Download Homework for Maths For Classes VII to XII

Summer Break Holiday Home Work for Class X A 2016-17
Q.1
Find the zeroes of the quadratic polynomial 𝑥 2 + 11𝑥 + 30
Q.2
If 𝑥 + 𝑎 is a factor of 2𝑥 2 + 2𝑎𝑥 + 5𝑥 + 10 , 𝑓𝑖𝑛𝑑 𝑎
Q.3
Find all the zeroes of the polynomial
𝑥 4 + 𝑥 3 − 34𝑥 2 − 4𝑥 + 120 , 𝑖𝑓 𝑡𝑤𝑜 𝑜𝑓 𝑖𝑡𝑠 𝑧𝑒𝑟𝑜 𝑎𝑟𝑒 2 𝑎𝑛𝑑 − 2
Q.4
If the product of zeroes of the polynomial 𝑎𝑥 2 − 6𝑥 − 6 𝑖𝑠 4 find the value of a.
Q.5
Use Euclid's division algorithm to find the HCF of 56 and 814
Q.6
Find HCF and LCM of 96 and 404 using fundamental theorem of arithmetic.
Q.7
Show that √5 is irrational.
Q.8
Find a quadratic polynomial whose zeroes are 5 and - 5
Q.9
If 1 is a zero of the polynomial 𝑝(𝑥) = 𝑎𝑥 2 − 3 (𝑎 − 1)𝑥 − 1 , 𝑡ℎ𝑎𝑛
Find the value of a
Q.10 Find all the zeroes of the polynomial
𝑥 4 + 𝑥 3 − 34𝑥 2 − 4𝑥 + 120 , 𝑖𝑓 𝑡𝑤𝑜 𝑜𝑓 𝑖𝑡𝑠 𝑧𝑒𝑟𝑜 𝑎𝑟𝑒 2 𝑎𝑛𝑑 − 2
Q.11 If the product of zeroes of the polynomial 𝑎𝑥 2 − 6𝑥 − 6 𝑖𝑠 4 find the value of a.
Q.12 If 𝑥 + 𝑎 is a factor of 2𝑥 2 + 2𝑎𝑥 + 5𝑥 + 10 , 𝑓𝑖𝑛𝑑 𝑎
Q.13 For what value of m the following pair of linear equations represent parallel
lines ?
4𝑥 + 𝑚𝑦 − 8 = 0
3𝑥 − 5𝑦 + 7 = 0
Q.14 For what value of K the following pair of linear equations has no
solutions.
3𝑥 + 𝑦 = 1
(2𝑘 − 1)𝑥 + (𝑘 − 1)𝑦 = 2𝑘 + 1
Q.15
Determine the values of a and b for which following system of linear equation
has infinitely many solutions.
2𝑥 − (𝑎 − 4)𝑦 = 2𝑏 − 1
4𝑥 − (𝑎 − 1)𝑦 = 5𝑏 − 1
Q.16
solution?
For what value of, a, the system of equation given below will have no
𝑎𝑥 + 3𝑦 = 𝑎 − 3
12𝑥 + 𝑎𝑦 = 𝑎
Q.17
Solve the following system of equation using the method of elimination by
substitution.
𝑥 + 𝑦 = 7 𝑎𝑛𝑑 3𝑥 − 2𝑦 = 11
Q.18
Solve graphically
(i)
2𝑥 − 3𝑦 = 2 ;
𝑥 + 2𝑦 = 8
(ii)
3𝑥 + 4𝑦 = 5 ;
3𝑥 − 2𝑦 + 7 = 0
(iii)
3𝑥 − 𝑦 = 5 ;
2𝑥 − 𝑦 = 3
(iv)
𝑥+𝑦 =3;
2𝑥 + 5𝑦 = 12
(v)
𝑥 − 2𝑦 = 2 ;
3𝑥 + 5𝑦 = 17
Q19. Find the HCF of 344 and 60 by the prime factorisation method.
Hence find their L.C.M.
Q20.
Using division algorithm, find the largest number which divides the three
numbers 120, 224, 256
Summer Break Holiday Home Work for Class IX 2016-17
Q.1 Factorise:
x2-7x+6
x2+5x+6,x2-11x+30,39x2-7x-22, x2-5x+6,
Q.2 Find: (a) (x3-y3)3 + (y3-z3)3 + (z3-x3)3
(b) (x-y) 3+(y-z) 3+ (z-x) 3
(x-y) (y-z) (z-x)
Q.3 Solve the all examples of chapter 6(lines & angles).
Q.4 Draw the spiral of root 7.
Q.5 Factorise: x3+512, 343y3-1000z3, 8x3+27y3+z3-18xyz,
x4-x, y3-1331z3,1+729x3,
P3q3r3-64z3,
1728a3+1.
125a3-
64/125b3,
49x2-1/9y2,
Summer Break Holiday Home Work for Class VII A
2016-17
Q.1 Write all the Prime & composite numbers upto 100.
Q.2 Find :
500005/5 ,1331/11 ,
1024/32 , 56275/2 .
Q.3 Learn the Tables upto 30.
Q.4 Add : 2/3 +7/8
¼ ,6 7/8 + 5 5/6 ,
,11/8 +3/7 ,54/7 +113/2 ,1 ¼ + 5
Q.5 Subtract : ½ -1/3 , 13/3 -11/7 ,11/7 -5/3
Q.6 Simplify : 23/5 *11/3 , 1 ½ * 3 2/3 , 5/7 * 8/3
Q.7 Divide : 4/3 ÷ 11/7 , 12/7 ÷ 13/3 , 7/8 ÷ 19/9
Q.8
Convert into Kg.
450 g ,2356 g ,4 kg 324 g, 8 kg 5678 g.
Q.9
8l.
Sum : 8 kg 950 g & 7 kg 657 g , 19 kl 6 l & 23 kl
Q.10
Solve all examples of chapter 3 ( data handling).
Summer Break Holiday Home Work for Class XII A
2016-17
1 marks questions
SECTION- A
1. Construct 2  3 matrix A = [a ij] whose elements a ij is given by a ij
2

