Plus One Maths Previous Year Question Paper 2018

Kerala Plus One Maths Previous Year Question Paper 2018

Time Allowed: 2 1/2 hours
Cool off time: 15 Minutes
Maximum Marks: 80

General Instructions to Candidates :

  • There is a ‘cool off time’ of 15 minutes in addition to the writing time.
  • Use the ‘cool off time’ to get familiar with the questions and to plan your answers.
  • Read instructions carefully.
  • Read questions carefully before you answering.
  • Calculations, figures and graphs should be shown in the answer sheet itself.
  • Malayalam version of the questions is also provided.
  • .Give equations wherever necessary.
  • Electronic devices except non programmable calculators are not allowed in the Examination Hall.

Plus One Maths Previous Year Question Papers and Answers 2018

Answer any six from question nunbers 1 to 7. Each carries three answers.
Plus One Maths Previous Year Question Papers and Answers 2018 QA

Question 1.
Find the sum to n terms of the sequence
4 + 44 + 444 +…………
Plus One Maths Previous Year Question Papers and Answers 2018 Q1

Question 2.
Solve : Sin 2x – Sin 4x + Sin 6x = 0
Plus One Maths Previous Year Question Papers and Answers 2018 Q2
Sin 2x – Sin 4x + Sin 6x = 0

Question 3.
If A and B are events such that P(A)= 1/4;
P(B) =1/2; P(A ∩ B) = 1\6 then find: 2 6
(a) P(A or B)
(b) P(not A and not B)
Plus One Maths Previous Year Question Papers and Answers 2018 Q3
Plus One Maths Previous Year Question Papers and Answers 2018 Q3.1

Question 4.
In a A ABC, prove that
Plus One Maths Previous Year Question Papers and Answers 2018 Q4

Question 5.
(a) The maximum value of the function f(x) = Sin x is………
(i) 1
(ii) √3/2
(iii) 1/2
(iv) 2
(b) Prove that,
(Sin x + Cos x)2 = 1+Sin 2x.
(c) Find the maximum value of Sin x + Cos x.
Plus One Maths Previous Year Question Papers and Answers 2018 Q5

Question 6.
\(\underset { x\rightarrow 2 }{ Lim } \) [x] = …….
i. 2
ii. 3
iii. 0
iv. does not exist
(b) Evaluate: \(\underset { x\rightarrow 2 }{ Lim } \) \(\frac { { x }^{ 3 }-\quad { 4x }^{ 2 }+\quad 4x }{ { x }^{ 2 }-4 } \)
Plus One Maths Previous Year Question Papers and Answers 2018 Q6

Question 7.
Once card is drawn at random from a pack of 52 playing cards . Find the probability that,
(a) the card drawn is black.
(b) the card drawn is a face card.
(c) the card drawn is a black face card
Plus One Maths Previous Year Question Papers and Answers 2018 Q7

Answer any eight from question numbers 8 to 17. Each carries four scores.
Plus One Maths Previous Year Question Papers and Answers 2018 QB

Question 8.
(a) If A={a, b, c}, then write Power Set P(A).
(b) If the numbed of subsets with two elements of a set P is 10, then find the total number of elements in set P.
(c) Find the number of elements in the power set of P.
Plus One Maths Previous Year Question Papers and Answers 2018 Q8

Question 9.
Consider Venn diagram of the Universal Set
U = {1,2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}
U = {1, 2, 3,4, 5, 6, 7, 8, 9, 10, 11, 12, 13}
Plus One Maths Previous Year Question Papers and Answers 2018 Q9
(a) Write sets A, B in Roster form.
(b) Verify (A ∪ B)=A ∩ B
(c) Find n(A ∩ B).
Plus One Maths Previous Year Question Papers and Answers 2018 Q9.1

Question 10.
Consider the following graphs :
Plus One Maths Previous Year Question Papers and Answers 2018 Q10
(a) Which graph does not represent a function?
(b) Identify the function f(x)=1/x. from the above graphs.
(c) Draw the graph of the function f(x)=(x-1)2 .
Plus One Maths Previous Year Question Papers and Answers 2018 Q10.1

Question 11.
The figure shows the graph of a function f(x) which is a semi circle centred at origin.
Plus One Maths Previous Year Question Papers and Answers 2018 Q11
(a) Write the domain and range of f(x).
(b) Define the function f(x).
Plus One Maths Previous Year Question Papers and Answers 2018 Q11.1

