Wednesday, 30 April 2014
Monday, 28 April 2014
bio question to be done in notebook
Why is small intestine
in herbivores longer than in carnivores?
2. What will happen if mucus is not secreted by the gastric
glands?
3. What is the
significance of emulsification of fats?
4. What causes
movement of food inside the alimentary canal?
5. Why does
absorption of digested food occur mainly in the small intestine?
5 marks
1. Explain the process of nutrition in Amoeba.
2. Describe the alimentary canal of man.
3 Draw the diagram of alimentary canal of man and label the
following parts. Mouth, Oesophagus,
Stomach, Intestine .
4.How do
carbohydrates, proteins and fats get digested in human beings?
- “All plants give out oxygen during day and carbon dioxide during night”. Do you agree with this statement? Give reason.
2. Why do fishes die when taken out of water?
3. How does aerobic respiration differ from anaerobic
respiration?
4.Why is the rate of
breathing in aquatic organisms much faster than in terrestrial organisms?
5. Name the energy currency in the living organisms. When
and where is it produced?
Long answer
1. Explain the three pathways of breakdown in living
organisms.
Short answer 2 mark
1. Differentiate between an artery and a vein.
2. Why is blood circulation in human heart called double
circulation?
3. What is the
advantage of having four chambered heart? Why do veins have thin walls as
compared to arteries?
4. What will happen
if platelets were absent in the blood?
Long answer
1.
Describe the flow of blood through the heart of
human beings.
2 marks
1. Why and how does water enter continuously into the
root xylem?
2. Why is transpiration important for plants?
3. How do leaves of plants help in excretion?
4. What is translocation? Which part of plant help in
that?
5 marks
Describe the process of urine formation in kidneys.
practicals to be written in holiday home work for bio
1.To prepare a
temporary mount of a leaf peel to show stomata.
2.To show
experimentally that light is necessary for photosynthesis.
3. To show
experimentally that carbon dioxide is given out during respiration.
Thursday, 24 April 2014
Wednesday, 23 April 2014
SOURCES OF ENERGY-QUESTION BANK
(Question Bank)
Very Short Answers (1 Mark)
1. What is a good source of energy.
2. Expand CNG and LPG
3. What is the minimum wind velocity required to obtain useful energy with a wind mill?
4. Name the main constituent of biogas.
5. Give two examples of fossil fuels
6. Name the device which directly converts solar energy into electric energy.
7. What does “OTEC” stand for?
8. What is nuclear energy?
9. Which one out of these is renewable source of energy solar energy, coal, petroleum, bio gas.
10. Which source of energy would you use to heat your food and why?
Short Answers (2 or 3Marks)
1. State two disadvantages of using fossil fuels as a source of energy.
2. Write two disadvantages of constructing high rising dams.
3. Give (i) two limitations and (ii) two advantages of wind mill.
4. Name any three forms of energy of the oceans which can be converted into usable energy forms. Describes how it is done in each case.
5. Explain the working of biogas plant with the help of labelled diagram
6. Explain the principle on which the solar cooker works.
7. Write the advantages and disadvantages of using a solar cooker.
8. How does hydro electric power plant operate? Draw diagram
Long Answer Type Questions (5 Marks)
1. (a) Why is the solar cooker box covered with plane glass plate?
(b) Why is nuclear fission reaction considered better.
(c) Use of wood as a domestic fuel is not considered as good. State two reasons for it
2. Distinguish between renewable and non renewable sources of energy? Which one of them you consider as better? Why?
REAL NUMBERS-KEY POINTS
(A)
Main Concepts and Results
• Euclid’s Division
Lemma :
Given two positive
integers a and b, there exist unique
integers q and
r satisfying a = bq + r, 0 £ r <
b.
• Euclid’s Division
Algorithm to obtain the HCF of two positive integers, say c and d,
c > d.
Step
1 : Apply Euclid’s division lemma to c and d, to find
whole numbers q and r, such that c = dq + r,
0 £r < d.
Step
2 : If r = 0, d is the HCF of c and d.
