Model papers for class xii (science)

MODEL PAPER CLASS-XII
CLASS -XII Mathematics

Instructions
1. Questions 1 to 10 carry 1 mark each.
2. Questions 11 to 22 carry 4 marks each.
3. Questions 23 to 29 carry 6 marks each.

1. Differentiate the function with respect to x.

2. Find the value of

.

3. Let A be a non-singular square matrix of order 3 × 3. Then find
4. Find the unit vector in the direction of the vector

.

5. Evaluate :

6. If

, then write the value of k.

7. Find the unit vector in the direction of the vector

.

8. If the binary operation * on the set of integers Z , is defined by a * b = a + 3b2 , then find the value
of 2 * 4.

9. Evaluate :
10. Find the distance between the two planes: 2x + 3y + 4z = 4 and 4x + 6y + 8z = 12.

11. Prove that
12. Define a binary operation *on the set {0, 1, 2, 3, 4, 5} as

Show that zero is the identity for this operation and each element a ≠ 0 of the set is invertible with 6
− a being the inverse of a.
13. If

are such that

is perpendicular to

then

find the value of λ.
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14. Find the points on the line

at a distance of 5 units from the point P (1, 3, 3).

15. By using properties of determinants, show that:

16. Prove
17. If

show that

.

18. Write the value of the following integral:
19. Find the intervals in which the function f(x) = 2x3 − 15x2 + 36x + 1 is strictly increasing or
decreasing. Also find the points on which the tangents are parallel to the x-axis.

20. Integrate:

.

21. If x, y, z are nonzero real numbers, then find the inverse of matrix
22. In a hurdle race, a player has to cross 10 hurdles. The probability that he will clear each hurdle

is

. What is the probability that he will knock down fewer than 2 hurdles?

23. Find the distance of the point (−1, −5, −10) from the point of intersection of the
line

and the plane

.

24. Find the area bounded by the curve x2 = 4y and the line x = 4y – 2.
25. Form the differential equation corresponding to

where a and b are arbitrary

constants.
26. One kind of cake required 300g of flour and 15g of fat, another kind of cake requires 150g of
flour and 30g of fat. Find the maximum number of cakes which can be made from 7.5 kg of flour and
600g of fat, assuming that there is no shortage of the other ingredients used in making the cakes.
Make it as an L.P.P and solve it graphically.
27. Using matrices , solve the following system of equations:


2x – 3y + 5z = 11
3x + 2y – 4z = -5
x + y – 2z = -3
28. Find the equation of the plane passing through the point (−1, 3, 2) and perpendicular to each
of the planes x + 2y + 3z = 5 and 3x + 3y + z = 0.
29. An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers.
The probability of an accident involving a scooter, a car and a truck are 0.01, 0.03 and 0.15
respectively. One of the insured persons meets with an accident. What is the probability that he is a
scooter driver.


CLASS-XII Physics
Instructions:
1. Section-A Q. no. 1-8 carry 1 mark each.
2. Section-B Q. no. 9-18 carry 2 marks each.
3. Section-C Q. no. 19-27 carry 3 marks each.
4. Section-D Q. no. 28-30 carry 5 marks each.
Section-A
1. S1 and S2 are two hollow concentric spheres enclosing charges q and 2q respectively.

(i) What is the ratio of electric flux through S1 and S2?
(ii) How will the electric flux through sphere S1 change is a medium of dielectric constant 5 is
introduced in the sphere S1 in place of air ?
2. For the potentiometer circuit shown in the figure, points X and Y represent the two terminals of
an unknown emf E’. A student observed that when the jockey is moved from the end A to the end
B, deflection in galvanometer remains in same direction. What may be two possible faults?
3. Define 1mH Inductance.
4. Derive an expression for capacitance of a parallel plate capacitor.
5. How does the intensity of magnetization of paramagnetic sample vary withtemperature ?
6. A circular coil of N turn and radius R is kept normal to a magnetic field given by B=Bo cos wt.
State the rule which helps to detect the direction of induced current?
7. A bulb of resistor 10? connected to an Inductor of inductance L is in serieswith an a.c. source
marked 100v 50Hz. If phase angle between the voltage and current is π/4 radian. Calculate the
value of L.
8. An electron and a proton have same De broglie wavelength associated with them. How are their
Kinetic energies related to each other ?
SECTION-B
9. Two radioactive nuclei X & Y initially contain an equal number of atoms. Their half life is 1 hour
and 2 hour respectively. Calculate the ratio of their rates of disintegration after two hours.
10. A message signal of frequency 15 KHz. and peak voltage of 5 volts is used to modulation a
carrier of frequency 1 MHz . and peak voltage 20 volt .Determine the modulation index and the

side bands.
11. Two rectangular metal plates, each of area A are kept parallel to each other at a distance ‘d’
apart to form a parallel plate capacitor. If the area of each of the plates is doubled and their
distance of separation decreases to 1/2 of its initial value. Calculate the ratio of
their capacitance in the two cases?
12. Show that energy stored in a parallel plate capacitor is 1/2CV2.
13. A conductor of length ‘l’ connected to a d.c. source of potential V. If the length of
the conductor is tripled by streching it keeping ‘V’ constant. Explain how do the following factors
vary in the conductor?

(2 marks)

(1) Drift speed of electrons
(2) Resistance
(3) Resistivity
14. Distinguish between paramagnetic, diamagnetic and ferromagnetic material.
15. A particle of mass ‘m’ with charge ‘q’ moving with a uniform speed ? normal to a
uniform magnetic field B, describes a circular path of radius r. Describe an expression for the (i)
time period of revolution & (ii) Kinetic energy of the particle.
16. Draw a schematic arrangement of Geiger-Marsden experimental setup. How does it explain the
size of nucleus.
17. Calculate the maximum kinetic energy of α particle emitted during α-decay of
92U

238

→ 90Th234 + 2He4

M(92U238) = 238.05079U, M(90Th234) = 234.04363U, M(2He4) = 4.00260U
18. State the laws of Photoelectric effect. Explain it on the basis of Einstein equation.
SECTION-C
19. Explain with the help of a labeled diagram the underlying the principle and working of a step
down transformer.
20. The magnitude of magnetic field in a plane e.m. wave is given as BX = 0, BY = 2 x 10-7 sin(0.5 x
103 x + 1.5 x 1011t)T.
(a) Determine the wavelength and frequency of wave.
(b) Write an expression for the electric field.
21. The energy level of an element are given below. Which corresponds to emission of spectral
line of wavelength 482nm?

23. Why do we require modulation? Explain the AM with block diagram.

24. Define coefficient of mutual inductance of two coils. A secondary coil of n2turns is wound on a
long solenoid of area of cross section A having a primary coil of n1 turns per unit length. What is
the mutual inductance of the two coils ?
25. Find the value of unknown resistance X in the following circuit, if no current flows through the
section AO. Also calculate the current drawn by the circuit from the battery of emf CV.
26. The following data was obtained for the dependence of the magnitude of electric field with
distance, from a reference point o, within the charge distribution in shaded region.
(I) Identify the charge distribution
(II) Identify the location points A B C and A1 B1 C1
27. A short bar magnet which is placed with its axis at 30o experiences a torque of 0.016Nm in an
external field of 800G.
(i) Determine the magnetic moment of magnet.
(ii) What is work done by an external force is moving it from its most stable to most unstable
position.
SECTION-D
28. (a) Derive an expression for energy stored per unit volume in parallel plate Capacitor.
(b) A 10 µF Capacitor is charged by a 30 v d.c. Supply and then connected t across an uncharged
50 µF Capacitor. Calculate the final potential difference across the combination and loss of energy
in the process?
29. State gauss theorem. Use gauss theorem to obtain the expression for electric field due to
linearly charged wire. Sketch the graphical variation of electric field with distance r from wire.
30. Explain briefly, with the help of a labeled diagram the basic principle of working of a.c.
generator. In an a.c. generator coil of N turns and area A is rotated at rotation per second in a
uniform magnetic field B. Write the expression of the emf produced.


CLASS-XII Chemistry
Instructions:
1. Section-A Q. no. 1-8 carry 1 mark each.
2. Section-B Q. no. 9-18 carry 2 marks each.
3. Section-C Q. no. 19-27 carry 3 marks each.
4. Section-D Q. no. 28-30 carry 5 marks each.

Section-A
1. Name the type of potential difference produced between the fixed charged layer and diffused
layer having opposite charges around the colloidal particles.
2. Which point defect in crystals does not affect the density of the relevant solid?
3. Give the IUPAC name:

4. Draw the structure of O3 molecule.
5. A solution of KOH hydrolyses CH3CHClCH2CH3 and CH3CH2CH2Cl. Which one of these is more
easily hydrolysed?
6. Give an example of ionization isomerism.
7. Why is the froth flotation method selected for the concentration of sulphide ores?
8. Give the IUPAC name of H2N − CH2 − CH2 − CH = CH2.
Section-B
9. Draw the structural formula of 1-phenylpropan-1-one molecule.
10. Non-ideal solutions exhibit either positive or negative deviations from Raoult’s law. What are
these deviations and why are they caused? Explain with one example for each type.
11. Draw the structures of white phosphorus and red phosphorus. Which one of these two types of
phosphorus is more reactive and why?
12. Explain the role of
(i) Cryolite in the electrolytic reduction of alumina.
(ii) Carbon monoxide in the purification of nickel.
13. A reaction is of first order in reactant A and of second order in reactant Β. How is the rate of
this reaction affected when (i) the concentration of B alone is increased to three times (ii) the
concentrations of A as well as B are doubled?
14. Illustrate the following reactions giving a chemical equation for each:
(i) Kolbe’s reaction,
(ii) Williamson synthesis.

15. Complete the following chemical reaction equations:
(i) P4 + NaOH + H2 O →
(ii) I- + H2 O + O3 →
16. Which ones in the following pairs of substances undergoes SN2 substitution reaction faster
and why?
(I)

(II)

or
17. Explain the following terms:
(i) Invert sugar
(ii) Polypeptides
18. Draw the structures of the monomers of the following polymers:

(i) Teflon
(ii) Polythene

Section-C
19. A first-order reaction has a rate constant of 0.0051 min−1. If we begin with 0.10 M concentration
of the reactant, what concentration of reactant will remain in the solution after 3 hours?
20. Name the following coordination compounds according to IUPAC system of nomenclature:
(i) [Co(NH3)4 (H2O)Cl] Cl2
(ii) [CrCl2 (en)2] Cl, (en = ethane − 1, 2 − diamine)
21. Account for the following:
(i) NH3 is a stronger base than PH3.
(ii) Sulphur has a greater tendency for catenation than oxygen.
(iii) Bond dissociation energy of F2 is less than that of Cl2.
22. State clearly what are known as nucleosides and nucleotides.
23. Giving an example for each, describe the following reactions:

(3 marks)

(i) Hofmann’s bromamide reaction
(ii) Gatterman reaction
(iii) A coupling reaction
24. The density of copper metal is 8.95 g cm−3. If the radius of copper atom is 127.8 pm, is the
copper unit cell a simple cubic, a body-centred cubic or a face centred cubic structure? (Given: At.
Mass of Cu = 63.54 g mol−1 and NA = 6.02 × 1023 mol−1)

25. Explain the following types of substances with one suitable example, for each case:
(i) Cationic detergents
(ii) Food preservatives
(iii) Analgesics
26. A solution prepared by dissolving 1.25 g of oil of winter green (methyl salicylate) in 99.0 g of
benzene has a boiling point of 80.31 °C. Determine the molar mass of this compound. (B.P. of pure
benzene = 80.10 °C and Kb for benzene = 2.53 °C kg mol−1)
27. Describe how the following changes are brought about:
(i) Pig iron into steel
(ii) Zinc oxide into metallic zinc
(iii) Impure titanium into pure titanium.

Section-D
28. How would you account for the following?

(5 marks)

(i) The atomic radii of the metals of the third (5d) series of transition elements are virtually the
same as those of the corresponding members of the second (4d) series.
(ii) The E° Value for the Mn3+/Mn2+ couple is much more positive than that for Cr3+/Cr2+ couple or
Fe3+/Fe2+ couple.
(iii) The highest oxidation state of a metal is exhibited in its oxide or fluoride.
29. (a) Define molar conductivity of a substance and describe how for weak and strong
electrolytes, molar conductivity changes with concentration of solute. How is such change
explained?
(b) A voltaic cell is set up at 25°C with the following half cells:
Ag+ (0.001 M) | Ag and Cu2+ (0.10 M) | Cu
What would be the voltage of this cell?
(E0cell = 0.46 V)
30. (a) Explain the mechanism of a nucleophillic attack on the carbonyl group of an aldehyde or a
ketone.
(b) An organic compound (A) (molecular formula C8H16O2) was hydrolysed with dilute sulphuric
acid to give a carboxylic acid (B) and an alcohol (C). Oxidation of (C) with chromic acid also
produced (B). On dehydration (C) gives but-1-ene. Write the equations for the reactions involved.


CLASS-XII Biology

SECTION-A
1. What is water pollution?
2. Define bio-magnification.
3. What is ART?
4. What is MTP?
5. Give salient features of the two strands of DNA?
6. Two villagers were arguing for the nutritive value of milk and curd? Being a normal science
student and having studied the biochemistry of both the products, tell which one is more nutritive
and justify it.
7. The name virus generally brings in our mind havoc that they are our enemies. There is a
category of virus which has species specific narrow spectrum, has insecticidal application, having
no impact on plants and other animals. Name the category and give one example.
8. Define semen and spermiation.

SECTION-B
9. Why it is essential that the chromosome number of an organism be the same from one
generation to the next generation?
10. What is central dogma of life and who proposed it?
11. Differentiate b/w GIFT and ICSI.
12. (i) Explain metastasis. Why is it fatal?
(ii) The lymphocytes are of two types B and T-cells. Why are they called so?
(iii) A person was injured in a road accident and required an urgent immune response. What
should be done?
13. Dicot plants do show tumorous growth (crown gall disease) on the stem.
a. Name the microorganism responsible for this growth?
b. What causes the production of tumors?
14. If total number of base pair is multiplied with distance between two consecutive bases,length
of DNA comes out to be appropriate 2.2 m .How is the packaging of DNA helix done in a tiny
nucleus of dimensions of approximately 10-6 m?
15. What is transforming principle? Explain with Griffith’s experiment.
16. Selection of recombinants due to inactivation of antibiotics is a cumbersome procedure. Why?
Explain the alternative method to overcome this difficulty?
17. What are e-wastes?
18. Madame Curie discovered Radium for the treatment of cancer. But she herself died of cancer.
What can be the reasons? Can virus and genes also cause cancer? Give some examples.


SECTION-C
19. Explain the term OUTBREEDING DEVICES?
20. What is artificial hybridisation?
21. State the qualities of a genetic material? Out of DNA & RNA, which one fulfills all the prerequisites of being a genetic material and why?
22. How to conserve biodiversity?
23.Define

the

following: L-H

SURGE, MENARCHE, OOGENESIS, PRIMARY

SEX

ORGANS, SECONDARY Sex Organs
24. What is Evolution?
25. What do you understand by AI?
26. Mutualism often involves co-evolution of the mutualist . Explain this statement taking example
of plant animal relationship?
27. Gobar gas can be abundantly produced in rural areas from gobar with the help of gobar gas
plants. Slury acts as an exellent increase of soil fertility. Ecofriendly i.e. it does not cause pollution
when burnt, Assuming you as a chairman of KVIC, suggest the points of maximum utilization of
Gobar Gas, the mechanism of its production & ecofriendly aspects of Gobar gas to the villages.

SECTION-D
28. What are the various methods of IVF?
29. How replication of DNA takes place in eukaryotes?
30.How r-DNA is used in Diagnosis of diseases?


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