1. C

2. A

3. B

## Tuesday, October 23, 2007

## Monday, October 22, 2007

### Questions for 22-10-2007

1.

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

2. 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 column is close to the wavelength of sound in air

(D) in one of the two resonances observed, the length of the resonating air column is close to half the wavelength of sound in air

3. If a, b, c be unit vectors such that a + b + c = 0. Which one of the following is correct?

(A) a × b = b × c = c × a = 0

(B) a × b = b × c = c × a is not equal to 0

(C) a × b = b × c = a × c is not equal to 0

(D) a × b, b × c, c × a are mutually perpendicular

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

2. 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 column is close to the wavelength of sound in air

(D) in one of the two resonances observed, the length of the resonating air column is close to half the wavelength of sound in air

3. If a, b, c be unit vectors such that a + b + c = 0. Which one of the following is correct?

(A) a × b = b × c = c × a = 0

(B) a × b = b × c = c × a is not equal to 0

(C) a × b = b × c = a × c is not equal to 0

(D) a × b, b × c, c × a are mutually perpendicular

## Saturday, October 20, 2007

### Questions for 21-10-2007

1. A student performs an experiment to determine the Young’s modulus of a wire, exactly 2m 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 ± 0.05 mm at a load of exactly 1.0 kg. The student also measures the diameter of the wire to be 0.4 mm with an uncertainty of ± 0.01 mm. Take g = 9.8 m/s^2 (exact). The Young’s modulus obtained from the reading is

(A) (2.0 ± 0.3)*10^11 N/m^2

(B) (2.0 ± 0.2)*10^11 N/m^2

(C) (2.0 ± 0.1)*10^11 N/m^2

(D) (2.0 ± 0.05)*10^11 N/m^2

2.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

IIT.JEE 2007 SOLUTIONS.MATHEMATICS

3. 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

(A) (2.0 ± 0.3)*10^11 N/m^2

(B) (2.0 ± 0.2)*10^11 N/m^2

(C) (2.0 ± 0.1)*10^11 N/m^2

(D) (2.0 ± 0.05)*10^11 N/m^2

2.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

IIT.JEE 2007 SOLUTIONS.MATHEMATICS

3. 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

## Friday, October 19, 2007

### Questions for 20-10-2007

**1.**

**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 beams strikes the target in an X-ray tube, part of the kinetic energy is converted into X-ray energy.

(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

**2.**

When 20 g of naphthoic acid (C-11 H-8 O-2) is dissolved in 50 g of benzene [K(f) = 1.72 K kg mol^ -1], a freezing point depression of 2 K is observed. The van’t Hoff factor (i) is

(A) 0.5

(B) 1

(C) 2

(D) 3

**3.**

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 x^2 + y^2 = 338.

(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

## Thursday, October 18, 2007

### Questions for 19-10-2007

**1.**

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 surface after moving through a certain distance. The surface is

now tilted to an angle 30° with the horizontal and the same block is made to go up on the surface

with the same initial velocity v. The decrease in the mechanical energy in the second situation is

smaller than that in the first situation.

Because

Statement - 2

The coefficient of friction between the block and the surface decreases with the increase in the

angle of inclination.

(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

**2.**

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.

**3.**

The differential equation dy/dx = [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

## Wednesday, October 17, 2007

### Questions for 18-10-2007

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

Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces

(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

2.

Boron always forms covalent bond

Because

The small size of B^3+favours formation of covalent bond.

(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

3. Let F(x) be an indefinite integral of sin^2 x.

The function F(x) satisfies F(x +Pi) = F(x) for all real x.

Because

sin^2 (x+ Pi) = sin^2 x for all real x.

(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

**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 surfaces

(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

2.

**Statement - 1**Boron always forms covalent bond

Because

**Statement - 2**The small size of B^3+favours formation of covalent bond.

(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

3. 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.

(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

## Tuesday, October 16, 2007

### Q's for the day 17-10-2007

1. The size of the image of an object, which is at infinity, as formed by a convex lens of focal length 30 cm is 2 cm. If a concave lens of focal length 20 cm is placed between the convex lens and the image at a distance of 26 cm from the convex lens, calculate the new size of the image.

(A) 1.25 cm (B) 2.5 cm

(C) 1.05 cm (D) 2 cm

2. Among the following, the molecule with the highest dipole moment is:

(A) CH-3Cl (B) CH-2Cl-2

(C) CHCl-3 (D) CCl-4

3. The number of integral points (integral point means both the coordinates should be integer) exactly in the interior of the triangle with vertices (0, 0), (0, 21) and (21, 0), is

(A) 133 (B) 190

(C) 233 (D) 105

(A) 1.25 cm (B) 2.5 cm

(C) 1.05 cm (D) 2 cm

2. Among the following, the molecule with the highest dipole moment is:

(A) CH-3Cl (B) CH-2Cl-2

(C) CHCl-3 (D) CCl-4

3. The number of integral points (integral point means both the coordinates should be integer) exactly in the interior of the triangle with vertices (0, 0), (0, 21) and (21, 0), is

(A) 133 (B) 190

(C) 233 (D) 105

## Tuesday, October 2, 2007

### Questions for 2-10-2007

1. In an insulated vessel, 0.05 kg steam at 373 K and 0.45 kg of ice at 253 K are mixed. Then, find the final temperature of the mixture.

Given, L(fusion) = 80 cal/g = 336 J/g, L(vaporization) = 540 cal/g = 2268 J/g,

S(ice) = 2100 J/kg K = 0.5 cal/gK and S(water) = 4200 J/kg K = 1 cal /gK

2. If f″(x) = − f(x) and g(x) = f′(x) and F(x) = [f(x/2)]^2 + [g(x/2)]^2 and given that F(5) = 5 then F(10) is equal to

(A) 5

(B) 10

(C) 0

(D) 15

3. The edge length of unit cell of a metal having molecular weight 75 g/mol is 5

A^0 which crystallizes in cubic lattice. If the density is 2 g/cc then find the radius of metal atom. [N(A) = 6 × 10^23]. Give the answer in pm.

Given, L(fusion) = 80 cal/g = 336 J/g, L(vaporization) = 540 cal/g = 2268 J/g,

S(ice) = 2100 J/kg K = 0.5 cal/gK and S(water) = 4200 J/kg K = 1 cal /gK

2. If f″(x) = − f(x) and g(x) = f′(x) and F(x) = [f(x/2)]^2 + [g(x/2)]^2 and given that F(5) = 5 then F(10) is equal to

(A) 5

(B) 10

(C) 0

(D) 15

3. The edge length of unit cell of a metal having molecular weight 75 g/mol is 5

A^0 which crystallizes in cubic lattice. If the density is 2 g/cc then find the radius of metal atom. [N(A) = 6 × 10^23]. Give the answer in pm.

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