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1

PLUS ONE
MATHEMATICS REVISION QUESTIONS
CONTENTS
1
...
RELATIONS AND FUNCTIONS………………………
...
TRIGONOMETRIC FUNCTIONS………………………
...
MATHEMATICAL INDUCTION……………………
...
COMPLEX NUMBERS………………………………
...
LINEAR INEQUALITIES……………………………
...
PERMUTATIONS AND COMBINATIONS……………12
8
...
SEQUENCES AND SERIES…………………………
...
STRAIGHT LINES………………………………………17
11
...
19
12
...
21
13
...
22
14
...
STATISTICS……………………………………………
...
PROBABILITY…………………………………………
...
SETS
1
...

b) Find A B and B – A
c) Verify that (A B)-A = B – A
2
...

3
...

b) Verify that (A B) C = A (B C)
4
...
If A = {1} B = {{1}, 2} C = {{1}, 3}
U = {{1}, {2}, {3}, 1, 2, 3} then find
a) A B
b) B C
c) [
]
6
...
Find how many students were taking
neither apple juice nor orange juice
...
Let A = {x: x Z, x2 4} U = {-3, -2, -1, 0, 1, 2, 3, 4}
B = {x: x R, x3 - 3x2 – x – 3 = 0}
Write A and B in Roster form
...
Verify De-Morgan’s Law
...
Consider the set A = {x: x is a letter of the word BALL}
a) Write A in roster form
...

3

9
...

b) Find A B and A B
c) Find A-B and B-A
d) Verify that (A-B) (B-A) = (A B) – (A B)
10
...
Find A B , A B
ii
...
Verify
=A B
11
...
Find A B
ii
...
P(A B) has _______ elements
...
=A B (A B )
=A (B B )
=A U
=A

4

2
...
Consider the relation R={(x, 2x-1) / x
a) Write R in the roster form
...

2
...
g(x)
3
...
A relation from P to P is defined as R = {(x, y): x+y = 0}
a) Find P
b) Draw the relation using an arrow diagram
...

d) How many relations are possible from P to P?
4
...
Give reason
...
Identifies the function from the graph
Y

X’

O

O

Y

Y

X

X’

Y’

Y’

X’
X

O

X

Y’

6
...
14}
...

b) Find the domain and range of R
...
Consider the function
f(x) = 2 - 3x x R, x 0
a) Find its range
b) Draw its graph in the given domain
...
Let A = {1, 2, 3, 4, 5} and R be a relation on A defined by R = {(a, b):
b=a2}
a) Write R in the roster form
...

5

9
...

b) Prove that f(x)
...
If
a) Find the value of x and y
b) If A = {-1, 1} find AxAxA
11
...
Find

i
...
The value of ‘c’ when t(c) =212
...
A function is defined by
F(x) = 1-x : x < 0
1:x=0
x+1: x > 0
i
...

ii
...

13
...
Write the relation in Roster form
...
Write the domain and range of R
...
Is the relation R a function? Justify
14
...

b) What is the number of nonempty relations from A to B?
15
...
Find a & b
...
Let A & B be two sets such that n(A) = 3 & n(B) = 2
...

17
...
TRIGONOMETRIC FUNCTION
1
...
If the horse along a circular path
always keeping the rope tight and describes 88 meters when it has traced
out 72 at the center
...

2
...

Hence evaluate
3
...
Show that
5
...
If tan x= and x is in the third quadrant, find sin x, cos x and other ‘T’
ratios
...
Prove that
8
...


9
...
Find the value of
11
...
Convert

into degree measure and find

13
...
Prove that tan70=2tan50+tan20
15
...
Convert

radian into degree measure
...
Find the general solution of the equation
18
...
Prove that sin(A+B) sin(A-B)=
Hence prove that
20
...

21
...

22
...
Find the degree measure corresponding to
Ans
...


24
...


25
...
Find the general solution of the equation sinx=
27
...
Find the general solution of
29
...
Prove that
31
...
Simplify sin5x-sin3x
33
...
Solve sin2x-sin4x+sin6x=0
35
...
Find tan210
...
Prove that

8

4
...
Let P(n) be the statement 7n - 3n is divisible by 4
...

b) Prove the result by using mathematical induction
...
1+3+32+……
...