If r ≠¹
0, apply the division lemma to d and r.
Step
3 : Continue the process till the remainder is zero. The divisor at
this stage will be the required HCF.
• Fundamental
Theorem of Arithmetic : Every composite number can be expressed as a product of
primes, and this expression (factorisation) is unique, apart from the order in
which the prime factors occur.
• Let p be a
prime number. If p divides a2, then p divides a,
where a is a positive integer.
• √2 , √3 , √5 are
irrational numbers.
• The
sum or difference of a rational and an irrational number is irrational.
• The
product or quotient of a non-zero rational number and an irrational number is irrational.
• For
any two positive integers a and b,
HCF (a, b) × LCM (a, b) = a
× b.
• Let
x = p/q , p and q are co-prime, be a rational number whose
decimal expansion terminates. Then, the prime factorisation of q is of
the form 2m.5n; m, n are
non-negative
integers.
• Let x = p/q be
a rational number such that the prime factorisation of q is not of the form
2m.5n; m, n being
non-negative integers. Then, x has a non-terminating
repeating decimal
expansion.
(B)
Multiple Choice Questions
Choose the correct
answer from the given four options:
Sample
Question 1 : The decimal expansion of the rational number 33/
22 x 5 will terminate after
(A) one decimal
place (B) two decimal places
(C) three decimal
places (D) more than 3 decimal places
Solution
: Answer (B)
Sample
Question 2 : Euclid’s division lemma states that for two positive integers a
and b, there
exist unique integers q and r such that a = bq + r,
where r must satisfy
(A) 1 < r <
b (B) 0 < r £ b
(C) 0 £ r < b (D)
0 < r < b
Solution
: Answer (C)
EXERCISE
1.1
Choose the correct
answer from the given four options in the following questions:
1.
For some integer m, every even integer is of the form
(A) m (B) m
+ 1
(C) 2m (D) 2m
+ 1
2.
For some integer q, every odd integer is of the form
(A) q (B) q
+ 1
(C) 2q (D) 2q
+ 1
3.
n2 – 1 is divisible by 8, if n is
(A) an integer (B)
a natural number
(C) an odd integer
(D) an even integer
4.
If the HCF of 65 and 117 is expressible in the form 65m –
117, then the value of m is
(A) 4 (B) 2
(C) 1 (D) 3
5.
The largest number which divides 70 and 125, leaving remainders
5 and 8, respectively, is
(A) 13 (B) 65
(C) 875 (D) 1750
6.
If two positive integers a and b are written as
a = x3y2
and b = xy3; x, y are prime numbers,
then HCF (a, b) is
(A) xy (B) xy2
(C) x3y3 (D) x2y2
7.
If two positive integers p and q can be expressed
as
p = ab2
and q = a3b; a, b being prime
numbers, then LCM (p, q) is
(A) ab (B) a2b2
(C) a3b2 (D) a3b3
8.
The product of a non-zero rational and an irrational number is
(A) always
irrational (B) always rational
(C) rational or
irrational (D) one
9.
The least number that is divisible by all the numbers from 1 to
10 (both inclusive) is
(A) 10 (B) 100 (C)
504 (D) 2520
10.
The decimal expansion of the rational number
14587/1250 will
terminate after:
(A) one decimal
place (B) two decimal places
(C) three decimal
places (D) four decimal places
(C)
Short Answer Questions with Reasoning
Sample
Question 1: The values of the remainder r, when a positive integer a
is divided by 3 are 0 and 1 only. Justify your answer.
Solution
: No.
According to Euclid’s
division lemma,
a =
3q + r, where 0 £ r < 3 and r is an integer. Therefore, the values of r
can be 0, 1 or 2.
Sample
Question 2: Can the number 6n, n being a natural
number, end with the digit 5? Give reasons.
Solution
: No, because 6n = (2 × 3)n = 2n
× 3n, so the only primes in the factorisation of 6n are
2 and 3, and not 5. Hence, it cannot end with the digit 5.
EXERCISE
1.2
1.
Write whether every positive integer can be of the form 4q +
2, where q is an integer. Justify your answer.
