Kerala Plus One Maths Question Paper March 2020 with Answers

Reviewing Kerala Syllabus Plus One Maths Previous Year Question Papers and Answers Pdf March 2020 helps in understanding answer patterns.

Kerala Plus One Maths Previous Year Question Paper March 2020

Time: 2 Hours
Total Scores: 60

Questions 1 to 7 carry 3 scores each. Answer any 7 questions.

Question 1.
(i) If A = {x < x is a natural number, x < 5 and x > 7}, then n(A) is
(a) 1
(b) 0
(c) 2
(d) 3
Answer:
(b) 0

(ii) The set builder of (6, 12) is
(a) {x : x ∈ R, 6 < x ≤ 12}
(b) {x : x ∈ R, 6 < x < 12}
(c) {x : x ∈ R, 6 ≤ x ≤ 12}
(d) {x : x ∈ R, 6 ≤ x < 12}
Answer:
(b) {x : x ∈ R, 6 < x < 12}

(iii) If A and B are two sets such that A ⊂ B, then A ∪ B is
(a) A
(b) Null Set
(c) B
(d) {Φ}
Answer:
(c) B

Question 2.
In a survey of 600 students in a school, 150 students were found to be taking tea, 225 students were taking coffee, and 100 were taking both tea and coffee. Find how many students were taking neither tea nor coffee.
Answer:
Let the sets be defined as follows:
Tea = A, Coffee = B
n(U) = 600, n(A) = 150, n(B) = 225
n(A ∩ B) = 100
n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
= 150 + 225 – 100
= 275
n(neither tea nor coffee) = n(A’ ∩ B’)
= n(U) – n(A ∩ B)
= 600 – 275
= 325

Question 3.
Find the principal and general solutions of cosec x = -2.
Answer:
cosec x = -2
⇒ x = \(\frac{-1}{2}\)
x lies in the third or fourth quadrant
x = \(\pi+\frac{\pi}{6}=\frac{7 \pi}{6}\)
x = \(2 \pi-\frac{\pi}{6}=\frac{11 \pi}{6}\)
Principal solution are \(\frac{7 \pi}{6}\) and \(\frac{11 \pi}{6}\)
General solution
x = nπ + (-1)ⁿ y, n ∈ Z
x = nπ + (-1)ⁿ \(\frac{7 \pi}{6}\), n ∈ Z

Question 4.
(i) If the sum of first terms of an AP is equal to the sum of first 30 terms, then the sum of first 50 terms is
(a) 50
(b) 20
(c) 0
(d) 80
Answer:
(c) 0

(ii) Find the sum to infinity terms of the G.P \(\frac{-3}{4}, \frac{3}{16}, \frac{-3}{64}, \ldots\)
Answer:

Question 5.
Find the sum of n terms of the series 7 + 77 + 777 +…..
Answer:

Question 6.
Consider the following figure:

(i) Find the distance of PQ.
(ii) Find the coordinates of the point that divides the line segment by joining the points P and Q internally in the ratio 2 : 3.
Answer:

Question 7.
Find the derivative of cos x from first principles.
Answer:

Question 8.
(i) Derivative of
f(x) = 1 + x + x² + x³ +…+ x⁵⁰ at x = 1 is
(a) 50
(b) 1250
(c) 1275
(d) \(\frac{101}{2}\)
(ii) Find \(\lim _{x \rightarrow 0} f(x)\) if it exists, where
\(f(x)= \begin{cases}\frac{|x|}{x}, & x \neq 0 \\ 0, & x=0\end{cases}\)
Answer:
(i) (c) 1275
f'(x) = 1 + 2x + 3x² + … + 50x⁴⁹
f'(1) = 1 + 2 + 3 + ….. + 50 = \(\frac{50(50+1)}{2}\) = 1275

Questions 9 to 16 carry 4 scores each. Answer any 6.

Question 9.
Match the following:


Answer:
(a) f : R → R given by f(x) = x³
(b) f : R → R given by \(f(x)=\left\{\begin{array}{rc}
1, & x>0 \\
0, & x=0 \\
-1, & x<0
\end{array}\right.\)
(c) f : R → R given by f(x) = x
(d) f : R → R given by f(x) = \(\frac{1}{x}\), x ≠ 0

Question 10.
For every positive integer n, prove that 7ⁿ – 3ⁿ is divisible by 4 using the principle of mathematical induction.
Answer:
P(1) = 7¹ – 3¹ = 4
True for n = 1
Assume that P(k) is divisible by 4
P(k) = 7^k – 3^k = 4m, where m is a natural number
Prove for n = k + 1
P(k + 1) = 7^k+1 – 3^k+1
= 7 . 7^k – 3 . 3^k
= 7 . 7^k – (7 – 4) . 3^k
= 7 . 7^k – 7 . 3^k – 4 . 3^k
= 7(7^k – 3^k) – 4.3^k
= 7 . 4m – 4 . 3^k
= 4(m7^k – 3^k)
Hence P(k + 1) is true. Therefore P(n) is true for all natural numbers.

