- Prove that: tan -1
+
tan -1
+
tan -1
= 
- Prove that: tan -1
+
tan -1 +
tan -1
+ tan -1 = - Prove that: 2 tan -1+ tan -1= tan
-1
. - Find
the value of
- Prove
the following: tan -1x + tan -1
=
tan-1
. - Prove that:
- Prove that:
- Prove
that:
. - Solve tan -1 2x
+ tan -1 3x =
10.
If tan
-1 
+ tan
-1 
= , then find the
value of x
+ tan
-1 = , then find the
value of x 
= (x – y)(y –z)(z – x) (C.B.S.E.
1991)
2.
=(
C.B.S.E. 2006, 04)
=(
C.B.S.E. 2006, 04)
3.
= (a - b)(b - c)(c - a)(a + b + c)
(C.B.S.E. 1997, 96 ,2000, 2003C)
= (a - b)(b - c)(c - a)(a + b + c)
(C.B.S.E. 1997, 96 ,2000, 2003C)
4. 
= xyz(x – y)(y
– z)(z – x)
(C.B.S.E. 2000)
= xyz(x – y)(y
– z)(z – x)
(C.B.S.E. 2000)
5. 
= ((
) (C.B.S.E. 2008,
05)
= (() (C.B.S.E. 2008,
05)
6.
= (5x + 4)(x –
4)2
(C.B.S.E. 1996)
= (5x + 4)(x –
4)2
(C.B.S.E. 1996)
7. 
= 9 (a + b) b2(C.B.S.E.
2008, 02)
= 9 (a + b) b2(C.B.S.E.
2008, 02)
8. 
= (a + b + c)
(C.B.S.E. 2007, 06, 04,2000C,1998,97)
= (a + b + c)
(C.B.S.E. 2007, 06, 04,2000C,1998,97)
9. 
= 2(a + b + c)(C.B.S.E. 2006, 04, 1999)
= 2(a + b + c)(C.B.S.E. 2006, 04, 1999)
10.
= a2
(a + x + y + z)
(C.B.S.E. 2003)
= a2
(a + x + y + z)
(C.B.S.E. 2003)
1.
Using matrix method, solve the following system
of equations :
2x – y + z = 3 , - x +2y – z = - 4 , x
– 2y + 2z = 1
(C.B.S.E. 2008)
2.
Using matrix method, solve the following system
of equations :
x + 2y – 3z = - 4
, 2x + 3y + 2z = 2 , 3x – 3y – 4z =11 (C.B.S.E. 2008,07)
3.
Solve the following system of equations, using
matrices :
(C.B.S.E.
2002 C)
4.
Find A-1, where A = 
, Hence, solve
the system of linear equations :
, Hence, solve
the system of linear equations :
x – 2y = 10, 2x + y + 3z = 8, - 2y + z = 7.
(C.B.S.E. 1997)
5.
Given that
A = 
and B = 
, find AB and use it to solve the system
and B = , find AB and use it to solve the system
of equations : x –y + z = 4, x – 2y – 2z = 9, 2x + y + 3z =
1. (C.B.S.E. 2003 C)
6.
If A = 
and C = 
. Find AC and hence solve the
and C = . Find AC and hence solve the
equations x - 2 y = 10, 2 x + y + 3 z = 8, - 2 y + z = 7.
7.
The perimeter of a
triangle is 90 cm. The longest side exceeds the shortest side by 16 cm and the
sum of the
lengths of the longest and shortest side is twice the length of the other side.
Use thematrix method to find the sides of the triangle.
8.
The sum of three
numbers is 6. If 3rd number is multiplied by 2 and first number is
added, we get 7 and by adding second and third number to 3 times the first
number we get 12. Use matrix method to
find the numbers.
9.
The management committee of a residential colony
decided to award some of its members (say x) for honesty, some (say y) for
helping others and some others (say z) for supervising the workers to keep the
colony neat and clean. The sum of all the awardees is 12. Three times the sum
of awardees for cooperation and supervision added to two times the number of
awardees for honesty is 33. If the sum of the number of awardees for honesty
and supervision is twice the number of awardees for helping others, using
matrix method, find the number of awardees of each category. Apart from these
values, namely, honesty, cooperation and supervision, suggest one more value
which the management of the colony must include for awards.
10.
A school wants to award its students for the
values of Honesty, Regularity and Hardwork with a total cash award of ₹ 6,000.
Three times the award money for Hardwork added to that given for Honesty
amounts to ₹ 11,000.The award money given for Honesty and Hardwork together is
double the one given for Regularity. Represent the above situation
algebraically and find the award money for each value, using matrix method.
Apart from these values, namely Honesty, Regularity and Hardwork, suggest one
more value which the school must include for awards.
