Plus One Maths Model Question Paper 1

Kerala Plus One Maths Model Question Paper 1

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 1A
Question 1.
Write the set \(\left\{ \frac { 1 }{ 2 } ,\frac { 2 }{ 3 } ,\frac { 3 }{ 4 } ,\frac { 4 }{ 5 } ,\frac { 5 }{ 6 } ,\frac { 6 }{ 7 } \right\} \) r in the set- builder form.
a. If A and B are two sets such that A ⊂ B , then what is A ∪ B
b. There are 200 individuals with a skin disorder, 120 had been exposed to the chemical C1 50 to the chemical C2, and 30 to both the chemicals C1 and C2. Find the number of individuals exposed to Chemical C1 but not chemical C2.
Plus One Maths Model Question Papers Paper 1Q1

Question 2.
A lamp post is situated at the middle point M of the side AC of a triangular plot ABC with BC=7m CA = 8m, AB = 9m. Lamp post subtends an angle 15° at the poiny B. Determine the height of the lamp post.
Plus One Maths Model Question Papers Paper 1Q2
Plus One Maths Model Question Papers Paper 1Q2.1

Question 3.
Find square root of the complex number 8- i6.
Plus One Maths Model Question Papers Paper 1Q3

Question 4.
Arathi took 3 examinations in an year. The marks obtained by her in the second and third examinations are more than 5 and 10 respectively than in the first examination. If her average mark is at least 80 find the minimum mark that she should get in the first examination?
Plus One Maths Model Question Papers Paper 1Q4

Question 5.
a. A die is thrown until a six comes up. Write down the sample space for this experiment.
b. What is the probability of getting a doublet in throws of a pair of dice.
Plus One Maths Model Question Papers Paper 1Q5

Question 6.
(a) A hyperbola with a = b is known as…………..

A. rectangular hyperbola
B. isosceles hyperbola
C. equilateral hyperbola
D. None of these

(b) Find the equation of an ellipse whose length of major axis is 26 and foci (± 5, 6)
Plus One Maths Model Question Papers Paper 1Q6

Question 7.
Plus One Maths Model Question Papers Paper 1Q7

Questions from 8 to 17 carry 4 score each. Answer any 8.
Plus One Maths Model Question Papers Paper 1B

Question 8.
Plus One Maths Model Question Papers Paper 1Q8

Question 9.
Let P(n) be the statement : 13 + 23 + 33 +………+n3
 \(={ \left[ \frac { n(n+1) }{ 2 } \right] }^{ 2 }\)
a.Verify whether the statement is true for n = 1
b. Prove the result by using mathematical induction
Plus One Maths Model Question Papers Paper 1Q9
Plus One Maths Model Question Papers Paper 1Q9.1

Question 10.
a. Express (5 – 3i)3 in the form a + ib
b. Solve the equation -x+ x – 2 = 0
Plus One Maths Model Question Papers Paper 1Q10

Question 11.
Solve the folowing linear inequalities graphically:
Plus One Maths Model Question Papers Paper 1Q11

Question 12.
a. How many 3 digit even number can be formed form the digits 1,2,3,4,5 and 6, if the digits can be repeated?
b. In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?
Plus One Maths Model Question Papers Paper 1Q12

Question 13.
a. The base of an equilateral triangle with side 2 a lies along they-axis such that the mid-point of the base is at the origin. Find vertices of the triangle….
b. Find the equation of the line passing through (-3, 5) and perpendicular to the line through the points (2, 5) and (-3, 6)
Plus One Maths Model Question Papers Paper 1Q13

Question 14.
a. find the centere and radius of the circle x2+ y– 8x + 10y – 12 = 0
b. Find the equation of the circle passing through (0,0) and making intercepts a and b on the coordinate axes.
Plus One Maths Model Question Papers Paper 1Q14

Question 15.
a. If p is the length of perpendicular from the origin to the line whose intercepts on the exes are a and b, then show that
Plus One Maths Model Question Papers Paper 1Q15
b. If the lines 2x + y-3=0, 5x + ky -3=0 and 3x – y-2=0 are concurrent, find the value of k.
Plus One Maths Model Question Papers Paper 1Q15.1
Plus One Maths Model Question Papers Paper 1Q15.2

Question 16.
a. Find the octant in which the points (-3,1,2) and (-3,1,-2) lie.
b. Find the coordinates of a point on y-axis which are a distance of 5√2 from the point P (3,-2,5)
Plus One Maths Model Question Papers Paper 1Q16

Question 17.
a. Write the negation of the following statement: If you do all the exercises in this book, you get an A grade in the class,
b. Verify by the method of contradiction, p: √2 is irrational.
Plus One Maths Model Question Papers Paper 1Q17

Questions from 18 to 24 carry 6 score each. Answer any 5.
Plus One Maths Model Question Papers Paper 1C