Question 12.
a. If 32n+2 – 8n – 9 is divisible by ‘k’ for all n ∈ N is true, then which one of the following is a value of ‘k’ ?
i.8
ii. 6
iii. 3
iv. 12
b. Prove by using the principle of Math­ematical Induction
P(n) = 1+3+32+…………….. +3n-1 = \(\frac { { 3 }^{ n }-1 }{ 2 } \) is true for all n ∈ N.
Plus One Maths Previous Year Question Papers and Answers 2018 Q12

Question 13.
(a) Solve the inequality
Plus One Maths Previous Year Question Papers and Answers 2018 Q13
(b) Represent the solution on a number line.
Plus One Maths Previous Year Question Papers and Answers 2018 Q13.1

Question 14.
(a) Find the nth term of the sequence 3,5,7……………..
(b) Find the sum to n terms of the series. 3xl2 + 5 x22 + 7×32+ ……..
Plus One Maths Previous Year Question Papers and Answers 2018 Q14

Question 15.
Find the equation of the circle passing through the points (4, 1) and (6, 5) and whose centre is on the line 4x + y = 16.
Plus One Maths Previous Year Question Papers and Answers 2018 Q15

Question 16.
Consider a point A(4, 8, 10) in space.
(a) Find the distance of the point A from XY – plane.
(b) Find the distance of the point A from X – axis.
(c) Find the ratio in which the line segm­entjoining the point A and B (6,10, -8) is divided by YZ -plane.
Plus One Maths Previous Year Question Papers and Answers 2018 Q16

Question 17.
(a) Which one of the following sentences is a STATEMENT?
i. 275 is a perfect square.
ii. Mathematics is a difficult subject.
iii. Answer this question.
iv. Today is a rainy day.
(b) Verify by method of contradiction: ‘√2 is irrational’.
Plus One Maths Previous Year Question Papers and Answers 2018 Q17

Answer any five from question numbers 18 to 24. Each carries six scores.
Plus One Maths Previous Year Question Papers and Answers 2018 QC

Question 18.
Consider the quadratic equation x2 + x + 1 = 0
(a) Solve the quadratic equation.
(b) Write the polar form of one of the roots.
(c) If the two roots of the given quadratic are α and β . Show that α2 = β .
Plus One Maths Previous Year Question Papers and Answers 2018 Q18

Question 19.
The graphical solution of a system of linear inequalities is shown in the figure.
Plus One Maths Previous Year Question Papers and Answers 2018 Q19
Plus One Maths Previous Year Question Papers and Answers 2018 Q19.1
(a) Find the equation of the lines L1, L2, L3
(b) Find the inequalities representing the solution region.
Plus One Maths Previous Year Question Papers and Answers 2018 Q19.2

Question 20.
(a) Which one of the following has its middle term independent
i.\({ \left( x+\frac { 1 }{ x } \right) }^{ 10 }\)
ii. \({ \left( x+\frac { 1 }{ x } \right) }^{ 9 }\)
iii. \({ \left( { x }^{ 2 }+\frac { 1 }{ x } \right) }^{ 9 }\)
iv. \({ \left( { x }^{ 2 }+\frac { 1 }{ x } \right) }^{ 10 }\)
(b) Write the expansion of \({ \left( { x }^{ 2 }+\frac { 3 }{ x } \right) }^{ 4 }\)
(c) Determine whether the expansion of  \({ \left( { x }^{ 2 }+\frac { 2 }{ x } \right) }^{ 18 }\)  will contain a term containg x10.
Plus One Maths Previous Year Question Papers and Answers 2018 Q20
Plus One Maths Previous Year Question Papers and Answers 2018 Q20.1

Question 21.
The figure shows an ellipse \(\frac { { x }^{ 2 } }{ 25 } +\frac { { y }^{ 2 } }{ 9 } \)= 1 and a line
Plus One Maths Previous Year Question Papers and Answers 2018 Q21
(a) Find the eccentricity and focus of the ellipse.
(b) Find the equation of the line
(c) Find the equation of the line parallel to line L and passing through any one of the foci.
Plus One Maths Previous Year Question Papers and Answers 2018 Q21.1

Question 22.
(a) Find the derivative of y = Sin x from the first principle.
Plus One Maths Previous Year Question Papers and Answers 2018 Q22