2i  j
=
3
x  y
z  2 3  2 2  6
0
0




x 6  1 0  1 5 2 x  y 5
2  1
1
Given a matrix A = 
. Find matrix kA , where k =

2
4 2 
2. Find the value of variables if 
 4
3.
4.
.
6
Find the value of x , such that the points (0,2),(1,x),(3,1) are collinear.
5.How many orders are possible for a matrix having 15 elements?
If A be square matrix of order 3x3 and IAI=5 then find the value of I3AI.
7. If A be nonsingular matrix of order 3x3 and IAI=5 then find the value of I adjAI.
Ans 135
Ans 25
8. Find equation of line joining (1, 2) and (3, 6) using determinants .
9.If A and B are symmetric matrices of the same order, then AB-BA is skew symmetric or symmetric
matrices.
Ans skew symmetric
10.
x
 1 0 
+   =  .

2 y 
 4  3
Find x and y.if 
4 marks questions
SECTION-B
b 2c 2
1. Show that value of determinant is zero c 2 a 2
b.c b  c
c.a c  a
a 2b 2
a.b a  b
 1 2
2.Express the matrix as sum of symmetric and skew-symmetric matrices 

 5 4
1 a a3
3.Using the properties show that 1 b
b 3 = (a - b)(b – c )(c - a)(a + b + c)
1 c
c3
4.Using PMI
1  2n  4n 
3  4 
Show that An = 

1  2n 
 n
  1
If A = 
1
 2 3
5.Find the inverse of matrix using elementary transformation 