3
...
+n3 =
a) Prove that P(1) and P(2) are true
...
Prove that P(k+1) is true
...
Prove by mathematical induction
...
P(n) = 1+
6
...
Consider the statement
P(n) = 1
...
3+3
...
Prove by mathematical induction
P(n) = 1+3+5+……+(2n-1) =
8
...
verify that
P(k+1) is true
...
Show that 41n – 14n is a multiple of 27
...
For every positive integer n, n(n+1)(n+5) is divisible by 3
...
Prove that 2n > n for all n N
...
Prove principle of mathematical induction 102n-1+1 is divisible by 11
...
Prove that 32n+2 – 8n – 9 are divisible by 64 for any positive integer n
...
Prove by principle of mathematical induction that 12+22+……+n2 >
n

N

9

,

5
...
Consider the complex number
Z=
a) Express z in the form a+ib
b) Represent z in the polar form
...
Express the complex number Z =

in the form a+ib
...

3
...
+i99

a) Convert

into a+ib form
...

4
...

5
...
Solve

in the polar form
...

b
...
Represent the complex number z = -1 + i and its conjugate on the
Argand plane
...
(i) Express in polar form of
(ii) Solve
8
...
Find the multiplicative inverse of 2-3i
...

10

10
...


?

11
...

Solve the quadratic equation (x + i) (x + 3) + 7 = 0
12
...
Find a and b
...
LINEAR INEQUALITIES
1
...
Solve the inequality
a) 3(x-1) 2(x-3)
b) Solve geographically
5x + 4y 20
x 1, y 2
3
...
The marks obtained by her in the
second and third examinations are more than 5 and 10 respectively than
in the first examinations
...

Ans
...
(i) Solve the inequality 6 – 3x 2 – 2x
(ii) Solve the following system of inequalities
x+y 6
x + y 4, x 0, y 0
5
...
Solve
a) The longest side of a rectangle is 3 times the shortest side and the
third side is 2cm shorter than the longest side
...
find the minimum length of the
shortest side
...
x+3x+3x-2 61
X 9
7
...

Solve geographically
4x + 3y 12
12

4x – 5y 20
x 1, y 4
8
...
Solve graphically
2x + y 8
x + 2y 10
10
...
PERMUTATIONS AND COMBINATIONS
1
...
How many 4 digit numbers are there with distinct digits
...
In how many distinct ways can be the product
be written without
using exponents
...
If n=5 then evaluate
5
...
n-1 = 5
...
In how many ways can 7 athletes be chosen out of 12?
7
...
The English alphabet has 5 vowels and 21 consonants
...
If there are 12 persons in a party and each of them shake hands with all
others
...
In how many ways can a committee of 3 men and 2 women be selected
out of 7 men and 5 women?
11
...
In how many different ways can the letters of the word HEXAGON be
permuted?
13
...
How many 4 digit numbers are there with no digit repeated?
15
...
If
, then find
17
...

b) How many of these arrangements start with y?
18
...
Find the
number of ways in which the girls are
(i) Together
(ii) Not together
...
Find the value of n if 2n : n =11:1

14

20
...
Find the value of n

=42
...
Find n
23
...
Find r if
25
...
BINOMIAL THEOREM
1
...
1)4
2
...
a) Write the general term in the expansion of
b) Find the term independent of x in the expansion of
4
...

5
...
Expand (a+b)4 – (a-b)4
a) Hence evaluate (
)4 – (
)4
b) Expand (a+b)n
7
...
Hence find the term
independent of x in the above expansion
...
Find the coefficient of x9 in the expansion of (x2 - )9
9
...

10
...

b) If n=5 find its middle term
...
Find the general term in the expansion of
Find the term independent of x in the above expansion
...

a) Expand (x-1)3
b) Compute 993
13
...


14
...

a) Write the general term in the expansion
b) Find the coefficient of the term containing
15
...

16
...


9
...
If the nth term of a sequence is

, then find its first two terms
...
How many terms of the AP -6, -11/2, -5…… are needed to give the sum
-25?
3
...

4
...

5
...
Find the sum of all natural numbers between 100 and 1000 which are
multiplies of 5
...
The 5th, 8th and 11th terms of a GP are p, q and s respectively
...

8
...
and 1, 2, 22……… find the nth term of the AP
and GP
...
The second term of a GP is 3
...

a) Find common ratio
b) Find 8th term
...
Find the sum of n terms of series whose nth term is n(n+3)
...
Find the sum of n terms of series 7+77+777+…
...
Find the 10th term of a GP whose 3rd term is 24 and 6th term is 192
...
Write the two terms of the sequence whose nth term is an=1+(-1)n
14
...
6+0
...
666+……
15
...
If the sum of three numbers in an AP is 24 and their product is 440
...

