XII-Prayaas MainsPaper-1 PT-2 Marks : 300

JEE MAINS

LakshyaSUBJECT : Physics, Chemistry, Mathematics

XII-Prayaas Mains Paper-1 PT-2 Time (mm:ss) : 180:00

Physics Section_I (Single Type Answer) 80

1. Two point charges -q and +q are located at points (0, 0, -a) and (0, 0, a) respectively.What is the electric potential at point (0, 0, z)?

4

(a)

(b)

(c)

(d)

Ans :3Exp :

2. Two concentric spheres or radii r1 and r2 carry charges q1 and q2 respectively.If the surface charge density is the same for both sphere,the electric potential at the common centre will be

4

(a)

(b)

(c)

(d)

Ans :4Exp :Given

and

3. A particle carrying a charge q is shot with a speed v towards a fixed particle carrying a charge Q.It approaches Q up to a certain distance r and then returns as shown in figure.

If charge q were moving with a speed 2v, the distance of the closest approach would be

4

(a) r(b) 2r

(c)

(d)

Ans :4Exp :K.E. = P.E.

i.e.,

4. Two point charges and are placed at points A and B 6 cm apart as shown in figure.A third charge is moved from C to D along the arc of a circle of radius 8 cm as shown.The change in the potential energy of the system is

4

(a) 3.0 J(b) 3.6 J(c) 5.0 J(d) 7.2 JAns :2Exp :

5. Four charges, each equal to -Q, are placed at the corners of a square and a charge +q is placed at its centre.If the system is in equilibrium, the value of q is

4

(a)

(b)

(c)

(d)

Ans :2Exp :The system is in equilibrium means the force experienced by each charge is ‘0'.

It is clear that charge placed at centre would be in equilibrium for any value of ‘q',so we consider the equilibrium of charge placed at any corner.

6. A charge having magnitude Q is divided into two parts q and (Q - q) which are held a certain distance r apart.The force of repulsion between the two parts will be maximum if the ratio q/Q is

4

(a)

(b)

(c)

(d)

Ans :1Exp :

7. Three capacitors, each of capacitance C are connected to a battery of voltage V. When key K is closed,the charge which will flow through the battery is (see figure).

4

(a) 2CV(b) CV

(c)

(d)

Ans :4Exp :Initially

Charge flows through battery is

Now when key is closed,

Q = CVSo the charge will flow through the battery is

8. In the circuit shown in figure, when the steady state is reached,the energy stored in C1 is E1 and that stored in C2 is E2. The ratio E2/E1 is

4

(a) 1.5(b) 1.25(c) 0.75(d) 0.5Ans :1Exp :Under steady state the current flows through ADBC

Applying Kirchhoff's law ABDA

9. A parallel plate capacitor of plate area A has a charge Q. The force on each plate of the capacitor is 4

(a)

(b)

(c)

(d) ZeroAns :3Exp :For an isolated charged

Capacitor

10. The capacitance of a parallel plate capacitor is . When a glass slab of thickness equal to theseparation between the plates is introduced between the plates, the potential differencereduces to 1/8 of the original value. The dielectric constant of glass is

4

(a) 1.6(b) 5(c) 8(d) 40Ans :3Exp :In this case capacity changes to

ChargePotential of the capacitor

11. Four metal plates numbered 1, 2, 3 and 4 are arranged as shown in figure.The area of each plate is A and separation between the plates is d.The capacitance of the arrangement is

4

(a)

(b)

(c)

(d)

Ans :2Exp :

12. The introduction of a metal plate between the plates of a parallel plate capacitor increasesits capacitance by 4.5 times. If d is the separation of the two plates of the capacitor,the thickness of the metal plate introduced is

4

(a)

(b)

(c)

(d) dAns :3Exp : for metal slab

Given

13. A parallel plate capacitor of plate area A and plate separation d is charged by a battery of voltage V.The battery is then disconnected. The work needed to pull the plates to a separation 2d is

4

(a)

(b)

(c)

(d)

Ans :3Exp :

14. In the circuit shown in figure, the current through the 4

(a)

(b)

(c)

(d)

Ans :2Exp :Total current in circuit

Now equivalent diagram

15. In the circuit shown in figure, if a wire of negligible resistance is connected between P and Q, a current of 4

(a) A flows from P to Q.

(b) A flows from Q to P.

(c) A flows from P to Q.