Question 18.
a. Draw the graph of the function f: R→ R defined by f(x) = xx ∈ R
b. If set A has 2 elements and set B has 3 elements, then the number of function from A to B is
(i) 64
(ii) 6
(iii) 9
(iv) 8
Plus One Maths Model Question Papers Paper 1Q18
Plus One Maths Model Question Papers Paper 1Q18.1

Question 19.
a. If sec x = 13/5, x lies in fourth quadrant, find other t-functions.
b. Prove that show that tan 3x tan 2x tan x = tan 3x – tan 2x – tan x
c. Find the value of tan π/8
Plus One Maths Model Question Papers Paper 1Q19

Question 20.
a. Find the sum of the sequence 7, 77, 777,  7777, ………….. to n terms.
b. Find the sum of first n terms of the series: 3 12 + 5 x 22 + 7 x 32+…….
Plus One Maths Model Question Papers Paper 1Q20

Question 21.
a. Find the middle term in the expansion of
Plus One Maths Model Question Papers Paper 1Q21
b. Find the term independent in the expansion of
Plus One Maths Model Question Papers Paper 1Q21.1
Plus One Maths Model Question Papers Paper 1Q21.2
Plus One Maths Model Question Papers Paper 1Q21.3

Question 22.
a. Find the derivative of x sin x form first principles.
Plus One Maths Model Question Papers Paper 1Q22

Question 23.
a. Find mean deviation about median for the following data.
Plus One Maths Model Question Papers Paper 1Q23
b. Calculate mean, variance and standard deviation of the following distribution:
Plus One Maths Model Question Papers Paper 1Q23.1

Question 24.
Four cards are drawn from a well shuffled pack of 52 cards. Find the probability that it contains
a. all aces
b. atmost 2 aces
c. atleast two aces
Plus One Maths Model Question Papers Paper 1Q24

Answers

Answer 1.
Plus One Maths Model Question Papers Paper 1A1

Answer 2.
Plus One Maths Model Question Papers Paper 1A2

Answer 3.
– 15 – 8i
Let \(\sqrt { 8-6i } \) = x + iy……….. (1)
Squaring we have,
8 – i6=(x + iy)2 = x2 + i2xy + i2y2 = (x– y2)  +i2xy
Equating the real and imaginary parts, we have
x– y2= 8 ………….. (2)
2xy = – 6 ……………….. (3)
We know that (x+ y2)2
= (x– y2)2 + 4xy2
= (8)2+(-6)2= 64+36 = 100
∴ x+ y= 4m = √100 = 10 ………….. (4)
(2) + (4) we have,
x2 -y = 8 x2 + y= 10 2x2 = 18
x2 = 9 ⇒ x = ± 3
In (4), we have, 32+y2=10 ⇒ y2
=10 – 9 = 1 ⇒ y = ± 1
Since 2xy = -6,
When x = 3, y = -1 and when x = -3, y = 1
3-i and -3 + i are the square roots.

Answer 4.
Let the mark in the first exam = x
Mark in the second exam = x+5
Mark in the third exam = x + 10 x + x + 5 + x + 10.
Plus One Maths Model Question Papers Paper 1A4
x >75
Minimum mark Arathi should get in the first exam = 75.

Answer 5.
a. s = {6,(1,6),(1, 1, 6),….,(2, 6),(2, 1, 6),…. }
b. n (s) = 36
doublets are (1,1), (2,2), (3,3),
(4,4),(5,5) and (6,6)
∴ P (getting a doublet) =  \(\frac { 6 }{ 36 } \) = \(\frac { 1 }{ 6 } \)

Answer 6.
a. C.
b. 2a = 26 => a = 13
foci = (±5,0) => c = 5
But c2 = a2– b2 ⇒ b=a– c= 132-5= 144
Plus One Maths Model Question Papers Paper 1A6

Answer 7.
Plus One Maths Model Question Papers Paper 1A7

Answer 8.
Plus One Maths Model Question Papers Paper 1A8
Plus One Maths Model Question Papers Paper 1A8.1

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

Answer 10.
a. (5 – 3i)= 5– 3 x 52(3i)+3 x 5(3i)2– (3i)3
= 125 – 225i+ 135i2 – 21 i3
= 125 – 225i+ 135(-1)-27(-i)
= 125 – 225i – 135 + 27i
= -10 – 198i
b. -x+ x + 2 = 0
a = 1 ; b = 1 ; c = 2
D = b2 – 4ac = (1)2 – 4 (-1) (2)
= 1 – 8 = -7 < 0
Plus One Maths Model Question Papers Paper 1A10

Answer 11.
Plus One Maths Model Question Papers Paper 1A11
The shaded region is the solution region.