17
...
Prove that x, y, z are in GP
...
If the nth of a sequence is n2+3n, then find the sum of first 10 terms
...
If the first and the nth term of a GP are ‘a’ and ‘b’ respectively and P is
the product of n terms
...
Find the 10th term of an AP whose nth term is
21
...


22
...


17

23
...


is the A
...
what is the value of n?

25
...
The sum of the third and the fifth term is 90
...

26
...
(2n)2
27
...

b) Find the 20th term
...
If AM and GM of two numbers are 10 and 8 respectively
...

29
...
Find the (m+n)th term
...
The first term of an A
...
What is the common
difference?
31
...
P
...
Then determine
a) Its first term
b) Common ratio
c) Sum to n terms
32
...
P is

and their product is -1
...

33
...
P whose 3rd term is 24 and 6th term is 192
...
STRAIGHT LINES
1
...

b) Find the equation of the line passing through the points A and B
...

Y
2
...
Find the equation of the line which is perpendicular to 3x+2y-8=0 and
passes through the midpoint of the segment joining the points (5,-2) and
(2, 2)
...
Find the angle between the X-axis and the line through (1, 2) and (5, -2)
i
...
Consider the line x cos 30+y sin 30=5
i
...

ii
...

iii
...
The vertices of ABC are A (-2, 3) B (2,-3) and C (4, 5)
i
...

ii
...

7
...

(b) Find the equation of the line passing through the above point of
intersection and parallel to the line x+y+1=0
...
(i) Find the slope and Y intercept of the line 6x+3y-5=0
(ii) Find the equation of the right bisector of the line segment joining the
points (3, 4) and (-1, 2)
9
...

(ii) Point R (h, k) divides a line segment between the axes in the ratio 1:2
...
For what value of X the points (X, -1) (2, 1) and (4, 5) collinear?
11
...

(b) Find the equation of a line perpendicular to the above line passing
through (1, 1)
...
The points A (2, -1) B (0, 2) C (3, 3) D(5, 0) are the vertices of a
quadrilateral ABCD
...

(ii) Write the equations of AC and BD
...

13
...
Find the image of the point (1, 2) through the line joining (6, -1) & (2, 3)
...
(i) A straight line passes through the point (1, 1)
...
Write the equation
(ii) If this has a perpendicular passing through the point (3, 5)
...

(iii) What will be the point of intersection of the line and the
perpendicular?
16
...

(b)Convert the equation of the line 2x-3y+6=0 in to intercept form
...
If the lines joining the points (0, 0) (1, 1) and (2, 2) (4, y) are
perpendicular
...
Find the distance of the point (3, -5) from the line 3x-4y-26=0
...
Find the equation of line that cut off equal intercepts on the co-ordinate
axes and passes through the points (2, 3)
...
Find angles between the lines
,

...
Find the distance between the parallel lines 3x-4y+7=0 and 6x-8y+10=0
...
Consider the line x+3y-7=0
a) The slope of the line is __________
b) Find the equation of line perpendicular to x+3y-7=0 and passing
through (3, 8)
c) Find the point of intersection of the perpendicular line &x+3y-7=0
...
(-1, -4)

20

11
...
Find the equation of the parabola with vertex at (0, 0) and focus at (0, 2)
...
Find the co-ordinates of the foci and the latus rectum of the ellipse
3
...

b) Find the equation of the circle with centre at c and passing through
the point (1, 2)
4
...
Consider the ellipse
(i)
Foci
(ii) Eccentricity
(iii) Length of latus rectum
6
...

7
...

b) Find the equation of an ellipse with eccentricity 0
...

8
...

a) Find the equation of the hyperbola
...

9
...

a) Find the area of the triangle formed by the lines joining the vertex
of the parabola
to the ends of its latus rectum
...

10
...


21

11
...
It is 10m long and is
4m high at the centre
...

c) Find the length of the bridge 3m from the centre
...
Write the equation of the circle passing through the origin and having
(a, 0) (0, b) as the end points of a diameter
...
Find the centre and the radius of the circle
=0
14
...

15
...

16
...
Write an equation in the
standard form
...

17
...

a) Find the equation of the ellipse
...


22

12
...
Three vertices of a parallelogram ABCD are A (3, -1, 2) B (1, 2, -4)
C (-1, 1, 2)
...

2
...