Question 23.
Find n, if
(a) 12 x (n-1) p3 =5 x (n+1) p3
(b) If npr = 840; nCr = 35 find r.
(c) English alphabet has 5 vowels and 21 consonants. How many 4 letter words with two different vowels and two different consonants canbe formed without repetition of letters?
Plus One Maths Previous Year Question Papers and Answers 2018 Q23

Question 24.
Consider the following data:
Plus One Maths Previous Year Question Papers and Answers 2018 Q24
Plus One Maths Previous Year Question Papers and Answers 2018 Q24.1
(a) Find the standard deviation of the distribution.
(b) Find the coefficient of variation of the distribution.
Plus One Maths Previous Year Question Papers and Answers 2018 Q24.2

Answers

Answer 1.
S = 4 + 44 + 444 + 4444+ …. to n terms
Plus One Maths Previous Year Question Papers and Answers 2018 A1

Answer 2.
sin2x – sin4x + sin6x = 0
sin6x + sin2x – sin4x = 0
Plus One Maths Previous Year Question Papers and Answers 2018 A2
Plus One Maths Previous Year Question Papers and Answers 2018 A2.1

Answer 3.
Plus One Maths Previous Year Question Papers and Answers 2018 A3

Answer 4.
Plus One Maths Previous Year Question Papers and Answers 2018 A4
Plus One Maths Previous Year Question Papers and Answers 2018 A4.1

Answer 5.
(a) 1
(b)   (sin x + cosx)2
= sin2x + cos2x + 2sinx cosx
= 1 + sin2x
(c)   Maximum value of sin2x = 1
Maximum value of sinx + cosx
= \(\sqrt { 1+1 } =\sqrt { 2 } \)

Answer 6.
Plus One Maths Previous Year Question Papers and Answers 2018 A6

Answer 7.
Plus One Maths Previous Year Question Papers and Answers 2018 A7

Answer 8.
Plus One Maths Previous Year Question Papers and Answers 2018 A8

Answer 9.
(a) A= {3,4,6,10} B = {2,3,4,5,11}
(b) (A∪B)’ = { 1, 7, 8, 9, 12, 13}
A’ = { 1, 2, 5, 7, 8, 9, 11, 12, 13}
B’ = {1, 6, 7, 8, 9, 10, 12, 13 }
A’∩B’ = {1,7, 8, 9, 12, 13}
∴ (A∪B)’ =A’ ∩B’
(c) n(A∩B)’ = n(U)-n(A∩B)=13-2=11

Answer 10.
a. (b) or (c)
b. (a)
Plus One Maths Previous Year Question Papers and Answers 2018 A10

Answer 11.
(a) Domain = [-4,4]
Range = [0,4]
(b) x2 + y2=16
y2= 16-x2
y= \(\sqrt { 16-{ x }^{ 2 } } \)
i.e.,f (x)= \(\sqrt { 16-{ x }^{ 2 } } \)

Answer 12.
(a) 8
(b) P(n):1 + 3 + 32 + ……..3n-1 =\(\frac { { 3 }^{ n }-1 }{ 2 } \)
Let P(1): 1 =\(\frac { { 3 }^{ 1 }-1 }{ 2 } \)=2/2=1
Hence, P(1) is true.
P(k): 1 + 3 + 32 +…… + 3k-1=\(\frac { { 3 }^{ k }-1 }{ 2 } \)
To prove that P(k+1) is true. P(k+1):
1 + 3 +32 + + 3i_1 +3k+1-1 =\(\frac { { 3 }^{ k+1 }-1 }{ 2 } \)
⇒ P(k)+3k = \(\frac { { 3 }^{ k+1 }-1 }{ 2 } \)
⇒ \(\frac { { 3 }^{ k }-1 }{ 2 } \) + 3k= \(\frac { { 3 }^{ k+1 }-1 }{ 2 } \)
= \(\frac { { 3 }^{ k }-1 }{ 2 } \) + 3k= \(\frac { { { 3 }^{ k } }-1+2\times { 3 }^{ k } }{ 2 } \)
Now, LHS = \(\frac { { { 3\times 3 }^{ k } }-1 }{ 2 } \) =  \(\frac { { 3 }^{ k+1 }-1 }{ 2 } \) = RHS
Hence, P(k+1) is true.
Hence, P(n) is true for all n∈N

