Plus One Maths Model Question Paper 3

Kerala Plus One Maths Model Question Paper 3

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

Questions 1 to 7 carry 3 score each. Answer any 6.
Plus One Maths Model Question Papers Paper 3A
Question 1.
a. Write set is the subset of all the given sets?
(a) {1,2,3,….}
(b) {1}
(c) {0}
(d) {}
b. Write down the power set of A = {1,2,3}
Plus One Maths Model Question Papers Paper 3Q1

Question 2.
In any triangle ABC, prove that
a(SinB- sinC) + b(sinC- sinA) +c(sinA- sinB) = 0
Plus One Maths Model Question Papers Paper 3Q2

Question 3.
a. Solve x2 + 2 = 0
b. Find the multiplicative inverse of 2-3i
a. x2 + 2 = 0
Plus One Maths Model Question Papers Paper 3Q3

Question 4.
a. Solve
Plus One Maths Model Question Papers Paper 3Q4
b. Find the graphical solution of the above inequality.
Plus One Maths Model Question Papers Paper 3Q4.1
Plus One Maths Model Question Papers Paper 3Q4.2

Question 5.
a. A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of atmost 3 girls,
b. Find n if 2nC3: nC3 = 12 : 1
Plus One Maths Model Question Papers Paper 3Q5

Question 6.
a. The new coordinates of the points (2, 5) if the origin is shifted to the point (1, 1) by translation of axes.
A) (3, 1) B(1, 3) C (-1, 3) D (3, -1)
b. Find what the equation x+ xy – 3y2– y + 2 = 0 becomes when the origin is shifted to the point (1,1)?
Plus One Maths Model Question Papers Paper 3Q6

Question 7.
Evaluate :
Plus One Maths Model Question Papers Paper 3Q7

Questions from 8 to 17 carry 4 score each. Answer any 8.
Plus One Maths Model Question Papers Paper 3B

Question 8.
Plus One Maths Model Question Papers Paper 3Q8

Question 9.
Consider the statement 1.3 + 2.32 + 3.33
Plus One Maths Model Question Papers Paper 3Q9
a. Verify whether the statement is true for n =1.
b. Prove the result by using principle of mathematical induction.
Plus One Maths Model Question Papers Paper 3Q9.1

Question 10.
a. Express (1 + i)3 + (1 – i)3 in a + ib form.
b. Find the polar form of the complex number – 1 – i.
Plus One Maths Model Question Papers Paper 3Q10

Question 11.
solve the following linear inequalities graphically:
Plus One Maths Model Question Papers Paper 3Q11

Question 12.
a. “P=
Plus One Maths Model Question Papers Paper 3Q12
b. The letters of the word FATHER be permuted and arranged in a dictionary, find the rank of the word FATHER?
Plus One Maths Model Question Papers Paper 3Q12.1

Question 13.
a. The distance of the point P(1,-3) from the line 2y – 3x = 4 is
A) 13
B)  \(\frac { 7 }{ 13 } \sqrt { 3 } \)
C) √13
D) None of these
b. Reduce the equation√3x + y + 8 = 0 in to normal form. Find the values of P and ω
imagee

Question 14.
a. A conic with e = 0 is known as
A) a parabola
B) an ellipse
C) a hyperbola
D) a circle
b. Consider the circle x+ y+ 8x + 10y – 8 = 0
i) Find the centre C and radius ‘r’.
ii) Find the equation of the circle with centre at C and passing through the point (1, 2)
Plus One Maths Model Question Papers Paper 3Q14

Question 15.
a. What is the perpendicular distance from the point P(6,7,8) from XY plane.
A) 8
B) 7
C) 6
D) 9
b. Find the equation of the set of points P, the sum of whose distances from A(4,0,0) and B(-4,0,0) is equal to 10.
Plus One Maths Model Question Papers Paper 3Q15