Answer 12.
a. Here unit place can filled in three ways (i.e. by 2, 4, 6), whereas tens and hundred place can be filled in 6 ways.
b. Out of available nine courses, two are compulsory, Hence the student is free select 3 courses out of 7 remaining courses. Then the number if ways of selecting courses out of 7 courses
Plus One Maths Model Question Papers Paper 1A12

Answer 13.
(a) Let ABC be the given equilateral triangle with side 2a. Assume that base BC lies along the y-axis such that the mid-point of BC is at the origin. i.e., BO = OC = a, where O is the origin Now, it is clear that the coordinates of point B are (-a, 0) and C are (a,0), while the coordinates of point. Using Pythagoras theorem to ΔAOC, we obtain
AC2 = OA2 + OC(2a)2
= OA2+ a2 4a2– a2 = OA2
⇒ OA=3a2 ⇒ OA = √3a
Plus One Maths Model Question Papers Paper 1A13
∴ co-ordinates of A are (±√3a ,0). Thus, the vertices of the given equilat­eral triangle are (0, a),(0,-a), and (√3a,0) or (0, a), (0, -a), and (-√3a ,0)
(b) Any line through (-3,5) is y-5 = m(x-(-3)) = m(x + 3) Slope of line joining (2, 5) and (-3, 6) =
Plus One Maths Model Question Papers Paper 1A13.1
∴  slope of a line⊥ to it = 5
∴reqd. line is y-5 = 5(x+3)
⇒ 5x – y + 20=0

Answer 14.
a. centre = (-g, -f) = (4, -5)
Plus One Maths Model Question Papers Paper 1A14
b. Equation is
(x1 – x) (x – x2)+(y1 – y) (y – y1)
(x – a)(x – 0)+(y – 0)(y – b) = 0
x2-ax + y2 – by = 0
x2 + y2 – ax -by = 0

Answer 15.
a. The equaton of line making intercepts a and b on the axes is
Plus One Maths Model Question Papers Paper 1A15
(intercept from) ….(i)
Given p = perpendicular distance from
Plus One Maths Model Question Papers Paper 1A15.1
b. Three lines are said to be concurrent, if they pass through a common point, i.e., point of intersection of any two lines lies on the third line. Here given lines are
2x + y – 3 = 0 ……….. (1)
5x + ky – 3 = 0……….. (2)
3x – y – 2 = 0 …………. (3)
Solving (1) and (3) by cross – multipli­cation method, we get,
Plus One Maths Model Question Papers Paper 1A15.2
Therefore, the point of intersection of two lines is (1, 1). Since above three lines are concurrent, the point (1, 1) will satisfy equation (2) so that
5.1+k.1- 3 = 0 ⇒ k = -2.

Answer 16.
a. (-3,1,2) – 2nd octant
(-3,1,-2) – 6th octant
b. Let A (0,y,0) be a point on y-axis having distance 5 √2 from (3,-2,5)
Plus One Maths Model Question Papers Paper 1A16
⇒ y+ 4y – 12 = 0
⇒ (y + 6) (y-  2) =0
⇒ y = -6,2
∴ A(0,-6,0) and ,4(0,2,0) are the required points

Answer 17.
a. If you do not do all the exercises in this book, you will not get an a grade in the class.
b. Let us assume that be rational.
∴ √2 = a/b, where a and b are co-prime,
i.e., a an b have no other common factors except 1.
Then 2b2 = a2 ⇒ 2 divides a.
∴ there exists an integer tk> such that a – 2k
∴ 2b2 = 4k2 ⇒ 4k= 2b= 2k2 = ⇒ b2=⇒ 2 divides b.
i.e., 2 devides both a and b, which is contradiction to our assumption that a and b have no common factor.
∴ our supposition is wrong.
∴  √2 is an irrational number.

Answer 18.
a.
Plus One Maths Model Question Papers Paper 1A18
b. (iii) n(b)n(A) =3= 9

Answer 19.
Plus One Maths Model Question Papers Paper 1A19
Plus One Maths Model Question Papers Paper 1A19.1
Plus One Maths Model Question Papers Paper 1A19.2
Answer 20.
a. This is not a G.P., however, we can relate it to a G.P by writing the terms as Sn =7 + 77 + 777 + 7777 + …….. to n terms
Plus One Maths Model Question Papers Paper 1A20
b. Let Tn denote the nth term of the given series
Plus One Maths Model Question Papers Paper 1A20.1

Answer 21.
a. Here n = 10 is even
Middle term \(\frac { 10 }{ 2 }\) +1 = 6th term
Plus One Maths Model Question Papers Paper 1A21
Since we have to find a term indepen­dent of x, i.e., term not having x, so
Plus One Maths Model Question Papers Paper 1A21.1

Answer 22.
Plus One Maths Model Question Papers Paper 1A22
Plus One Maths Model Question Papers Paper 1A22.1
Plus One Maths Model Question Papers Paper 1A22.2
Answer 23.
a. We have
Plus One Maths Model Question Papers Paper 1A23
b. We first make the data continuous by making classes as below :
Plus One Maths Model Question Papers Paper 1A23.1
Plus One Maths Model Question Papers Paper 1A23.2

Answer 24.
Plus One Maths Model Question Papers Paper 1A24
Plus One Maths Model Question Papers Paper 1A24.1

Plus One Maths Previous Year Question Papers and Answers

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