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.
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