2.
“The product of two consecutive positive integers is divisible
by 2”. Is this statement true or false? Give reasons.
3.
“The product of three consecutive positive integers is divisible
by 6”. Is this statement true or false”? Justify your answer.
4.
Write whether the square of any positive integer can be of the
form 3m + 2, where m is a natural number. Justify your answer.
5.
A positive integer is of the form 3q + 1, q being
a natural number. Can you write its square in any form other than 3m +
1, i.e., 3m or 3m + 2 for some integer m? Justify your
answer.
6.
The numbers 525 and 3000 are both divisible only by 3, 5, 15, 25
and 75. What is HCF (525, 3000)? Justify your answer.
7.
Explain why 3 × 5 × 7 + 7 is a composite number.
8.
Can two numbers have 18 as their HCF and 380 as their LCM? Give
reasons.
9.
Without actually performing the long division, find if
987/ 10500 will
have terminating or non-terminating (repeating) decimal expansion. Give reasons
for your answer.
10.
A rational number in its decimal expansion is 327.7081. What can
you say about the prime factors of q, when this number is expressed in
the form p/q ? Give reasons.
(D)
Short Answer Questions
Sample
Question 1: Using Euclid’s division algorithm, find which of the following
pairs of numbers
are co-prime:
(i) 231, 396 (ii)
847, 2160
Solution
: Let us find the HCF of each pair of numbers.
(i) 396 = 231 × 1 +
165
231 = 165 × 1 + 66
165 = 66 × 2 + 33
66 = 33 × 2 + 0
Therefore, HCF =
33. Hence, numbers are not co-prime.
(ii) 2160 = 847 × 2
+ 466
847 = 466 × 1 + 381
466 = 381 × 1 + 85
381 = 85 × 4 + 41
85 = 41 × 2 + 3
41 = 3 × 13 + 2
3 = 2 × 1 + 1
2 = 1 × 2 + 0
Therefore, the HCF
= 1. Hence, the numbers are co-prime.
Sample
Question 2: Show that the square of an odd positive integer is of the form 8m
+ 1, for some whole number m.
Solution:
Any positive odd integer is of the form 2q + 1, where q
is a whole number.
Therefore, (2q +
1)2 = 4q2 + 4q + 1 = 4q (q +
1) + 1, (1)
q (q
+ 1) is either 0 or even. So, it is 2m, where m is a whole
number.
Therefore, (2q +
1)2 = 4.2 m + 1 = 8 m + 1. [From (1)]
Sample
Question 3: Prove that √2 + √3 is
irrational.
Solution
: Let us suppose that 2 + √3 is
rational. Let 2 +√ 3 = a
, where a is rational.
Therefore, √2 = a- √3
Squaring on both
sides, we get
2 = a2
+ 3 – 2a √3
Therefor
√ 3=
a2 +1/2a
which is a contradiction as the right hand
side is a rational number while√ 3 is
irrational. Hence, √2 + √3 is
irrational.
EXERCISE
1.3
1.
Show that the square of any positive integer is either of the
form 4q or 4q + 1 for some integer q.
2.
Show that cube of any positive integer is of the form 4m, 4m +
1 or 4m + 3, for some integer m.
3.
Show that the square of any positive integer cannot be of the
form 5q + 2 or 5q + 3 for any integer q.
4.
Show that the square of any positive integer cannot be of the
form 6m + 2 or 6m + 5 for any integer m.
5.
Show that the square of any odd integer is of the form 4q +
1, for some integer q.
6.
If n is an odd integer, then show that n2 – 1 is
divisible by 8.
7.
Prove that if x and y are both odd positive
integers, then x2 + y2 is even but not divisible
by 4.
8.
Use Euclid’s division algorithm to find the HCF of 441, 567,
693.
9.
Using Euclid’s division algorithm, find the largest number that
divides 1251, 9377 and 15628 leaving remainders 1, 2 and 3, respectively.
10.
Prove that 3+ 5 is
irrational.
11.
Show that 12n cannot end with the digit 0 or 5 for any
natural number n.