3
...
Find the ratio in which YZ plane divides the line segment formed by
joining the points (-2, 4, 7) and (3, -5, 8)
...
Show that the point A (-3, 2, 4) B (-1, 5, 9) and C (1, 8, 14) are collinear
...
If (

) is the centroid of PQR with vertices P (a, 7, -10)

Q (1, 2b, -6) R (4, 9,3c)
...

Prove that PQR is isosceles
...
Find the third vertex of the triangle whose centroid (7, -2, -1) and whose
other two vertices are (2, 6, -4) and (4, -2, 3)
...
Show that the point (-2, 3, 5) (1, 2, 3) and (7, 0, -1) are collinear
...
Consider the points A (-2, 4, 7) and B (3, -5, 8)
a) If P divides AB is the ratio k: 1 then find the co-ordinates of P
...

10
...
Also find the point of division
...
Find the co-ordinates of the points which trisect the line segment joining
the point P (4, 0, 1) Q (2, 4, 0)
...
Consider the point A (2, 1, 3) and B (1, 2, 1)
a) Find the midpoint
...

c) Also find the point of division
...
Find the equation of the set of points P such that PA2+PB2=2K2 where A
& B are the points (3, 4, 5) and (-1, 3, -7) respectively
...
Consider the points A (4, 8, 10) and B (6, 10, -8)
a) If P divides AB in the ratio K: 1 then find the co-ordinate of P
...


23

13
...
Differentiate from first principles
2
...
r
...
Evaluate
4
...
(i) if f(n)= then
=_____
(ii) if f(x)= then
=_____
6
...

7
...

8
...
Evaluate
10
...
Find the derivative of

w
...
t x

12
...

13
...
Evaluate a)

b)

15
...
Fill in the blanks
a) 1-cos x=_____
b) Sin 2x=______
c) Evaluate
17
...
Find the derivative of a)
19
...
r
...


20
...
Evaluate
22
...
Find the derivative of the function f(x)=
that (0) - (-1) = 2
...
Also prove

24
...
Find the derivative of
26
...

27
...
Evaluate a)

using quotient rule
...
Find the derivative of using first principle
...
Evaluate
31
...
Find the derivative of x2+x+1 from first principles
...
Evaluate
34
...
Find
36
...
The limit of f(x) =

is 108
...
Evaluate
39
...
Evaluate

25

14
...
By giving an example, show that the following statement is not true
...

2
...
Consider the statement “if x is an integer and

is even, then x is also

even
...

b) Prove the statement by the contra-positive method
...
(i) Check whether the statement is true or false
‘The integer n is odd if n2 is odd’
(ii) Write the contrapositive of the following statement
“x is an even number implies that x is divisible by 4
...
“The number 7 is greater than 11” write its negation
...
Write the contrapositive of the following statement
“If a triangle is equilateral, it is isosceles
...
Check whether the following statement is true or false by contrapositive
method
...
”
8
...

P: 25 is a multiple of 5
Q: 25 is a multiple of 8
9
...
Verify by the method of contradiction
P:

is irrational
...
Write the contrapositive of the statement
P: if the physical environment changes then the biological environment
changes
...
Write the negation of the following statement
“Delhi is in India and Moscow is in Russia”
13
...
If b is a multiple of a, then a divides b
...
Consider the compound statement
P: 2+2is equal to 4 or 6
a) Write the component statements
b) Is the compound statement true? Why?
Ans
...
Here connecting word is or
...
Write the negation of the statement
...
it is false that both the diagonals of a rectangle have the same length
...
Write the converse of the statement
If a number n is even, then n2 is even
Ans
...


27

15
...
The sum of 10 observations is 100 and the sum of their squares is 1090
...
Consider the frequency table
Classes

0-30 30-60 60-90 90-120

120-150 150-180 180-210

Frequencies 2
3
5
10
3
5
2
Find the mean and variance
...
Consider the following data
...

b) Find its MD about mean
...
D
...

4
...

Class
10-20
20-30
30-40
40-50
50-60
Frequency
6
15
13
7
9
a) Calculate the mean of the distribution
...

5
...

x
15
21
27
30
35
f
3
5
6
7
8
a) Find its mean
...

c) Find the S
...
Hence find the coefficient of variation
...
From the following frequency distribution
...

b) Calculate variance and standard deviation
...
V
...
Consider the following table
...

b) Find its variance
...
For the frequency distribution
...
V
...
Consider the following numbers
6, 7, 10, 12, 13, 4, 8, 12
a) Find the mean
b) Calculate MD about mean
...
Consider the numbers
4, 7, 8, 9, 10, 12, 13, 17
a) Find mean
...

c) Find standard deviation
...
Find the mean and variance of the first 10 multiplies of 3
...
16
...
25
12
...