Question 16.
a. Convert 20°40‘ into radian measure.
b. If sin x = \(\frac { 12 }{ 13 } \) and x is an acute angle, find the value of cos 2x.
c. Prove that
\(\frac { sinx-sin\quad 3x }{ { sin }^{ 2 }x-{ cos }^{ 2 }x } \)
= 2 sin x.
Plus One Maths Model Question Papers Paper 3Q16

Question 17.
a. Write the component statements of the following statement: All prime numbers are either even or odd
b. Verify by the method of contradiction, p = √7 is irrational
Plus One Maths Model Question Papers Paper 3Q17

Questions from 18 to 24 carry 6 score each. Answer any 5.
Plus One Maths Model Question Papers Paper 3B
Question 18.
a. Write the interval (6,12) in the set-builder form.
b. Draw the Venn diagram of the following sets :
i) A’ ∩ B’
ii)A – B
c. In a group of 65 people, 40 like cricket, 10 like both cricket and tennis. How many like tennis? How many like tennis only and not cricket?
Plus One Maths Model Question Papers Paper 3Q18

Question 19.
a. Write the number of terms in the expansion of (a – b)2n
b. Find the general term in the expansion of (x2– yx)12, x ≠ 0
c. Find the coefficient of xy3 in the expansion of (x + 2y)9
Plus One Maths Model Question Papers Paper 3Q19

Question 20.
a. The common ratio of the G.P is \(\frac { -4 }{ 5 } \) and the sum to infinity is \(\frac { -80 }{ 9 } \). Find the first term.
b. Evaluate:
Plus One Maths Model Question Papers Paper 3Q20
c. Find the sum of first n terms of the series : 0.6+0.66+0.666+…….to n terms.
Plus One Maths Model Question Papers Paper 3Q20.1

Question 21.
a. Find the derivative of xn from first principles.
Plus One Maths Model Question Papers Paper 3Q21

Question 22.
a. Find the point of intersection of the lines 2x + y = 5 and x + 3y + 8 = 0.
b. Find the equation of a line passing through the point of intersection of the above lines and parallel to the line 3x + 4y =7.
c. Find the distance between these two paralle lines.
Plus One Maths Model Question Papers Paper 3Q22

Question 23.
a. Find the Mean deviation of the data 3, 10, 10, 4, 7, 10, 5 from mean is ………
Plus One Maths Model Question Papers Paper 3Q23
b. Calculate mean, variance and standard deviation of the following distribution:
Plus One Maths Model Question Papers Paper 3Q23.1

Question 24.
a. In aleap year the probability of having 53 Sundays is ……..
Plus One Maths Model Question Papers Paper 3Q24
b. Events E and F are such that P (not E or not F) = 0.25, state whether E and F are mutually exclusive.
c. How many points are there in a sample space, if a card is selected from a pack of 52 cards.
Plus One Maths Model Question Papers Paper 3Q24.1

Answer

Answer 1.
a. d) { }
b. P(A)={{1,2,3}, {1,2}, {2,3}, {1,3}, {1}, {2}, {3}, ø}

Answer 2.
LHS = a (sinB-sinC) + 6(sinC-sinA) +c (sinA-sinB)
= 2R sin A(sinB-sinC) + 2R sin B (sinC-sinA)+2R sinC (sinA – sinB)
= 2R [sin A sin B – sinAsinC + sinB sinC – sinBsinA + sinCsinA – sin C sinB]
= 2R x 0 = 0 = RHS

Answer 3.
Plus One Maths Model Question Papers Paper 3A3

Answer 4.
Plus One Maths Model Question Papers Paper 3A4
Plus One Maths Model Question Papers Paper 3A4.1

Answer 5.
Plus One Maths Model Question Papers Paper 3A5

Answer 6.
a. B) (1, 3) since [2 – 1, 5 – 2]
b. Let the coordinates of a point P changes from (x,y) to (X,Y) when origin is shifted to (1,1)
∴ x = X + 1, y = Y + 1 Substituting in the given equation, we get
(X+1)2 + (X + 1) (7 + 1) -3 (7 + 1)2 -(7 + 1) + 2 = 0
⇒ X2+2X + 1 + XY + X+ Y+ 1-3 (P + 27 + 1) – (7+ 1) + 2 – 0
⇒ X2 – 3Y2 + XY + 3X- 6Y = 0
∴ Equation in new system is
X– 3Y2 + XY + 3X -6Y = 0