(d) A flows from Q to P.

Ans :1Exp :

Applying loop law for APQAand

And along APB and battery

from P to Q

16. In the circuit shown in figure. The reading of ammeter is 4

(a) 1A(b) 2A(c) 3A(d) None of theseAns :1Exp :Total current flowing from battery

Equivalent diagram

and

17. Figure shows a network of eight resistors numbered 1 to 8, each equal to ,connected to a 3V battery of negligible internal resistance.The current I in the circuit is :

4

(a) 0.25 A(b) 0.5 A(c) 0.75 A(d) 1.0 AAns :4

Exp :

18. A uniform wire of resistance is bent into the form of a circle of radius r.A specimen of the same wire is connected along the diameter of the circle.What is the equivalent resistance across the ends of this wire?

4

(a)

(b)

(c)

(d)

Ans :1Exp :For

Length of specimen 2r, i.e

are

In parallel

19. If a wire is stretched to make it 0.1 times longer, its resistance will 4(a) increase by 0.05(b) increase by 0.2(c) decrease by 0.2(d) remain unchangedAns :2Exp :

20. A galvanometer together with an unknown resistance in series is connected across two identical batteries eachof 1.5 V.When the batteries are connected in series, the galvanometer records a current of 1A,and when the batteries are in parallel, the current is 0.6 A. What is the internal resistance of the battery?

4

(a)

(b)

(c)

(d)

Ans :4Exp :In series

------- (1)

In parallel

----- (2)

Solving

Physics Section_II (Integer Type Answer) 20

1. Two small identical balls P and Q, each of mass gram, carry identical charges and are suspended bythreads of equal lengths.At equilibrium, they position themselves as shown in figure. Charge on each ball is 10-x. Find x. Given

and take g = 10 ms-2.

4

Ans :7Exp :

Under equilibrium

2. Two point charges and are placed at distances b = 1 cm and a = 2 cmfrom the origin on the y and x axes as shown in figure. The electric field vector at pointP(a, b) will subtend an angle with the x-axis. Find tan .

4

Ans :2Exp :

3. A capacitor of capacitance C is fully charged by a 200 V supply. It is then discharged through a smallcoil of resistance wire embedded in a thermally insulated block of specific heat

and of mass 0.1 kg. If the temperature of the blockrises by 0.4 K, what is the value of C

4

Ans :500Exp :

4. Four capacitors are connected as shown in figure. The effective capacitance between points A and B will be 4

Ans :5Exp :Equivalent circuit

5. A wire of resistance 0. /cm is bent to form a square ABCD of side 10 cm.A similar wire is connected between corners B and D to form the diagonal BD.The effective resistance of this combination between corners A and C is

4

Ans :1Exp :

Here r =

Chemistry Section_I (Single Type Answer) 80

1. Give the major product of the following reaction: 4

(a)

(b)

(c)

(d)

Ans :4Exp :

2. What is the product of the reaction sequence shown? 4

(a)(b)(c)(d)Ans :1Exp :

3.

Product (B) is:

4

(a) Diastereomer(b) Meso(c) Racemic(d) Geometrical isomerAns :2Exp :

4. Which of the following is most reactive toward the acid-catalyst dehydration? 4

(a)

(b)

(c)

(d)

Ans :3Exp :Stability of carbocation decides the reactivity towards dehydration.

Resonance stabilized carbocation.

5. Which is the product of the following reaction? 4

(a)

(b)

(c)

(d)

Ans :2Exp :

Reaction takes place from O and therefore there is retention of configuration.

6.

Product (B) is;

4

(a)

(b)

(c)

(d)

Ans :2Exp :

7.

Product (A) is:

4

(a)

(b)

(c)

(d)

Ans :1Exp :

8. Compare the reactivities, towards hydrolysis: 4

(a) 1-a, 2-c(b) 1-b, 2-c(c) 1-b, 2-d(d) 1-a, 2-dAns :3Exp :In (1), attack favourable on in (b).

In (2), attack favourable due to stability of carbocation of the right fragment of ether in (d).

9.

Product of above reaction is:

4

(a)

(b)

(c)

(d)

Ans :2Exp :

10.Product of above reaction is:

4

(a)

(b)(c)(d)Ans :1Exp :

11. The compound :

can form a hemiacetal by reacting with itself in solution. What is the structure of this hemiacetal?