=212
=902
...
6
Which is more varying the length or weight?
Ans
...
604, 26
...
The mean and standard deviation of 6 observations are 8 and 4
respectively of each observation is multiplied by 3
...

Ans
...
i) Find the mean of the data 5, 8, 9, 10, 11, 13
...

iii) The following values are calculated in respect of heights and weights
of the students of a class
Height
Weight
Mean
162
...
36 kg
2
Variance
127
...
1361kg2
Which of these heights or weights show greater variation?

29

16
...
If

is the probability of an event what is the probability of the event not

A
...
Consider the experiment of throwing three dice
a) Find the number of sample points
...

c) Find the probability of getting the sum 18
...
Three coins are tossed once
...

4
...
If each outcome
is equally likely
...

5
...

6
...
Consider the following events
A: the sum is a multiple of 3
B: the sum is less than 4
C: the sum is greater than 11
Do they from a set of mutually exclusive events
...
One card is drawn from a well shuffled deck of 52 cards
...
Calculate the probability that the card will be
(i)
A diamond
(ii) Not an ace
...
Two dice are thrown, the events A, B and C are as follows
A: Getting an even number on the first dice
B: Getting an odd number on the first dice
...

9
...

b) Find P (A and B) if A and B are independent events
...
A pair of dice is thrown, then estimate the event of getting an even
number on the first dice
...
A bag contains 9 balls of which 4 are red, 3 are white and 2 are green
...

12
...

30

a) Find P(A or B)
b) P (not A and not B)
13
...
4, P(B)=0
...
(Given that A and B are
mutually exclusive)
...
Two students A and B appeared in an examination
...
25 and B passes is 0
...
Also the probability that both
will passes is 0
...
Find the probability that
a) Both will not pass b) Only one of them will pass
15
...
Consider the following events
A: No head appears
...

C: At least two heads appear
...
A committee of 3 persons is selected from 3 men and 4 women
...
Three coins are tossed once
...
b) Exactly 1 head
...
d) At least 2 heads
...
Two students Anil and Ashima appeared in an examination
...
05 and that Ashima
will qualify the examination is 0
...
the probability that both will qualify
the examination is 0
...
find the probability that
a) Both Anil and Ashima will not qualify the examination
...

19
...
2 balls are drawn at random
...

20
...
If one of these students is selected at
random, find
a) The probability that the student opted for NCC and NSS
...

21
...
Find the
probability that
a) It is either a heart or a queen
...

22
...
Two balls are drawn at
random
...

b) Find the probability that none of the balls drawn are yellow in
colour
...
If A = {5, 8, 4} and B ={8, 4}
a) Which of the given statement is correct [ A=B, A B], A B, A⊃B
b) Which are the all possible subset of A?
c) Find the power set of A
d) If n(A)=5 what is n[P(A)]
e) Suppose P(A)=P(B), then prove that A = B
2
...
For the set A= {-1 0 1} and B= {1, 2}
...
Find the degree measure of the angle subtended at the center of a circle of
radius 100cm by an arc of length 22cm (use
5
...
Find the value of cos 15
...
Solve sin2x-sin4x+sin6x=0
7
...

b) P(n) is the statement 32n – 1 is divisible by 8
...

8
...
Reduce
10
...
a) Calculate 12th term in the expansion of
b) Find term independent of x
12
...

32

c) Given 5flags of different colours, how many different signals can be
generated if each signal requires the use of 2 flags? One below the other?
13
...

b) The sum of two numbers 6 times their G
...
show that numbers are in
the ratio 3 + 2 : 3 - 2
14
...
Find the value of m
...
Find
the image of the point (12) on the line x – 3y+4=0
15
...

b) A coin is tossed and then a die is rolled only in case a head is shown on
the coin
...
A card is drawn from a well-shuffled deck of 52 cards
...

17
...
25 respectively
...
Find the remaining two
observations
...
A) Let P and Q stand for the statement is “Mona Speaks Hindi” and
“Mehul Speaks English”
...

B) Find the truth value of the statement 4 divides 17 or 3+4=7
19
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Find
the ratio in which Q divides PR
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Find the vertex axis, focus, directrix, latus rectum of the parabola
y2 - 8y - x+19=0
21
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22
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23
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Evaluate
25

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