Answer 13.
\(\frac { 2x-1 }{ 3 } \ge \frac { 5(3x-3)-4(2-x) }{ 20 } \)
40x-20 ≥ (15x-10-8+4x)3
40x-20 ≥ -54
40x-57x ≥ -54 + 20
-17x ≥-34
x ≤ 2 ⇒ x∈(-∞, 2)
Plus One Maths Previous Year Question Papers and Answers 2018 A13

Answer 14.
(a) tn= 3+(n-1)2 = 2n+1
(b) Let Tn denotes the nth term of the given series.
Tn = (nlh term of 3, 5, 7……….. )(nth term of 12, 22, 32…….. )
= [3+(n-1)2].n2 = (2n+1)n2 = 2n3 + n2
Plus One Maths Previous Year Question Papers and Answers 2018 A14

Answer 15.
Let the equation of the circle be
(x – h)2 + (y – k)2 = r2
Since the circle passes through (4, 1) and (6,5), we have
(4-h)2 + (1 -k)2 = r2……….. (1)
and (6 -h)2 + (5 – k)2 = r2………… (2)
Also since the centre lies on the line 4x + y = 16, we have
4h + k = 16…………. (3)
Solving the equations (1), (2) and (3), we get
h = 3 and k = 4
(4 – 3)2 + (1 – 4)2 = r2
r2=10
Hence, the equation of the required circle is
(x-3)2+1 (y-4)2= 10
x2-6x + 9 + y2-8y + 16-10 = 0
x2 + y– 6x –  8y + 15 = 0

Answer 16.
(a) 10 [Z coordinate of the point]
(b) Let P(4,0,0) be a line on the X-axis.
distance = \(\sqrt { { (4-4) }^{ 2 }+{ (8-0) }^{ 2 }+{ (10-0) }^{ 2 } } \)
= \(\sqrt { 64+100 } =\sqrt { 164 } =2\sqrt { 41 } \)
(c) Since the line segment divided the YZ plane, its x coordinate is zero.
So =\(\frac { { mx }_{ 1 }+{ nx }_{ 1 } }{ m+n } \)
⇒ mx2 + nx1=0
\(\frac { m }{ n } =\frac { { -x }_{ 1 } }{ { x }_{ 2 } } =\frac { -2 }{ 3 } \)
⇒m : n=-2 : 3

Answer 17.
(a) 275 is a perfect square,
(b) Let -√2 is rational.
\(\sqrt { 2 } =\frac { p }{ q } \) , p and q have no common factor.
p2 = 2q2
i.e., 2 divides p2 is 2 divides p
∴ p = 2k, p2 = 4k2
2q2 = 4k2, q2 = 2k2
2 divides q2 is 2 divides q.
p and q have a commonfactor 2.

Answer 18.
Plus One Maths Previous Year Question Papers and Answers 2018 A18

Answer 19.
Plus One Maths Previous Year Question Papers and Answers 2018 A19
b. The inequalities are: x + y ≤ 4, y ≥ 1, y ≤ x

Answer 20.
Plus One Maths Previous Year Question Papers and Answers 2018 A20

Answer 21.
Plus One Maths Previous Year Question Papers and Answers 2018 A21
In (1),3x + 5y-12 = 0

Answer 22.
a. Let f[x) = sinx
f(x + h) = sin(x + h)
f (x + h) – f(x)= sin(x + h) – sinx
Plus One Maths Previous Year Question Papers and Answers 2018 A22
Plus One Maths Previous Year Question Papers and Answers 2018 A22.1

Answer 23.
(a) 12 x (n-1)P3 = 5 x (n+1)P3
12 x (n-1 )(n – 2)(n – 3) = 5 x (n+1 )n(n-1)
12n2 – 6Qn + 72 – 5n2 – 5n = 0
7n2-65n+72 = 0
\(\frac { 65+\sqrt { 4225-2016 } }{ 14 } =\frac { 67647 }{ 14 } \)
\(\frac { 112 }{ 14 } ,\frac { 18 }{ 14 } =8,\frac { 9 }{ 7 } \)
But n cannot be a fraction. n = 8
(b) nP = r! x nCr   840=r! x 35
r! = 24 ⇒ r = 4
Two different vowels can be selected in 5C2 ways .Two different consonents can be selected in 2ICWays.
Total selection 4 letters = 5C2 x 21C2
Total words = 4! x 5C2 x21C2
= 10 x 210 x 24 = 50400

Answer 24.
a.
Plus One Maths Previous Year Question Papers and Answers 2018 A24

Plus One Maths Previous Year Question Papers and Answers

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