4

(a) i(b) ii(c) iii(d) ivAns :2Exp :

12. What is the correct structure for the major compound produced by the following reaction sequence? 4

(a)

(b)

(c)

(d)

Ans :2Exp :Reaction involves rearrangement of carbocation.

13. In the following hydrolysis reaction, the major final product is 4

(a)

(b)

(c)

(d)

Ans :1

Exp :

On protonated epoxide, nucleophilic attack occur at -carbon.Where more stable carbocation could be formed.

14. Identify the end product B of the following sequence of reactions. 4

(a)

(b)

(c)

(d)

Ans :4Exp :

15. The major product formed in the following reaction is 4

(a)

(b)

(c)

(d)

Ans :4Exp :It is an example of intramolecular Cannizaro reaction.

16. Which of the following pairs is expected to exhibit same colour in solution? 4(a) VOCl2; FeCl2(b) CuCl2; VOCl2(c) MnCl2; FeCl2(d) FeCl2; CuCl2Ans :2Exp :In CuCl2, Cu2+ has d9 configuration, exhibit d-d transition and show colour. Similarly, in VOCl2, V4+ has d1

configuration, can exhibit d-d transition and show colour.

17.

Here X, Y and Z are

4

(a) X = K2MnO4, Y = MnO2, Z = KMnO4(b) X = K2MnO4, Y = MnO4, Z = KMnO4(c) X = MnO2, Y = K2MnO4, Z = KMnO4(d) X = MnO2, Y = KMnO4, Z = K2MnO4Ans :3Exp :

18. Which statement given below is correct regarding dichromate ion? 4(a) In the reaction between and H2O2, oxidizing agent is H2O2(b) A strong acid changes the ion to the ion(c) In an acidic medium, the ion behaves as reducing agent

(d)In the reaction between and H2O2, the solution colour changes from orange of dichromate ionthrough green to the blue of the Cr3+ ion

Ans :2

Exp :

19. Arrange the transition metals Ti, Ni, Mn and La in order of increasing atomic radii. 4(a)(b)(c)(d)Ans :4Exp :

20. Which of the following is amphoteric oxide among Mn2O7, CrO3, Cr2O3, CrO, V2O5, V2O4? 4(a) Cr2O3 and V2O5(b) Mn2O7 and CrO3(c) CrO and V2O5(d) V2O5 and CrO3Ans :1Exp :Mn2O7 = acidic, CrO3 = acidic, Cr2O3 = amphoteric, CrO = basic, V2O5 = amphoteric, V2O4 = amphoteric

oxides.

Chemistry Section_II (Integer Type Answer) 20

1.

Sum of -hydrogen in (A + B + C = ?)

4

Ans :19

Exp :

2. How many hydrogen is replaced by deuterium? 4

Ans :3Exp :

3. Find out number of alcohols that can give positive iodoform test. 4

Ans :4

Exp :

4. If all the ketone isomers of C6H12O are reduced independently with NaBH4, how many of them will produceracemic mixture of alcohols?

4

Ans :5Exp :

All the above shown ketones on reduction with NaBH4 will produce racemic mixtures of alcohols. The isomerbelow already has a chiral carbon, show enantiomerism. A pure enantiomer of this ketone, on reduction withNaBH4, will produce pair of diastereomers.

5. The sum of oxidation states of Cr in and is ………………. . 4Ans :9Exp :

has butterfly structure

Sum of O.S of Cr = (+6) + (+3) = 9

Mathematics Section_I (Single Type Answer) 80

1. The curve y - exy + x = 0 has a vertical tangent at : 4(a) (1,1)(b) (0,1)(c) (1,0)(d) no pointAns :3

Exp :y - exy + x = 0

for the vertical tangents

2. 4

(a)(b)(c)(d)Ans :1Exp :

3. 4

(a)

(b)

(c)

(d)

Ans :4

Exp :we know that

4. 4

(a)

(b)

(c)

(d)

Ans :3Exp :x = ey+x

log x = y + xy = log x - x

5. The circumference of a circle is measured as 56 cm with an error 0.02 cm.The percentage error in its area is

4

(a)

(b)

(c)

(d)

Ans :3Exp :Let A,c,r be the area, circumference and radius of the circle

6. OB and OC are two roads enclosing an angle of 1200. X and Ystart from ‘O' at the same time. X travels along OB with a speedof 4 km/h and Y travels along OC with a speed of 3 km/h. The rateat which the shortest distance between X and Y is increasing after 1 h is