12.
On a morning walk, three persons step off together and their
steps measure 40 cm, 42 cm and 45 cm, respectively. What is the minimum
distance each should walk so that each can cover the same distance in complete
steps?
13.
Write the denominator of the rational number
257/ 5000 in
the form 2m × 5n, where m, n
are non-negative integers. Hence, write its decimal expansion, without
actual division.
14. Prove
that p + q is
irrational, where p, q are primes.
(E)
Long Answer Questions
Sample
Question 1 : Show that the square of an odd positive integer can be of the
form 6q + 1
or 6q + 3 for some integer q.
Solution
: We know that any positive integer can be of the form 6m,
6m + 1, 6m + 2,
6m + 3, 6m
+ 4 or 6m + 5, for some integer m.
Thus, an odd
positive integer can be of the form 6m + 1, 6m + 3, or 6m + 5
Thus we have:
(6 m +1)2
= 36 m2 + 12 m + 1 = 6 (6 m2 +
2 m) + 1 = 6 q + 1, q is an integer
(6 m + 3)2
= 36 m2 + 36 m + 9 = 6 (6 m2 + 6 m
+ 1) + 3 = 6 q + 3, q is an integer
(6 m + 5)2
= 36 m2 + 60 m + 25 = 6 (6 m2 + 10 m
+ 4) + 1 = 6 q + 1, q is an integer.
Thus, the square of
an odd positive integer can be of the form 6q + 1 or 6q + 3.
EXERCISE
1.4
1.
Show that the cube of a positive integer of the form 6q +
r, q is an integer and
r =
0, 1, 2, 3, 4, 5 is also of the form 6m + r.
2.
Prove that one and only one out of n, n + 2 and n
+ 4 is divisible by 3, where n is any positive integer.
3.
Prove that one of any three consecutive positive integers must
be divisible by 3.
4.
For any positive integer n, prove that n3 – n is
divisible by 6.
5.
Show that one and only one out of n, n + 4, n +
8, n + 12 and n + 16 is divisible by 5, where n is any
positive integer.
[Hint:
Any positive integer can be written in the form 5q, 5q+1,
5q+2, 5q+3, 5q+4].
Question-Bank
Section-A Objectives(1 mark Q.)
1)
Express 140 as a product of its prime factors.
2)
Find the LCM and HCF of 12, 15 and 21 by the prime
factorization method.
3)
Find the LCM and HCF of 6 and 20 by the prime factorization
method.
4)
State whether 3125/13
will have a terminating decimal expansion or a non-terminating repeating
decimal.
5)
State whether 8/17 will have a terminating decimal expansion
or a non-terminating repeating decimal.
6)
Express 156 as a product of its prime factors.
7)
Find the LCM and HCF of 17, 23 and 29 by the prime
factorization method.
8)
Find the HCF and LCM of 12, 36 and 160, using the prime
factorization method.
9)
State whether 15/6
will have a terminating decimal expansion or a non-terminating repeating decimal.
10)
State whether 50/35
will have a terminating decimal expansion or a non-terminating repeating decimal.
11)
Express 3825 as a product of its prime factors.
12)
Find the LCM and HCF of 8, 9 and 25 by the prime
factorization method.
13)
Find the HCF and LCM of 6, 72 and 120, using the prime factorization
method.
14)
State whether 343/29 will have a terminating decimal
expansion or a non-terminating repeating decimal.
15)
State whether 23/ 23
X 52 will have a terminating decimal expansion or a
non-terminating repeating decimal.
16)
Express 5005 as a product of its prime factors.
17)
Find the LCM and HCF of 24, 36 and 72 by the prime
factorization method.
18)
Find the LCM and HCF of 96 and 404 by the prime
factorization method.
19)
State whether 455/64 will have a terminating decimal
expansion or a non-terminating repeating decimal.
20)
State whether 1600/15 will have a terminating decimal
expansion or a non-terminating repeating decimal.
21)
What is the maximum no. of factors of a prime number?
22)
Given HCF of (16, 100) = 4. Find L.C.M of L (16, 100).
