JEE Advanced 2007 · 08 Apr 2007 · Paper 1

Q1.A resistance of $2\Omega$ is connected across one gap of a metre-bridge (the length of the wire is 100 cm) and an unknown resistance, greater than $2\Omega$, is connected across the other gap. When these resistances are interchanged, the balance point shifts by 20 cm. Negle …

Q2.In an experiment to determine the focal length $(f)$ of a concave mirror by the $u-v$ method, a student places the object pin A on the principal axis at a distance $x$ from the pole P. The student looks at the pin and its inverted image from a distance keeping his/her eye i …

Q4.A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral.
(A) A potential difference appears between the two cylinders when a charge density is given to the inner c …

Q5.Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then,

Q6.A circuit is connected as shown in the figure with the switch S open. When the switch is closed, the total amount of charge that flows from Y to X is

Q7.A ray of light traveling in water is incident on its surface open to air. The angle of incidence is $\theta$, which is less than the critical angle. Then there will be

Q8.In the options given below, let $E$ denote the rest mass energy of a nucleus and $n$ a neutron. The correct option is

Q9.The largest wavelength in the ultraviolet region of the hydrogen spectrum is 122 nm. The smallest wavelength in the infrared region of the hydrogen spectrum (to the nearest integer) is

Q10.STATEMENT-1
A block of mass $m$ starts moving on a rough horizontal surface with a velocity $v$. It stops due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle of 30° with the horizontal and the same b …

Q11.STATEMENT-1
In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision.
because
STATEMENT-2
In an elastic collision, the linear momentum of the system is conserved.

Q12.STATEMENT-1
The formula connecting $u,v$ and $f$ for a spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvature.
because
STATEMENT-2
Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfac …

Q13.STATEMENT-1
If the accelerating potential in an X-ray tube is increased, the wavelengths of the characteristic X-rays do not change.
because
STATEMENT-2
When an electron beam strikes the target in an X-ray tube, part of the kinetic energy is converted into X-ray energy.

Q14.Two discs A and B are mounted coaxially on a vertical axle. The discs have moments of inertia $I$ and $2I$ respectively about the common axis. Disc A is imparted an initial angular velocity $2\omega$ using the entire potential energy of a spring compressed by a distance …

Q15.Two discs A and B are mounted coaxially on a vertical axle. The discs have moments of inertia $I$ and $2I$ respectively about the common axis. Disc A is imparted an initial angular velocity $2\omega$ using the entire potential energy of a spring compressed by a distance …

Q16.Two discs A and B are mounted coaxially on a vertical axle. The discs have moments of inertia $I$ and $2I$ respectively about the common axis. Disc A is imparted an initial angular velocity $2\omega$ using the entire potential energy of a spring compressed by a distance …

Q20.Some physical quantities are given in Column I and some possible SI units in which these quantities may be expressed are given in Column II. Match the physical quantities in Column I with the units in Column II and indicate your answer by darkening appropriate bubbles in the 4 × …

Q21.Column I gives certain situations in which a straight metallic wire of resistance $R$ is used and Column II gives some resulting effects. Match the statements in Column I with the statements in Column II and indicate your answer by darkening appropriate bubbles in the 4 × 4 mat …

Q22.Some laws / processes are given in Column I. Match these with the physical phenomena given in Column II and indicate your answer by darkening appropriate bubbles in the 4 × 4 matrix given in the ORS.
| (A) Transition between two atomic ener …

Q20.Match the complexes in Column I with their properties listed in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 × 4 matrix given in the ORS.
| (A) …

Q21.Match the chemical substances in Column I with type of polymers/type of bonds in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 × 4 matrix given in the ORS.
| (B) nylon- …

Q22.Match gases under specified conditions listed in Column I with their properties/laws in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 × 4 matrix given in the ORS.
| (A) hydrogen gas (P=200 atm, T=273 K) | (p) …

Q1.Let $\alpha ,\beta$ be the roots of the equation $x^2-px+r=0$ and $\frac{\alpha }{2},2\beta$ be the roots of the equation $x^2-qx+r=0$. Then the value of $r$ is

Q2.Let $f(x)$ be differentiable on the interval $(0,\infty )$ such that $f(1)=1$, and

for each $x>0$. Then $f(x)$ is

Q3.One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is

Q4.The tangent to the curve $y=e^x$ drawn at the point $(c,e^c)$ intersects the line joining the points $(c-1,e^{c-1})$ and $(c+1,e^{c+1})$