 2 4
1 a b.c
6.Using the properties show that 1 b c.a
1 c a.b
=
1 a a2
1 b b2
1 c c2
x  4 2x
2x
2
7. Using the properties show that 2 x
x  4 2 x = 5 x  44  x 
2x
2x x  4
1 a a 2  b.c
8. Show that value of determinant is zero 1 b b 2  c.a
1 c
c 2  a.b
9. Using the properties show that
a  b  2c
a
b
c
b  c  2a
b
= 2(a + b + c) 3
c
a
c  a  2b
a 2  1 a.b
10. Show that (1 + a 2  b 2  c 2 ) is a factor of a.b
b2 1
a.c
b.c
6marks question
SECTION-C
1  1 0

 and
1.Given that A  2 3 4


0 1 2
2  4
2
B   4 2  4
 2  1 5 
a.c
b.c
c2 1
Find AB, hence use this to solve the following system of linear equations
x  y  3 ,2 x  3 y  4 z  17 , y  2 z  7
Ans. AB  61 , x  2
y  1 , z  4
2. Prove that
(b  c) 2
Q.3.
Ans.
a2
a2
b2
(c  a ) 2
b2
c2
c2
 2abc(a  b  c)3
( a  b) 2
Solve the equations using matrix method
x + 2y  3z = 6
3x + 2y  2 z = 3
2x  y  z = 2
x = 1, y = 5, z = 5
.
1  1 1 


4. For A  2 1  3  ,Find A–1 and hence solve the system of equations


1 1
1
x  2y  z  4
x yz  0
x  3y  z  2
Ans  x 
9
,
5
y
2
, and
5
z
7
is the required solution
5
2 4  1