23)
Write a rational no. between √2 and √3.
24)
Write if 343/28 is a terminating or non-terminating repeating decimal
without doing actual division.
25)
Tell whether the prime factorization of 15 is 1× 3× 5 or not.
26)
If x and y are two irrational numbers then tell whether x - y is always irrational or not.
27)
What is the L.C.M of x and y is
a multiple of x?
28)
Write the sum of exponents of
prime factors of 98.
29)
State if (√2 – √3) (√2 + √3) is
rational or irrational.
30)
Express 0.03 as a rational number in the form of p/q.
Section-B(3 marks Q.)
31)
Find the LCM and HCF
of 26 and 91 and verify that LCM × HCF = product of the two numbers.
32)
Use Euclid’s division algorithm to find the HCF of 135 and 225
33)
Use Euclid’s division lemma to show that the square of any
positive integer is either of the form 3m or 3m + 1 for some integer m.
34)
Prove that 3 is irrational.
35)
Show that 5 – root 3
is irrational.
36)
Show that any
positive odd integer is of the form 6q + 1, or 6q + 3, or 6q +
5, where q is some integer.
37)
An army contingent of
616 members is to march behind an army band of 32 members in a parade. The two
groups are to march in the same number of columns. What is the maximum number
of columns in which they can march?
38)
Find the LCM and HCF
of 192 and 8 and verify that LCM × HCF = product of the two numbers.
39)
Use Euclid’s
algorithm to find the HCF of 4052 and 12576.
40)
Show that any positive odd integer is of the form of 4q + 1
or 4q + 3, where q is some integer.
41)
Use Euclid’s division
lemma to show that the square of any positive integer is either of the form 3m
or 3m + 1 for some integer m.
42)
Prove that 3- root 2 5 is irrational.
43)
Prove that Root 2 is
irrational.
44)
In a school there are two sections- section A and Section B
of class X. There are 32 students in section A and 36 students in section B.
Determine the minimum number of books required for their class library so that
they can be distributed equally among students of section A or section B.
45)
Find the LCM and HCF
of 336 and 54 and verify that LCM × HCF = product of the two numbers.
46)
Use Euclid’s division algorithm to find the HCF of 867 and
255
47)
Show that every
positive even integer is of the form 2q, and that every positive odd
integer is of the form 2q + 1, where q is some integer.
48)
Use Euclid’s division lemma to show that the cube of any
positive integer is of the form 9m,9m + 1 or 9m + 8
49)
Prove that 7 5 is irrational.
50)
Prove that 5 is
irrational.
51)
There is a circular
path around a sports field. Sonia takes 18 minutes to drive one round of the field,
while Ravi takes 12 minutes for the same. Suppose they both start at the same
point and at the same time, and go in the same direction. After how many
minutes will they meet again at the starting point?
52)
Find the LCM and HCF
of 510 and 92 and verify that LCM × HCF = product of the two numbers.
53)
Use Euclid’s division algorithm to find the HCF of 196 and
38220
54)
Use Euclid’s division
lemma to show that the cube of any positive integer is of the form 9m,9m + 1 or
9m + 8.
55)
Show that every positive odd integer is of the form 2q, and
that every positive odd integer is of the form 2q + 1, where q is some integer.
56)
Show that√ 3+√ 2 is
irrational.
57)
Prove that 3 + √ 5 is
irrational.
58)
A sweetseller has 420
kaju barfis and 130 badam barfis. She wants to stack them in such
a way that each stack has the same number, and they take up the least area of
the tray. What is the maximum number of barfis that can be placed in
each stack for this purpose?
59)
Explain why 7 ×13× 13 + 13 and 7× 6× 5 ×4× 3 ×2 ×1 +5 are composite
numbers.
60)
Show that one and only one out
of n, n+4, n+8, n+12 and n+ 16 is division by 5 where n is any positive
integer.
61)
Show that the sum and product
of two irrational numbers 7+√5 and 7-√5 are rational numbers
62)
Use Euclid’s division lemma to find the H.C.F of 615 and 154.
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