Differentiate w.r. to x
(1) 
+(sinx)x (2) 
+ 
(3) ( cos x) y = ( cos y )x
+(sinx)x (2) + (3) ( cos x) y = ( cos y )x
(4) 
= e x – y
Show that 
(5)
(6) (sinx)x+sin-1√x
= e x – y
Show that (5)
(6) (sinx)x+sin-1√x
(7) (x)sinx +(logx)x
(8) (x)cosx +(sinx)tanx
(9)
(x)sinx +(sinx)cosx
(10) 
Find the shortest distance between the lines
2. Find the shortest distance between the lines
3. Find the shortest
distance between the lines
4. Find the shortest
distance between the lines 
5. Find the shortest
distance between the lines 
1. Find
the angle between following pair of lines 
and
and 
.
7. Find the angle between following pair of lines 
and 
and
8. Find the
value of 
, so that the following lines are perpendicular
to each other 
and 
, so that the following lines are perpendicular
to each other and
9.
Find the value of , so that the following lines are perpendicular
to each other
and 
, so that the following lines are perpendicular
to each other and
10.Find the
value of 
, so that the following
lines are perpendicular to each other
, so that the following
lines are perpendicular to each other
and
.
.
1. Find
the equation of plane passing through
the point (-1, 3, 2) and perpendicular to each of the planes x + 2y +3z = 5 and
3x + 3y +z = 5.
2. Find
the equation of plane passing through
the point (1, 1, -1) and perpendicular to each of the planes x + 2y +3z - 7 = 0
and 2x -3y +4z = 0.
3. Find
the vector equation of plane passing through the points A(2, 2, -1),
B(3, 4, 2) and C(7, 0, 6). Also,
find the cartesian equation of plane.
4. Find the vector and cartesian equations of line passing
through point (1, 2, -4) and perpendicular to the lines 
and 
and
5. Find
the equation of plane passing through points (3, 4, 1) and (0, 1, 0) and
parallel to line 
.
.
6.
Find the coordinates of the foot of
perpendicular and perpendicular distance of point P(3, 2, 1)
from the plane 2x – y + z +1 = 0. Find also image of the
point in the plane.
7. Find
the coordinates of image of point (1, 3, 4) in the plane 2x – y +z + 3 = 0.
8. From
the point P (1, 2, 4) a perpendicular is drawn on the plane 2x + y – 2z +3 = 0. Find the equation, the
length, and the coordinates of foot of perpendicular.
9. Find
the image of the point (1, 6, 3) on the line 
. Also, write the equation of the line joining the
given points and its image and find the length of segment joining given point
and its image.
. Also, write the equation of the line joining the
given points and its image and find the length of segment joining given point
and its image.
10.
Find the perpendicular distance of the point (2,
3, 4) from the line
Also find
coordinates of foot of perpendicular.
Also find
coordinates of foot of perpendicular.
11.Find
the equation of plane through the intersection of the planes 3x – y + 2z -4 = 0
and x + y +z – 2 = 0 and the point (2, 2, 1).
12.Find the equation of plane which contains the line of intersection
of planes 
and which is perpendicular to plane 
13. Find the equation of plane(s) passing through the intersection of
planes x + 3y + 6 = 0 and3x – y - 4z = 0.
and whose perpendicular distance
from origin is unity.
14. Find the equation of plane passing through the line of
intersection of planes 2x + y – 6 = 3
and 5x
– 3y + 4z +9 = 0.and parallel to the line 
15. Find the equation of plane which contains the line of intersection
of planes
and parallel to X – axis.
Class 12
1: Revise all the all chapters done in class till October.
2: prepare viva of project of CBSE practical examination.
3: Solve selection Test paper.
4: Complete practical Files of Chemistry.
HOLIDAY HOME WORK
XII C
1. Solve selection test paper again to correct
your mistakes.
2. Thoroughly revise entire syllabus
covered till now in class.
MRS. RANJANA VIRMANI
HOLIDAY HOMEWORK CLASS 12
1.
REVISE ALL CHAPTERS OF SELECTION PAPER AND
PREPARE FOR TEST.
2.
SOLVE SELECTION TEST PAPER IN ASSIGNMENT COPY.
3.
COMPLETE PRATICAL FILE.
4.
PREPARE FOR VIVA OF THE PROJECT TO BE SUBMITTED
FOR BOARD PRACTICAL EXAM.
5.
SOLVE 10 SAMPLE PAPER/PREVIOUS YEAR BOARD
PAPERS.
HOLIDAY HOME WORK
XII A + B +C
Computer
Science
Five years
board papers solved.
+
Complete
practical files and any one Project.