 and
Q5. Given that A  3 0 2


1 5 2 
 10  13 8 
B    4
5
 7 
 15  6  12
Find the product of matrices AB, and hence solve the system of linear equations
2 x  4 y  z  10 ,3x  2 z  5 , x  5 y  2 z  7
Ans
x
7
38
32
,y  ,z  
17
17
17
5. Solve the following system of equation by matrix method
3x-2y+3z=8, 2x+y-z=1, 4x-3y+2z=4
Ans: x=1, y=2,z=3
2 −3 5
6. If A= [3 2 −4] Find A -1 Solve the system of equation 2x-3y+5z=11,
1 1 −2
3x+2y-4z=-5, x+y-2z=-3
x=1,y=2,z=3
0 −1 2
−2 0 1
7. Use product [0 2 −3] [ 9 2 −3] and hence solve the system of equation x-y+2z=1
3 −2 4
6 1 −2
2y-3z=1, 3x-2y+4z=2
Ans: x=0, y=5,z=3
8. Solve the following system of equation by matrix method
X-y+2z=7, 3x+4y-5z=-5, 2x-y+3z=12
Ans: x=2, y=1, z=3
Using elementary transformation find the inverse of the following matrices if exists
9
2
[2
3
−3 3
2 3]
−2 2
−2 0
Ans: 1/5 [−1 1
2 1
3
0]
−2
10
2
[5
0
0 −1
1 0]
1 3
3
−1 1
Ans: [−15 6 −5]
5
−2 2
Topic :- Continuity And Differentiability
(One Mark Questions)
1. The radius of a circle is increasing uniformly at the rate of 3cm/sec. Find the
rate at which the area of circle is increasing when the radius is 10cm.
2. A balloon which always spherical, has a variable diameter 3/2(2x+1). Find
the rate of change of its volume with respect to x.
3. The total revenue in rupees received from the sale of x units of a product is
given by
R(x) = 13x2 + 26x + 15 , find the marginal revenue when x = 7.
4. Find the rate of change of area of a circle when r = 5cm.
5. The cost function of a firm is given by c 3x2 + 2x -3. Find the marginal cost
when x = 3.
6. Find the slope of the tangent to the curve y = x3 – x at x =2.
7. Find the slope of the normal to the curve y = 2x2 + 3sinx at x = 0.
8. Find the point on the curve y = x2 – 2x + 3, where the tangent is parallel to
x-axis.
𝑥2
𝑦2
9. Find the points on the curve
+ = 1 , where the tangent is parallel to y9
4
axis.
10.Find the angle ∝ , which increase twice fast as fast its line.
Q.No 1
Ans 60π
cm2
/sec
2
27𝜋
(2𝑥 + 1)2
8
ANSWERS
3
4
5
Rs.208 10 π
20
2
cm /sec
6
11
7
8
9
-1/3 (1,2) (±3,0)
Increasing and Decreasing functions
Questions for Practice.
Q.1 Find the intervals in which the function f(x) = -2x3 – 9x2 – 12x + 1is increasing
or decreasing.
Q.2 Find the intervals in which the function f(x) = (x - 1)(x-2)2 is increasing or
decreasing.
Q.3 Find x for which y = [x(x- 2)]2 is an increasing function.
Q.4 Find the intervals in which the function f(x) = 2x3 – 3x2 – 36x + 7is strictly
increasing or strictly decreasing.
Q.5 Find the intervals in which the function f(x) = sinx +cosx, 0≤ x ≤ 2π is strictly
increasing or strictly decreasing.
4𝑠𝑖𝑛𝑥
Q.6 Prove that the function 𝑓(𝑥) =
− 𝑥 is an increasing function of x in [0,
2+𝑐𝑜𝑠𝑥
π/2].
Q.7 Find the intervals in which the function f(x) = (x+1)3 (x-3)3 is increasing or
decreasing.
2𝑥
Q.8 Show that 𝑦 = log(1 + 𝑥) −
, x> - 1 is an increasing function of x
2+𝑥
throught its domain.
Q.9 Show that the function 𝑓(𝑥) = tan−1 (𝑠𝑖𝑛𝑥 + 𝑐𝑜𝑠𝑥) is strictly increasing
function on the interval (0, π/4).
Q.10 Find the value of k for which f(x) = kx3 – 9kx2 + 9 x + 3 is increasing on R.
ANSWERS
10
π/3
Ans.1 Increasing in (-2, -1) and decreasing in (-∞,-2) ∪(-1,∞)
Ans.2 decreasing in (4/3, 2) and increasing in (-∞,4/3) ∪(2,∞)
Ans.3 Increasing in (0, 1) and (2, ∞)
Ans.4 Strictly increasing in (-∞,-2) ∪(3,∞) and decreasing in (-2, 3).
Ans.5 Increasing in [0, π /4 ) ∪ (5 π/4, 2 π] and decreasing in (π/4, 5 π/4).
Ans.7 Increasing in (1,3) ∪ (3, ∞) and decreasing in (-∞, −1) ∪(-1,1).
1
Ans.10 Increasing on R if k∈ (−∞, ).
3
Tangents and Normals
QUESTIONS FOR PRACTICE
Q.1 Find the points on the curve x2 +y2 - 2x – 3 = 0j at which the tangents are
parallel to the x-axis.
Q.2 Find the equation of the tangent line to the curve y= x2 -2x + 7 which is
(i) parallel to the line 2x – y + 9 =0
(ii) perpendicular to the line 5y -15x = 13.
Q.3 Find the points on the curve y = x3 at which the slope of the tangent is equal to
y coordinate of the point.
Q.4 For the curve y = 4x3 -2x5 , find all the points at which the tangent passes to
the origin.
Q.5 Find the equation of the tangent to the curve 𝑦 = √3𝑥 − 2 which is parallel to
the line
4x – 2y + 5 = 0.
Q.6 Find the point at which the tangent to the curve 𝑦 = √4𝑥 − 3 − 1 has its
slope 2/3.
𝑥−7
Q.7 Find the equation of the tangent to the curve 𝑦 = (𝑥−2)(𝑥−3) at the point where
it cuts x-axis.
Q.8 Find the equation of tangent and normal to the curve 𝑥 2/3 + 𝑦 2/3 = 2 at (1,1).
Q.9 Find the point on the curve y = (x-2)2 at which the tangent is parallel to the
chord joining the points (2,0) and (4,4) .
Q. 10 Find the equation of all lines having slope 2 which are tangents to the curve
1
𝑦=
, x≠ 3.
𝑥−3
ANSWERS
Ans.1 (1, ±2)
– 227 = 0
Ans.3 (0, 0) and (3, 27)
Ans.5 48x -24y -23 = 0
Ans.7 20y – x + 7 = 0
Ans.9 (3, 1)
has slope 2.
Ans.2
(i) 2x – y + 3 = 0 (ii) 12x + 36y
Ans.4
Ans.6
Ans. 8
Ans.10
(0,0) , (-1 ,-2), (1,2)
(3,2)
x + y – 2 = 0, x – y = 0
No tangent to the curve which