4

(a)

(b) 37 km/h(c) 13 km/h(d)Ans :1Exp :

After 1 hour , x = 4km, y = 3kmBy cosine rule z2 = x2 + y2 - 2xy cos 1200

Diff w.r.t ‘t'

7. 4

(a) (2a, 0)

(b)

(c)

(d)

Ans :4Exp :

8. 4(a) one maxima value(b) one minima value(c) no extreme value(d) one maxima and one minima valueAns :3

Exp :For f(x) to be min or max, f1(x) = 0

Hence f(x) has no extreme value

9. The shortest distance between the line y - x = 1 and the curve x = y2 is 4

(a)

(b)

(c)

(d)

Ans :1Exp :Slope of y - x = 1 is 1

y2 = xDiff w.r.t x

PA = The distance from P to x - y + 1 = 0

10. Angle between y2 = x and x2 = y at the origin is 4

(a)

(b)

(c)

(d)

Ans :3Exp :Tangent of y2 = x at origin is y - axis

Tangent of x2 = y at origin is x - axisAngle b/w two parabolas atOrigin = angle b/w x - axis and y- axis

11. If is the semi-vertical angle of a cone of maximum volume with givenslant height, then tan is given by

4

(a) 2(b) 1(c)(d)

Ans :3Exp :

12. 4

(a)

(b)

(c)

(d)

Ans :4Exp :

13. 4(a)(b)

(c)

(d)Ans :4

Exp :f(x) = x3 + px2 + qx + rf1(x) = 3x2 + 2px + q

14. 4(a) f(x) = x(b) f(x) = x2(c) f(x) = 2x3 + 3(d)Ans :2Exp :f(x) = x2 is continuous and differentiable on R

f(-1) = f(1) = 1f1(x) = 2x

15. The slope of the tangent to the curves x = t2 + 3t - 8, y = 2t2 - 2t - 5at the point (2, -1) is

4

(a)

(b)

(c) -6(d) -7Ans :2Exp :

16. 4

(a) nenx

(b) ne-nx(c) 1(d) -ne-nxAns :4

Exp :y = enx

17. The point (0, 5) is closest to the curve at 4(a)(b) (2, 2)(c)(d)Ans :4Exp :

Let be a point on and A be (0, 5)

If AP = d

At t = 0, is – ive

At t = is + ive

Hence, the closest point is

18. The function increases, if 4

(a)

(b)

(c)

(d)

Ans :2

Exp :

For

Now,

f(x) is increasing in

19. The function f (x) = is 4

(a) Increasing on(b) Decreasing on(c) Increasing on and decreasing on(d) Decreasing on and increasing onAns :2Exp :Since,

forHence, f(x) is decreasing function for

20. If , then the equation will have 4(a) no real solution(b) at least one real root in (-1,0)(c) at least one real root in (0,1)(d) None of theseAns :2Exp :at least one real root in (-1,0).

Mathematics Section_II (Integer Type Answer) 20

1. If the greatest and least values of the function on [0, 2] are then the valueof must be

4

Ans :626

Exp :Given

= 3 (x - 1) (x - 3)For maxima or minima

Only one critical point in [0, 2] is x = 1.Greatest value = max {f (0), f (1), f (2)}

= max {1, 5, 3}= 5and least = min {f (0), f (1), f (2)}= min {1, 5, 3} = 1

2. Let the tangents drawn to the circle, x2 + y2 = 16 from the point P (o, h) meet the X-axis at point A and B. If

the area of ΔAPB is minimum, then is equal to:

4

Ans :4Exp :4

3. If & f(0) = 1. Then f(1) can't be 4Ans :2Exp :

4. If (x) is larger of and (1 + x) ln (1 + x) for then the value of 502 ln mustbe

4

Ans :2008Exp :Let

g(x) is increasing function

Then,f(x) is increasing function

Then 502 ln

5. If has extreme value at (2, -1), then the value of 5050 (a + 10b) must be 4

Ans :5050

Exp : .......(i)

.......(ii)

Since (2, -1) will lie on the function (i)

2a + b = 2......(iii)

Also,

From eq. (iii), a = 1Hence, 5050 (a + 10b) = 5050 (1 + 0) = 5050

All The Best