Answer 7.
Plus One Maths Model Question Papers Paper 3A7

Answer 8.
Plus One Maths Model Question Papers Paper 3A8

Answer 9.
Plus One Maths Model Question Papers Paper 3A9
Plus One Maths Model Question Papers Paper 3A9.1

Answer 10.
Plus One Maths Model Question Papers Paper 3A10

Answer 11.
Plus One Maths Model Question Papers Paper 3A11

Answer 12.
a. D
b. The alphabetical order of the word ‘ FATHER are A, E, F, H, R, T No. of words beginning with
Plus One Maths Model Question Papers Paper 3A12

Answer 13.
Plus One Maths Model Question Papers Paper 3A13

Answer 14.
a. D
b. Comparing x2 + y1 – 8x +10 y – 12 = 0 with
Plus One Maths Model Question Papers Paper 3A14

Answer 15.
a. A. 8 [ || perpendicular distance of a point from XY plane = z coordinate
b. Let P(x, y, z) be the point such that PA + PB = 10
Plus One Maths Model Question Papers Paper 3A15

Answer 16.
Plus One Maths Model Question Papers Paper 3A16
Plus One Maths Model Question Papers Paper 3A16.1

Answer 17.
a. p: All prime numbers are even. q: All prime numbers are odd
b. Let us assume that √7 is a rational number
∴ √7 = , where a and b are co-prime, i.e. a and b have no common factors, which implies that 7b– a2 ⇒ 7 divides a.
∴ there exists an integer ‘k’ such that a = 7k
a= 49k2 ⇒ 7b= 49k2⇒b2= 7k2 7 divides b.
i.e., 7 divides both a and b, which is contradiction to our assumption that a and b have no common factor.
∴ our supposition √7 is wrong, is an irrational number.

Answer 18.
a. {x : x ∈ R, 6 < x ≤ 12}
Plus One Maths Model Question Papers Paper 3A18
Plus One Maths Model Question Papers Paper 3A18.1

Answer 19.
a. Number of terms in expansion can be given by 2n + 1
b. General term can be given by
Plus One Maths Model Question Papers Paper 3A19

Answer 20.
Plus One Maths Model Question Papers Paper 3A20
Plus One Maths Model Question Papers Paper 3A20.1

Answer 21.
Plus One Maths Model Question Papers Paper 3A21

Answer 22.
a.  2x + y =5 ……………. (1)
x + 3y = -8………………….. (2)
(1) x 3 – (2) ⇒
6x + 3y = 15 x + 3y = -8
(-) (-) (+)
————-
5x  = 7 7
∴ x = 7/5
Plus One Maths Model Question Papers Paper 3A22
b. Slope of the required line, m = \(-\frac { 3 }{ 4 } \)
|| slope of the parallel line Equation of the line is y – y = m (x – x1)
Plus One Maths Model Question Papers Paper 3A22.1
Plus One Maths Model Question Papers Paper 3A22.2

Answer 23.
a. b
Plus One Maths Model Question Papers Paper 3A23
Plus One Maths Model Question Papers Paper 3A23.1
c. The parallel lines 15x + 20y – 57 = 0 and
3x + 4y – 7 = 0 ⇒15x + 20y – 35=0 x ing by 5
Parallel distance
Plus One Maths Model Question Papers Paper 3A23.2

Answer 24.
a. (b) 7/3
b. (not E or not F)
= P(E ‘∪ F’) = P(E ∩ F)’ = 1 = 1P(E ∩ F)
⇒ 0.25 = 1 -P(E n F) ⇒ p(E ∩ F) = 1 -0.25 = 0.75 ≠ 0
⇒ E and F are not mutually exclusive
c. 52

Plus One Maths Previous Year Question Papers and Answers

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