which one of the following statements is correct?

A

$$A_1 > A_2 > A_3 > ...$$

B

$$A_1 < A_2 < A_3 < ...$$

C

$$A_1 > A_3 > A_5 > ...$$ and $$A_2 < A_4 < A_6 < ...$$

D

$$A_1 < A_3 < A_5 < ...$$ and $$A_2 > A_4 > A_6 > ...$$

View Solution

JEE Advanced 2007 Paper-2 - Question 60

Report

Which one of the following statements is correct?

A

$$H_1 > H_2 > H_3 > ...$$

B

$$H_1 < H_2 < H_3 < ...$$

C

$$H_1 > H_3 > H_5 > ...$$ and $$H_2 < H_4 < H_6 < ...$$

D

$$H_1 < H_3 < H_5 > ...$$ and $$H_2 > H_4 > H_6 > ...$$

View Solution

JEE Advanced 2007 Paper-2 - Question 61

Report

The line y = x meets $$y = ke^x$$ for $$k \leq 0$$ at

A

no point

B

one point

C

two points

D

more than two points

View Solution

JEE Advanced 2007 Paper-2 - Question 62

Report

The positive value of k for which $$ke^x - x = 0$$ has only one root is

A

$$\frac{1}{e}$$

B

1

C

e

D

$$\log_e{2}$$

View Solution

JEE Advanced 2007 Paper-2 - Question 63

Report

For $$k > O$$, the set of all values of k for which $$ke^x - x = 0$$ has two distinct roots is

A

$$\left(0, \frac{1}{e}\right)$$

B

$$\left(\frac{1}{e}, 1\right)$$

C

$$\left(\frac{1}{e}, \infty\right)$$

D

$$\left(0, 1\right)$$

View Solution

JEE Advanced 2007 Paper-2 - Question 64

Report

Let $$f(x) = \frac{x^2 - 6x + 5}{x^2 - 5x + 6}$$.
Match the expressions/statements in Column I with expressions/statements in Column II and indicate your answer by darkening the appropriate bubbles in the $$4 \times 4$$ matrix given in the ORS.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

JEE Advanced 2007 Paper-2 - Question 65

Report

Let (x, y) be such that $$\sin^{-1}(ax) + \cos^{-1}(y) + \cos^{-1}(bxy) = \frac{\pi}{2}.$$
Match the statements in Column I with statements in Column II and indicate your answer by darkening the appropriate bubbles in the $$4 \times 4$$ matrix given in the ORS.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

JEE Advanced 2007 Paper-2 - Question 66

Report

Match the statements in Column I with the properties in Column II and indicate your answer by darkening the appropriate bubbles in the $$4 \times 4$$ matrix given in the ORS.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution