HOLIDAY HOMEWORK

CLASS XII

ENGLISH CORE

1. Note-making of First 5 Chapters of the novel. Notes should be prepared for each chapter separately. Use proper abbreviations.

2. Draft Advertisements for the following (2 each):

A. Household item for sale

B. To-let

C. Required/Vacancy

D. Matrimony

E. Services (Showroom/Gym/Coaching etc.)

3. Write articles on the following topics:

A. Language as a means of suppression [ref.:– The Last Lesson]

B. The greatest challenge is to overcome fear. [ref.:- Deep Water]

4. Water is precious and each one of us must stop wastage. Prepare a poster in not more than 50 words urging people to employ various methods of rainwater harvesting in their colonies.

5. The recent rain caused great havoc in the city. Many buildings collapsed and several trees got uprooted blocking traffic at several places. Write a report to be published in a national daily.

6. Recently you went to you native village to visit your grandparents. You saw that some of the children in the age group 5-14 (the age at which they should have been at school) remained at home, were working in the fields or were simply loitering in the streets. Write a letter in 120-150 words to the editor of a national daily analysing the problem and offering solutions to it.

7. Bring out the elements of satire, irony and humour from the chapter ‘The Tiger King’.

8. Why it is important to keep one’s language alive? What are the reasons behind extinction of many languages?

9. Explain the following statements:

A. “Will they make them sing in German too?”

B. “The steel canister seemed heavier than the garbage bag.”

C. “Few airplanes fly over Firozabad.”

10. How is the plight of underprivileged children brought out it in the chapter ‘Lost Spring’?

11. What was Dr. Sadao’s dilemma? Do you agree that his final solution was the best under the circumstances?

12. Give character sketches of Griffin and Mrs. Hall.

KV 1, AFS, JAMNAGAR Biology

HOLIDAY HOMEWORK FOR SUMMER BREAK 2016 (CLASS-XII)

(1) What happens to corpus luteum in human female if the ovum is (i) fertilized, (ii) not fertilized?

(2) Write the difference between the tender coconut water and the thick, white kernel of a mature

coconut and their ploidy?

(3)Explain the events in a normal woman during her menstrual cycle on the following days:-

(i)Pituitary hormone levels from 8 to 12 days (ii) Uterine events from 13 to 15 days

(iii) Ovarian events from 16 to 23 days.

(4) Describe in sequence the process of microsporogenesis in angiosperms.

(5) Draw a labeled sectional view of seminiferous tubule of human. Write the function of sertoli cells,

spermatogonia and leyding cells.

(6) A childless couple has agreed for attest tube baby programme. List only the basic stepsthe

procedure would involve to conceive the baby.

(7) Draw a well labeled diagram of male and female reproductive system and write the functions of

each part.

(8) Mention the site of fertilization of a human ovum. List the events that follow in sequence until

the implantation of the blastocyst.

(9) Draw a diagram of fertilized embryo sac of a dicot flower. Label all its cellular components.

Explain the development of a mature embryo from this embryo sac.

(10) State what is apomixis. Comment on its significance. How can it be commercially used?

(11) Plan an experiment and prepare a flow chart of the steps that you would follow to ensure that

the seeds are formed only from the desired sets of pollen grains. Name the type of experiment that

you carried out. Write the importance of such experiments.

(12) Write the short notes on the following:-

(i) MTP (ii) Contraceptive (iii) sexually transmitted diseases (iv) Artificial incemination

(13) What is population explosion? Write its causes, impacts and preventions.

(14) Give the function of scrotum.

(15) Name the accessory genital glands in male and female.

HOMEWORK (SUMMER VACATION), 2016

CLASS-XII (CHEMISTRY)

SOLID-STATE

1 How will you distinguish between the following pairs of terms:

(i) Tetrahedral and octahedral voids (ii) Crystal lattice and unit cell

2 (i) Write the type of magnetism observed when the magnetic moments are aligned in parallel and anti-

parallel directions in unequal numbers.

(ii) Which stoichiometric defect decreases the density of the crystal?

(iii)Which stoichiometric defect increases the density of a solid?

3 Define the following terms in relation to crystalline solids: (i) Unit cell (ii) Coordination number

Give one example in each case.

4 Explain with suitable examples the following :

(a) n-type and p-type semiconductors (b) F-centres (c) Ferromagnetism

5 A compound forms hexagonal close-packed structure. What is the total number of voids in 0.5 mol of

it? How many of these are tetrahedral voids?

6 Analysis shows that a metal oxide has the empirical formula M 0.96 O1.00 Calculate the percentage of M2+

and M3+ ions in this crystal?

7 (i) What type of non-stoichiometric point defect is responsible for the pink colour of LiCl?

(ii) What type of stoichiometric defect is shown by NaCl?

8 The density of copper metal is 8.95 g cm –3 . If the radius of copper atom be 127.8 pm, is the copper unit

cell body-centred cubic or face-centred cubic? (Given: atomic mass of Cu = 63.54 g mol–1 and

N A = 6.02 × 10 23mol–1)

9 Niobium crystallises in body-centred cubic structure. If density is 8.55 g cm–3, calculate atomic radius

of niobium using its atomic mass 93 u.

10 Iron has a body centred cubic unit cell with a cell dimension of 286.65 pm. The density of iron is

7.87 g cm–3. Use this information to calculate Avogadro’s number. (At. mass of Fe = 56.0 u)

11 Calculate the packing efficiency of a metal crystal for a simple cubic lattice.

12 Account for the following: (i) Schottky defects lower the density of related solids.

(ii) Conductivity of silicon increases on doping it with phosphorus

SOLUTION

1 A solution containing 15 g urea (molar mass = 60 g mol–1) per litre of solution in water has the same

osmotic pressure (isotonic) as a solution of glucose (molar mass = 180 g mol–l) in water. Calculate the

mass of glucose present in one litre of its solution.

2 A solution of glucose (molar mass = 108 g mol–1) in water is labelled as 10% (by mass). What would

be the molality and molarity of the solution? (Density of solution = 1.2 g mL–1)

3 1.0 g of a non-electrolyte solute dissolved in 50 g of benzene lowered the freezing point of benzene by

0.40 K. Find the molar mass of the solute. (Kf for benzene = 5.12 kg mol–1)

4 A solution of glycerol (C3H8O3) in water was prepared by dissolving some glycerol in 500 g of water.

This solution has a boiling point of 100.42°C. What mass of glycerol was dissolved to make this

solution? (Kb for water = 0.512 K kg mol–1)

5 A solution prepared by dissolving 8.95 mg of a gene fragment in 35.0 mL of water has an osmotic

pressure of 0.335 torr at 25°C. Assuming that the gene fragment is a non-electrolyte, calculate its molar

mass.

6 What mass of NaCl must be dissolved in 65.0 g of water to lower the freezing point of water by 7.50°C?

The freezing point depression constant (Kf) for water is 1.86 C/m. Assume van’t Hoff factor for NaCl is

1.87. (Molar mass of NaCl = 58.5 g).

7 100 mg of a protein is dissolved in enough water to make 100 mL of a solution. If this solution has an

osmotic pressure 13.3 mm Hg at 25° C, what is the molar mass of protein? (R = 0.0821 L atm mol–1 K–1

and 760 mm Hg = 1 atm.)

8 State Raoult’s law for a solution containing volatile components. Name the solution which follows

Raoult’s law at all concentrations and temperatures.

9 Define the following terms: (i) Azeotrope (ii) Osmotic pressure (iii) Colligative properties (iv) Ideal

solution

10 How does Raoult’s law become a special case of Henry’s law?

11 Explain the following: (i) Henry’s law about dissolution of a gas in a liquid.

(ii) Boiling point elevation constant for a solvent.

12 Derive an equation to express that relative lowering of vapour pressure for a solution is equal to

the mole fraction of the solute in it when the solvent alone is volatile.

ELECTROCHEMISTRY

1 A solution of Ni(NO3)2 is electrolysed between platinum electrodes using a current of 5.0 ampere for

20 minutes. What mass of nickel will be deposited at the cathode?

(Given: At. Mass of Ni = 58.7 g mol–1, 1 F = 96500 C mol–1)

2 Express the relation among cell constant, resistance of the solution in the cell and conductivity of the

solution. How is molar conductivity of a solution related to its conductivity?

3 The molar conductivity of a 1.5 M solution of an electrolyte is found to be 138.9 S cm2 mol–1. Calculate

the conductivity of this solution.

4 How many moles of mercury will be produced by electrolysing 1.0 M. Hg(NO3)2 solution with a current

of 2.00 A for 3 hours?

5 A voltaic cell is set up at 25° C with the following half-cells Al3+ (0.001 M) and Ni2+ (0.50 M). Write an

equation for the reaction that occurs when the cell generates an electric current and determine cell

potential.

6 Three conductivity cells A, B and C containing solutions of zinc sulphate, silver nitrate and copper

sulphate respectively are connected in series. A steady current of 1.5 amperes is passed through them

until 1.45 g of silver is deposited at the cathode of cell B. How long did the current flow? What mass of

copper and what mass of zinc got deposited in their respective cells?

(Atomic mass : Zn = 65.4 u, Ag =108 u, Cu = 63.5 u)

7 Depict the galvanic cell in which the following reaction takes place:

Zn (s) + 2Ag+ (aq) → Zn 2+ (aq) + 2Ag (s)

Also indicate that in this cell : (i) which electrode is negatively charged.

(ii) what are the carrier of the current in the cell. (iii) what is the individual reaction at each electrode.

8 Define conductivity and molar conductivity for the solution of an electrolyte. How do they vary when

the concentration of electrolyte in the solution increases?

9 How do metallic and ionic substances differ in conducting electricity?

10 State Kohlrausch law of independent migration of ions. Why does the conductivity of a solution

decrease with dilution?

11 Define: (i)Fuel cell (ii) Secondary batteries

Holidays Home Work (Summer Vacation: 2016-17)

Class-XII-A & B Sub: Physics

Q.1 What is electrostatic shielding?

Q.2 What is relative electrical permittivity?

Q.3 Why must electrostatic field be normal to the surface at every point of a charged

conductor ?

Q.4 How resistance of metal & semiconductor does vary with temperature?

Q.5 Derive an expression for energy stored in a parallel plate capacitor and hence write the

expression for energy density.

Q.6 Establish a relation between electric current and drift velocity.

Q.7 The given graph shows that variation of charge q versus potential difference V for two

capacitors C1 and C2. The two capacitors have same plate separation but the plate area

of C2 is double than that of C1. Which of the lines in the graph correspond to C1 and C2

and why?

Q.8 A parallel plate capacitor with air between the plates has a capacitance of 8µF. What

will be the capacitance if the distance between the plates is reduced to half and the

space between them is filled with a substance of dielectric constant K=6?

Q.9 A charge of 24 μC is given to a hollow sphere of radius 0.2 m. Find the potential (i) at

the surface of the sphere, and

(ii) at a distance of 0.1 m from the centre of the sphere.

(iii) at a distance of 0.4 m from the centre of the sphere.

(iv)at the centre.

Q.10 Two charges 3 × 10-8 C and -2 × 10-8 C are located 15 cm apart. At what point on the

line joining the two charges is the electric potential zero ?

Q.11 A parallel plate capacitor is charged by a battery. After some time the battery is

disconnected and a dielectric slab of dielectric constant K is inserted between the

plates. How would (i) the capacitance, (ii) the electric field between the plates and

(iii) the energy stored in the capacitor, be affected? Justify your answer.

Q.12 A slab of material of dielectric constant K has the same area as the plates of a parallel

plate capacitor but has a thickness 3d / 4, where d is the separation of the plates.

How is the capacitance changed when the slab is inserted between the plates?

Q.13 Derive an expression for the electric field intensity at a point lying on (i)axial and

(ii)equatorial point of an electric dipole.

Q.14 A proton is placed in a uniform electric field directed along the positive x-axis. In which

direction will it tend to move?

Q.15 A cubical Gaussian surface encloses a charge 8.85x10-10 C in vacuum. Calculate

electric flux through one of its faces.

Q.16 Two identical parallel plate (air) capacitors C1 and C2 have capacitance C each. The

space between their plates is now filled with dielectric as shown. If the two capacitors

still have equal capacitance, obtain the relation between dielectric constant K, K1 and

K2.

Q.17 Find the ratio of potential difference that must be applied across the parallel and series

combination of two capacitors C1 and C2 with their capacitance in the ratio 1:3 so that

the energy stored in the two cases is same.

Q.18 A 500 µC charge is at the centre of a square of side 10 cm. Find the work done in

moving a charge of 10 µC between two diagonally opposite points on the square.

Q.19 The plot of the variation of potential difference across a combination of three identical

cells in Series, versus current is as shown below. What is the emf of each cell?

Q.20 Derive the expression for the electric potential at any point along the axial line of an

electric dipole?

Q.21 In a meter bridge the balance point is found to be 39.5 cm from one end A, when the

resistor Y is of 12.5 . Determine the resistance of X.

Q.22 Out of the two bulbs marked 25W and 100W, which one has higher resistance & why?

Q.23 Two primary cells of emf E1 and E2 (E1 > E2) are connected to the potentiometer wire as shown in the figure. If the balancing lengths for the cells are 250 cm and 400 cm. Find the ratio of E1 and E2.

Q.24 Three cells of emf 2V, 1.8V and 1.5V are connected in series. Their internal resistances

are 0.05, 0.7 and 1 respectively. If this battery is connected to an external

resistance of 4, calculate :

(i) the total current flowing in the circuit. (ii) the p.d. across the terminals of the cell of emf 1.5V.

Q.25 A cylindrical metallic wire is stretched to increase its length by 10%. Calculate the

percentage change in its resistance.

Q.26 Two cells of emf 1.5 V and 2V and internal resistance 1 and 2 are connected in

parallel to pass a current in the same direction through an external resistance of 5 .

(a) Draw Circuit Diagram. (b) Using Kirchhoff’s laws, calculate the current through each

branch of the circuit and p.d. across the 5 resistor. (CBSE 05)

Q.27 AB=100 cm, RAB=10. Find the balancing length AC.

Q.28 Find the value of the unknown resistance X in the circuit, if no current flows through the section AO. Also calculate the current drawn from the battery of emf 6V.

Q.29 Define dielectric constant of a medium. What is its S.I. unit ? (CBSE AJMER-2015)

Q.30 (a) State Gauss’s law in electrostatics. Show, with the help of a suitable example along

with the figure, that the outward flux due to a point charge ‘q’, in vacuum within a closed

surface, is independent of its size or shape and is given by q/εo.

(b) Two parallel uniformly charged infinite plane sheets, ‘1’ and ‘2’, have charge densities

+σ and –2σ respectively. Give the magnitude and direction of the net electric field at a

point

(i) in between the two sheets and

(ii) outside near the sheet ‘1’. (CBSE AJMER-2015)

Q.31 (a) Define electrostatic potential at a point. Write its S.I. unit.

Three point charges q1, q2 and q3 are kept respectively at points A, B and C as shown in the

figure. Derive the expression for the electrostatic potential energy of the system.

(b) Depict the equipotential surfaces due to

(i) an electric dipole,

(ii) two identical positive charges separated by a distance.(CBSE AJ-2015)

Q.32 The given figure shows the experimental set up of a meter bridge. The null point is

found to be 60cm away from the end A with X and Y in position as shown. When a

resistance of 15Ω is connected in series with ‘Y’, the null point is found to shift by 10cm

towards the end A of the wire. Find the position of null point if a resistance of 30Ω were

connected in parallel with ‘Y’.

Q.33 A parallel plate capacitor is filled with dielectrics as shown in diagram.Find the

capacitance of the system .

Q.34 Two identical cells of emf 1.5 V each joined in parallel supply energy to an external

circuit consisting of two resistances of 7 Ω each joined in parallel. A very high resistance

voltmeter reads the terminal voltage of cells to be 1.4 V. Calculate the internal

resistance of each cell. (CBSE AJMER-2016)

Q.35 A capacitor of capacitance C is charged fully by connecting it to a battery of emf E. It is

then disconnected from the battery. If the separation between the plates of the

capacitor is now doubled, how will the following change ? (i) charge stored by the

capacitor

(ii) field strength between the plates

(iii) the energy stored by the capacitor? Justify your answer in each case.

(CBSE AJMER-2016)

Q.36 Prove that the current density of a metallic conductor is directly proportional to the

drift speed of electrons.

Q.37 A number of identical cells, n, each of emf E, internal resistance r connected in series

are charged by a d.c. source of emf E, using a resistor R.

(i) Draw the circuit arrangement.

(ii) Deduce the expressions for (a) the charging current and (b) the potential difference

across the combination of the cells.

Q.38 Write the principle of working of a potentiometer. Describe briefly, with the help of a

circuit diagram, how a potentiometer is used to determine the internal resistance of a

given cell.

Q.39 In a potentiometer arrangement; a cell of emf 1.25 V gives a balance point at 35.0 cm

length of the wire. If the cell is replaced by another cell and the balance point shifts to

63.0 cm, what is the emf of the second cell?

HOLIDAY HOMEWORK

CLASS-XII

Subject-CS

Q.1 What do you mean by CALL BY VALUE and CALL BY REFERENCE?

Q.2 What is the difference between TYPE CASTING and TYPE CONVERSION?

Q.3 Explain: DEFAULT ARGUMENT Vs FUNTION OVERLOADING.

Q.4 What is the difference between BREAK and CONTINUE?

Q.5 How STATIC DATA MEMBER is different from other data member ?

Q.6 What are the advantages and disadvantages of INLINE functions?

Q.7 What is the significance of ACCESS LABELS in a class?

Q.8 Define a class RESORT with the following description:

Private Members:

RNo //Data member to store Room No

Name //Date member to store Customer Name

Charges //Data member to store per day charges

Days //Data member to store number of days of stay

CALC() //A function to calculate and return Amount as

Days*Charges and if the value of Days*Charges

is more than 10000 then as 1.25*Days*Charges

Public Members:

CHECKIN() // A function to enter the content RNo, Name,

Charges and Days

CHECKOUT() //A function to display the content of RNo, Name,

Charges,Days and Amount (Amount to be displayed

by calling CALC()function)

Q.9 Define a class Departmental with the following specification :

private data members

Prod_name string (45 charactes) [ Product name]

Listprice long

Dis_Price long [ Discount Price]

Net long [Net Price ]

Dis_type char(F or N) [ Discount type]

Cal_price() – The store gives a 10% discount on every product it sells.

However at the time of festival season the store gives 7% festival discount after

10% regular discount. The discount type can be checked by tracking the

discount type. Where ‘F’ means festival and ‘N’ means Non- festival .The

Cal_price() will calculate the Discount Price and Net Price on the basis of the

following table.

public members

Constructor - to initialize the string elements with “NULL”, numeric elements with

0 and character elements with ‘N’

Accept() - Ask the store manager to enter Product name, list Price and discount

type . The function will invoke Cal_price() to calculate Discount Price and Net Price

.

ShowBill() - To generate the bill to the customer with all the details of his/her

purchase along with the bill amount including discount price and net price.

Q.10 Define a class Garments in C++ with the following descriptions:

Private members:

GCode of type string

GType of type string

Gsize of type integer

GFabric of type string

GPrice of type float

A function assign () which calculates and assigns the value of GPrice as follows:

for the value of Gfabric “COTTON”

GType GPrice (₹)

TROUSER 1300

SHIRT 1100

FOR GFabric other than “COTTON” the above mentioned GPrice gets reduced

by 10%

Public Members:

A constructor to assign initial values of GCode, Gtype and GFabric with the word

“NOT ALLOTTED” AND GSize AND GPrice WITH 0.

A FUNCTION Input() to input the values of the data members Gcode, Gtype, GSize

and GFabric and invoke the Assign() function.

A function Display() which displays the content of all the data members for a

Garment.

Q.11 The following code is from a game, which generate a set of 4 random numbers.

Praful is playing this game, help him to identify the correct option(s) out of the four

choices given below as the possible set of such numbers generated from the program

code so that he wins the game. Justify your answer.

#include<iostream.h>

#include<stdlib.h>

const int LOW=25;

void main()

Product Name List Price(Rs.)

Washing Machine 12000

Colour Television 17000

Refrigerator 18000

OTG 8000

CD Player 4500

randomize();

int POINT=5, Number;

for(int I=1;I<=4;I++)

Number=LOW+random(POINT);

cout<<Number<<":" <<endl;

POINT--;

(i) 29:26:25:28:

(ii) 24:28:25:26:

(iii) 29:26:24:28;

(iv) 29:26:25:26:

Q.12 What is the difference between GLOBAL and LOCAL variable?

Q.13 What is function overloading ? Give an example in C++ to illustrate function

overloading.

Q.14 What is copy constructor? Discuss the various situations when copy constructor is

automatically invoked?

Q.15 Consider the following declarations and answer the questions given below :

class WORLD

int H;

protected :

int S;

public :

void INPUT(int); void OUTPUT();

;

class COUNTRY : private WORLD

int T;

protected :

int U;

public :

void INDATA( int, int);

void OUTDATA();

;

class STATE : public COUNTRY

int M;

public :

void DISPLAY (void);;

(i) Name the base class and derived class of the class COUNTRY.

(ii) Name the data member(s) that can be accessed from function DISPLAY().

(iii) Name the member function(s), which can be accessed from the objects of class

STATE.

(iv) Is the member function OUTPUT() accessible by the objects of the class COUNTRY ?

Q.16. Draw a Logical Circuit Diagram for the following Boolean expression:

A.(B+C’)

Q.17 Express the F(X,Z)=X+X’Z into canonical SOP form.

Q.18 If F(a,b,c,d)=∑(0,2,4,5,7,8,10,12,13,15) obtain the simplified form using K-Map.

XII MATHS SUMMER BREAK HOLIDAY HOMEWORK KV1 JAMNAGAR

(2016-17) TOPIC - RELATION AND FUNCTIONS

1. If f(x) = x + 7 and g(x) = x – 7, x∈R, find )7(gf

2. Let * be a binary operation defined by a * b = 3a +4b -2. Find 4 * 5

3. Check whether the relation R defined in the set 1, 2, 3, 4 as R = (1, 2), (2, 2), (1,

1), (4, 4),( 1, 3), (3, 3), (3, 2) is Reflexive, Symmetric and Transitive.

4. Show that the relation R defined in the set A of all triangles as R = (T1, T2) : T1 is

similar to T2 is an equivalence relation.

5. Let A= N N and be the binary operation on A defined by (a,b)(c,d)=(a+c,b+d).

Show that is commutative and associative. Find the identity element for on A If

any.

6. Let A= R–2 and B=R–1, If f: AB is a function defined by ƒ(x)= x−1

x−2. Show that

f is a Bijective function. Also find the inverse of f.

7. Let f: N R be a function defined as f(x)= 4x2 + 12x + 15. Show that f: NRange f

is invertible. Also find the inverse of f.

8. f : RR be given by f(x) = (3-x3)1/3

, then find )(xff

9. Let Z be the set of all integers and R be the relation on Z defined as a R b ⇒∣ a − b ∣

is divisible by 4, Prove that R is an equivalence relation.

10. Let f : N →N be defined by f(x) =

𝒏+𝟏

𝟐 , 𝑖𝑓𝑛𝑖𝑠𝑜𝑑𝑑

𝒏

𝟐, 𝑖𝑓𝑛𝑖𝑠𝑒𝑣𝑒𝑛

for every n ∈ 𝑁. Check

whether the function is bijective.

TOPIC-INVERSE TRIGONOMETRIC FUNCTION

Q1. Solve for x:

a) 2𝒕𝒂𝒏−𝟏(𝒄𝒐𝒔𝒙) = 𝒕𝒂𝒏−𝟏(𝟐𝒄𝒐𝒔𝒆𝒄𝒙) Ans:x=𝝅

𝟒 b) 𝒕𝒂𝒏−𝟏 (

𝟐𝒙

𝟏−𝒙𝟐) + 𝒄𝒐𝒕−𝟏 (𝟏−𝒙𝟐

𝟐𝒙) =

𝟐𝝅

𝟑 ,x> 𝟎 Ans:x=

𝟏

√𝟑

c) 𝒔𝒊𝒏−𝟏(𝟏 − 𝒙) − 𝟐𝒔𝒊𝒏−𝟏𝒙 =𝝅

𝟐 Ans:x=0 d) 𝒕𝒂𝒏−𝟏 (

𝟏−𝒙

𝟏+𝒙) =

𝟏

𝟐𝒕𝒂𝒏−𝟏𝒙 ; 𝒙 >

𝟎 𝑨𝒏𝒔: 𝒙 =𝟏

√𝟑

e) 𝒕𝒂𝒏−𝟏 (𝟏+𝒙

𝟏−𝒙) =

𝝅

𝟒+ 𝒕𝒂𝒏−𝟏𝒙

Q2. Prove that:

a) 2𝒕𝒂𝒏−𝟏 (𝟏

𝟓) + 𝒕𝒂𝒏−𝟏 (

𝟏

𝟒) = 𝒕𝒂𝒏−𝟏 𝟑𝟐

𝟒𝟑 b) 𝒕𝒂𝒏−𝟏 𝟑

𝟒+ 𝒕𝒂𝒏−𝟏 𝟑

𝟓− 𝒕𝒂𝒏−𝟏 𝟖

𝟏𝟗=

𝝅

𝟒

c) 𝒔𝒊𝒏−𝟏 𝟑

𝟓− 𝒔𝒊𝒏−𝟏 𝟖

𝟏𝟕= 𝒄𝒐𝒔−𝟏 𝟖𝟒

𝟖𝟓 d) 𝒕𝒂𝒏−𝟏 𝟏

𝟒+ 𝒕𝒂𝒏−𝟏 𝟐

𝟗=

𝟏

𝟐𝒄𝒐𝒔−𝟏 𝟑

𝟓

e) 𝒔𝒊𝒏−𝟏 (𝟒

𝟓) + 𝒔𝒊𝒏−𝟏 (

𝟓

𝟏𝟑) + 𝒔𝒊𝒏−𝟏 (

𝟏𝟔

𝟔𝟓) =

𝝅

𝟐 f) 𝒕𝒂𝒏−𝟏√𝒙 =

𝟏

𝟐𝒄𝒐𝒔−𝟏 (

𝟏−𝒙

𝟏+𝒙)

g) sin[𝒄𝒐𝒕−𝟏𝒄𝒐𝒔(𝒕𝒂𝒏−𝟏𝒙)] = √𝒙𝟐+𝟏

𝒙𝟐+𝟐 h) 𝒕𝒂𝒏 (

𝝅

𝟒+

𝟏

𝟐𝒄𝒐𝒔−𝟏 𝒂

𝒃) + 𝒕𝒂𝒏 (

𝝅

𝟒−

𝟏

𝟐𝒄𝒐𝒔−𝟏 𝒂

𝒃)=

𝟐𝒃

𝒂

Q3. Evaluate:

a) 𝒔𝒊𝒏−𝟏 (−𝟏

𝟐) + 𝟐𝒄𝒐𝒔−𝟏 (

−√𝟑

𝟐) Ans:

𝟑𝝅

𝟐 b) 𝒕𝒂𝒏−𝟏 (𝒕𝒂𝒏

𝟕𝝅

𝟔) +

𝒄𝒐𝒕−𝟏 (𝒄𝒐𝒕𝟕𝝅

𝟔) Ans:

𝝅

𝟑

c) 𝒄𝒐𝒔𝒆𝒄−𝟏 (𝒄𝒐𝒔𝒆𝒄𝝅

𝟔) + 𝒕𝒂𝒏−𝟏 (𝒕𝒂𝒏

𝟕𝝅

𝟔) Ans:

𝝅

𝟑 d) 𝒔𝒊𝒏−𝟏 (𝒔𝒊𝒏

𝟑𝝅

𝟒) +

𝒄𝒐𝒔−𝟏 𝒄𝒐𝒔 (−𝝅

𝟑) Ans:

𝟕𝝅

𝟏𝟐

e) 𝒔𝒊𝒏 [𝝅

𝟐− 𝒔𝒊𝒏−𝟏 (

−√𝟑

𝟐)] Ans:

𝟏

𝟐

Q4. Write in the simplest form:

a) 𝒕𝒂𝒏−𝟏𝒙 + √𝟏 + 𝒙𝟐 Ans:𝝅

𝟐−

𝟏

𝟐𝒄𝒐𝒕−𝟏𝒙 b) 𝒕𝒂𝒏−𝟏√𝟏 + 𝒙𝟐 − 𝒙 Ans:

𝟏

𝟐𝒄𝒐𝒕−𝟏𝒙

c) 𝒕𝒂𝒏−𝟏 √𝟏+𝒙𝟐−𝟏

𝒙 Ans:

𝟏

𝟐 𝒕𝒂𝒏−𝟏𝒙 d) 𝒕𝒂𝒏−𝟏√

𝒂−𝒙

𝒂+𝒙 Ans:

𝟏

𝟐𝒄𝒐𝒔−𝟏 𝒙

𝒂

e) 𝒕𝒂𝒏−𝟏 𝒙

𝒂+√𝒂𝟐−𝒙𝟐 Ans:

𝟏

𝟐𝒔𝒊𝒏−𝟏 𝒙

𝒂 f) 𝒔𝒊𝒏−𝟏

√𝟏+𝒙+√𝟏−𝒙

𝟐 Ans:

𝝅

𝟒+

𝟏

𝟐𝒄𝒐𝒔−𝟏𝒙

g) 𝒔𝒊𝒏 𝟐𝒕𝒂𝒏−𝟏√𝟏−𝒙

𝟏+𝒙 Ans:√𝟏 − 𝒙𝟐

Q5. Simplify:

a) 𝒄𝒐𝒔−𝟏 (𝟑

𝟓𝒄𝒐𝒔𝒙 +

𝟒

𝟓𝒔𝒊𝒏𝒙) Ans: 𝒙 − 𝒕𝒂𝒏−𝟏 𝟒

𝟑

b) 𝒔𝒊𝒏−𝟏 (𝟓

𝟏𝟑𝒄𝒐𝒔𝒙 +

𝟏𝟐

𝟏𝟑𝒔𝒊𝒏𝒙) Ans: 𝒙 + 𝒕𝒂𝒏−𝟏 𝟓

𝟏𝟐

TOPIC- MATRICES AND DETERMINANT

Q1. A matrix of order 3x3 has determinant 5.What is the value of |𝟒𝐀| Ans:320

Q2. If A is a square matrix of order 3 such that |𝐚𝐝𝐣 𝐀| = 𝟔𝟒.find |𝐀|. Ans:±𝟖

Q3. If A =[𝟏 𝐬𝐢𝐧𝛉 𝟏

−𝐬𝐢𝐧𝛉 𝟏 𝐬𝐢𝐧𝛉−𝟏 −𝐬𝐢𝐧𝛉 𝟏

] where 0≤ 𝛉 ≤ 𝟐𝛑. Find |𝐀|

Q4.If a,b,c are in A.P,then |𝐱 + 𝟐 𝐱 + 𝟑 𝐱 + 𝟐𝐚𝐱 + 𝟑 𝐱 + 𝟒 𝐱 + 𝟐𝐛𝐱 + 𝟒 𝐱 + 𝟓 𝐱 + 𝟐𝐜

| =?

Q5.If A= [𝟏 𝟐𝟒 𝟐

] then find the value of 𝐤 if |𝟐𝐀| = 𝐤|𝐀| .

Q6. Using Properties of the determinant prove the following:

a) |𝒃𝟐 + 𝒄𝟐 𝒂𝒃 𝒂𝒄

𝒃𝒂 𝒄𝟐 + 𝒂𝟐 𝒃𝒄𝒄𝒂 𝒄𝒃 𝒂𝟐 + 𝒃𝟐

| = 𝟒𝒂𝟐𝒃𝟐𝒄𝟐 b) ||

𝒂𝟐+𝒃𝟐

𝒄𝒄 𝒄

𝒂𝒃𝟐+𝒄𝟐

𝒂𝒂

𝒃 𝒃𝒄𝟐+𝒂𝟐

𝒃

||

= 𝟒𝒂𝒃𝒄

c) |−𝒃𝒄 𝒃𝟐 + 𝒃𝒄 𝒄𝟐 + 𝒃𝒄

𝒂𝟐 + 𝒂𝒄 𝒄𝟐 + 𝒂𝟐 𝒃𝒄𝒄𝒂 𝒄𝒃 𝒂𝟐 + 𝒃𝟐

| = (𝒂𝒃 + 𝒃𝒄 + 𝒄𝒂)𝟑 d) |𝒃 + 𝒄 𝒂 𝒂

𝒃 𝒄 + 𝒂 𝒃𝒄 𝒄 𝒂 + 𝒃

| = 𝟒𝒂𝒃𝒄

e) |𝒂𝟐 + 𝟏 𝒂𝒃 𝒂𝒄

𝒂𝒃 𝒃𝟐 + 𝟏 𝒃𝒄𝒄𝒂 𝒄𝒃 𝒄𝟐 + 𝟏

| = 𝟏 + 𝒂𝟐 + 𝒃𝟐 + 𝒄𝟐 f) |𝒂 𝒃 𝒄

𝒂 − 𝒃 𝒃 − 𝒄 𝒄 − 𝒂𝒃 + 𝒄 𝒄 + 𝒂 𝒂 + 𝒃

| = 𝒂𝟑 + 𝒃𝟑 + 𝒄𝟑 −

𝟑𝒂𝒃𝒄

g) |𝒂𝟐 𝒃𝒄 𝒂𝒄 + 𝒄𝟐

𝒂𝟐 + 𝒂𝒃 𝒃𝟐 𝒂𝒄𝒂𝒃 𝒃𝟐 + 𝒃𝒄 𝒄𝟐

| = 𝟒𝒂𝟐𝒃𝟐𝒄𝟐 h) |𝒂𝟐 𝟐𝒂𝒃 𝒃𝟐

𝒃𝟐 𝒂𝟐 𝟐𝒂𝒃𝟐𝒂𝒃 𝒃𝟐 𝒂𝟐

| = (𝒂𝟑 + 𝒃𝟑)𝟐

i) |

(𝒃 + 𝒄)𝟐 𝒂𝟐 𝒃𝒄

(𝒄 + 𝒂)𝟐 𝒃𝟐 𝒄𝒂

(𝒂 + 𝒃)𝟐 𝒄𝟐 𝒂𝒃

| = (𝒂 − 𝒃)(𝒃 − 𝒄)(𝒄 − 𝒂)(𝒂 + 𝒃 + 𝒄)(𝒂𝟐 + 𝒃𝟐 + 𝒄𝟐)

j) |𝟏 𝒙 𝒙𝟐

𝒙𝟐 𝟏 𝒙𝒙 𝒙𝟐 𝟏

| = (𝟏 − 𝒙𝟑)𝟐 k) |𝒂 − 𝒃 − 𝒄 𝟐𝒂 𝟐𝒂

𝟐𝒃 𝒃 − 𝒄 − 𝒂 𝟐𝒃𝟐𝒄 𝟐𝒄 𝒄 − 𝒂 − 𝒃

| = (𝒂 + 𝒃 + 𝒄)𝟑

Q7.Without expanding shows their values as 0 or 1.

a) ||

𝟏

𝒂𝒂𝟐 𝒃𝒄

𝟏

𝒃𝒃𝟐 𝒂𝒄

𝟏

𝒄𝒄𝟐 𝒂𝒃

|| = 𝟎 b) |

𝟏 𝒂 𝒂𝟐 − 𝒃𝒄𝟏 𝒃 𝒃𝟐 − 𝒂𝒄𝟏 𝒄 𝒄𝟐 − 𝒂𝒃

| = 𝟎 c) |𝟎 𝒂 −𝒃

−𝒂 𝟎 −𝒄𝒃 𝒄 𝟎

| = 𝟎 d)

|𝒃𝟐𝒄𝟐 𝒃𝒄 𝒃 + 𝒄𝒄𝟐𝒂𝟐 𝒄𝒂 𝒄 + 𝒂𝒂𝟐𝒃𝟐 𝒂𝒃 𝒂 + 𝒃

| = 𝟎

e) |

𝟏 𝟏 + 𝒑 𝟏 + 𝒑 + 𝒒𝟐 𝟑 + 𝟐𝒑 𝟏 + 𝟑𝒑 + 𝟐𝒒𝟑 𝟔 + 𝟑𝒑 𝟏 + 𝟔𝒑 + 𝟑𝒒

| = 𝟏

Q8. Solve the system of equations, using matrix method: 2x+3y+3z=5 ; x-2y+z=-4 ; 3x-y-2y=3 Q9. Using matrix method, solve the following: x+y+z=4, 2x-y+z=-1, 2x+y-3z+9=0

Q10. Find the inverse of the matrix A= [𝟏 𝟏 𝟏𝟏 𝟐 𝟑𝟏 𝟒 𝟗

]and hence solve the following system of linear

equations:

x+y+z=3 ; x+2y+3z=4 ; x+4y+9z=6.

Q11. Given two matrices A= [𝟏 −𝟏 𝟎𝟐 𝟑 𝟒𝟎 𝟏 𝟐

] and B=[𝟐 𝟐 𝟒

−𝟒 𝟐 −𝟒𝟐 −𝟏 𝟓

] verify that BA=6I.Use the

result to solve the system x-y = 3 , 2x + 3y + 4z = 17 , y + 2z =7

Q12. Find the inverse of the matrix [𝟏 𝟏 𝟏𝟏 𝟐 𝟑𝟏 𝟒 𝟗

] using elementary transformations.

Q13 Express the matrix B= [𝟓 𝟒 −𝟑𝟓 𝟐 𝟑𝟒 𝟒 𝟗

] as the sum of a symmetric and a skew symmetric matrix.