Q5.${\lim }_{x\to \frac{\pi }{4}}\frac{{\int }_2^{{\sec }^{2}x}f(t)dt}{x^2-\frac{{\pi }^2}{16}}$ equals

Q6.A hyperbola, having the transverse axis of length $2\sin \theta$, is confocal with the ellipse $3x^2+4y^2=12$. Then its equation is

Q7.The number of distinct real values of $\lambda$, for which the vectors $-{\lambda }^2\hat{i}+\hat{j}+\hat{k}$, $\hat{i}-{\lambda }^2\hat{j}+\hat{k}$ and $\hat{i}+\hat{j}-{\lambda }^2\hat{k}$ are coplanar, is

Q8.A man walks a distance of 3 units from the origin towards the north-east $(N45^{\circ }E)$ direction. From there, he walks a distance of 4 units towards the north-west $(N45^{\circ }W)$ direction to reach a point $P$. Then the position of $P$ in the Argand plane is

Q9.The number of solutions of the pair of equations

in the interval $[0,2\pi ]$ is

Q10.Let $H_1,H_2,\cdots ,H_n$ be mutually exclusive and exhaustive events with $P(H_i)>0$, $i=1,2,\dots ,n$. Let $E$ be any other event with $0<P(E)<1$.

STATEMENT-1 : $P(H_i\mid E)>P(E\mid H_i)\cdot P(H_i)$ for $i=1,2,\dots ,n$.

because

STATEME …

Q11.Tangents are drawn from the point $(17,7)$ to the circle $x^2+y^2=169$.

STATEMENT-1 : The tangents are mutually perpendicular.

because

STATEMENT-2 : The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is …

Q12.Let the vectors $\overrightarrow{PQ},\overrightarrow{QR},\overrightarrow{RS},\overrightarrow{ST},\overrightarrow{TU}$ and $\overrightarrow{UP}$ represent the sides of a regular hexagon.

STATEMENT-1 : …

Q13.Let $F(x)$ be an indefinite integral of ${\sin }^{2}x$.

STATEMENT-1 : The function $F(x)$ satisfies $F(x+\pi )=F(x)$ for all real $x$.

because

STATEMENT-2 : ${\sin }^2(x+\pi )={\sin }^{2}x$ for all real $x$.

Q14.Let $V_r$ denote the sum of the first $r$ terms of an arithmetic progression (A.P.) whose first term is $r$ and the common difference is $(2r-1)$. Let


The sum …

Q15.Let $V_r$ denote the sum of the first $r$ terms of an arithmetic progression (A.P.) whose first term is $r$ and the common difference is $(2r-1)$. Let


$T_r$ is always

Q16.Let $V_r$ denote the sum of the first $r$ terms of an arithmetic progression (A.P.) whose first term is $r$ and the common difference is $(2r-1)$. Let


Which one of the following …

Q17.Consider the circle $x^2+y^2=9$ and the parabola $y^2=8x$. They intersect at $P$ and $Q$ in the first and the fourth quadrants, respectively. Tangents to the circle at $P$ and $Q$ intersect the $x$-axis at $R$ and tangents to the parabola at $P$ and $Q$ …

Q18.Consider the circle $x^2+y^2=9$ and the parabola $y^2=8x$. They intersect at $P$ and $Q$ in the first and the fourth quadrants, respectively. Tangents to the circle at $P$ and $Q$ intersect the $x$-axis at $R$ and tangents to the parabola at $P$ and $Q$ …

Q19.Consider the circle $x^2+y^2=9$ and the parabola $y^2=8x$. They intersect at $P$ and $Q$ in the first and the fourth quadrants, respectively. Tangents to the circle at $P$ and $Q$ intersect the $x$-axis at $R$ and tangents to the parabola at $P$ and $Q$ …

Q20.Consider the following linear equations

Match the conditions/expressions in Column I with statements in Column II and indicate your answer by darkening the appropriate bubbles in the 4 × 4 m …

Q21.In the following $[x]$ denotes the greatest integer less than or equal to $x$.
Match the functions in Column I with the properties in Column II and indicate your answer by darkening the appropriate bubbles in the 4 × 4 matrix given in the ORS.
| Column I | Column II || --- …

Q22.Match the integrals in Column I with the values in Column II and indicate your answer by darkening the appropriate bubbles in the 4 × 4 matrix given in the ORS.
| (A) ${\int }_{-1}^1\frac{dx}{1+x^2}$ | (p) …