Question 11.
(i) Modulus of a complex number is 2 and arg(z) = \(\frac{\pi}{3}\), write the complex number in the form a + ib.
(ii) Find the square root of the above complex number.
Answer:

Question 12.
Solve graphically:
2x + y ≥ 4; x + y ≤ 3; 2x – 3y ≤ 6; x ≥ 0; y ≥ 0
Answer:

Question 13.
(i) Expand \(\left(x+\frac{1}{x}\right)^6\).
(ii) Find the middle term in the expansion of \(\left(\frac{x}{3}+9 y\right)^{10}\).
Answer:

Question 14.
(i) Let A(1, 2) be a fixed point and, ‘P’ be a variable point in the same plane. P moves in the plane in such a way that its distance from A is always a constant. Suppose ‘P’ is at the point (3, 3), find the equation of the path traced by ‘P’.
(ii) Consider the following ellipse:

(a) Find the equation of the ellipse.
(b) Find the coordinates of the foci.
Answer:

Question 15.
(i) Write the contra positive of the statement:
“If a number is divisible by 9, then it is divisible by 3.”
(ii) By method of contradiction, prove that √5 is irrational.
Answer:
(i) Contrapositive statement is “If a number is not divisible by 3, then it is not divisible by 9.”
(ii) Let √5 be rational.
Then √5 = \(\frac{a}{b}\), where a and b have no common factors.
√5b = a
⇒ 5b² = a² ……….(1)
⇒ a² is divisible by 5
⇒ a is divisible by 5
Then a = 5c
⇒ a² = 25c²
(1) ⇒ 5b² = 25c²
⇒ b² = 5c²
⇒ b² is divisible by 5
⇒ b is divisible by 5.
Hence a and b have a common factor √5. Which contradicts our assumption that √5 is rational. Therefore √5 is irrational.

Question 16.
(i) If E and F are two events such that P(E) = \(\frac{1}{4}\), P(F) = \(\frac{1}{2}\), P(E and F) = \(\frac{1}{8}\), find
(a) P(E or F)
(b) P(not E and not F)
(ii) A committee of two persons is selected from two men and two women. What is the probability that the committee will have
(a) one man?
(b) two men?
Answer:

Questions from 17 to 20 carry 3 scores each. Answer any 5.

Question 17.
(i) If tan x = \(-\frac{5}{12}\), x lies in second quadrant. Find all trigonometric functions.
(ii) Without using a triangle, find the value of \(\frac{\sin x+\cos x}{\sin x-\cos x}\) if tan x = \(\frac{3}{4}\).
(iii) Prove that \(\frac{\sin 5 x+\sin 3 x}{\cos 5 x+\cos 3 x}\) = tan 4x
Answer:

Question 18.
(i) Find the number of different 8-letter arrangements that can be made from the letters of the word ‘DAUGHTER’ so that all vowels occur together.
(ii) Find the number of ways of choosing 4 cards from a pack of 52 playing cards. How many of these
(a) Are four cards of the same suit?
(b) Four cards belong to different suits?
(c) Two are red cards and two are black cards?
Answer:
(i) The vowels are A, E, U. These vowels can be arranged in 3! ways.
Count these 3 vowels as one unit.
Then the number of letters with vowels together = 6! × 3! = 4320
(ii) Number of ways of selecting 4 cards = ⁵²C₄ = 270725
(a) 4 cards from same suite = ¹³C₄ + ¹³C₄ + ¹³C₄ + ¹³C₄ = 4 × ¹³C₄ = 2860
(b) 4 cards belong to different suits = ¹³C₁ × ¹³C₁ × ¹³C₁ × ¹³C₁ = 134
(c) 2 are red cards and 2 are black cards = ²⁶C₂ × ²⁶C₂ = 105625

Question 19.
Consider the following diagram:

(i) Find equation of a line passing through the midpoint of AB and perpendicular to AB.
(ii) Find a point ‘C’ on the x-axis which is equidistant from A and B.
(iii) Find area of ΔABC.
Answer:
(i) Mid point of segment AB is (3, 2)
Slope of AB = -1
Slope of perpendicular line to AB = 1
Equation of perpendicular line is y – 2 = 1(x – 3)
⇒ x – y – 1 = 0
(ii) Let C be of the form (x, 0)
Then \(\sqrt{(x-2)^2+(0-3)^2}=\sqrt{(x-4)^2+(0-1)^2}\)
⇒ x² – 4x + 4 + 9 = x² – 8x + 16 + 1
⇒ 4x = 4
⇒ x = 1
Hence point C is (1, 0)
(iii) Area = \(\frac{1}{2}\) [x₁(y₂ – y₃) + x₂(y₃ – y₁) + x₃(y₁ – y₂)]
= \(\frac{1}{2}\) [2(1 – 0) + 4(0 – 3) + 1(3 – 1)]
= \(\frac{1}{2}\) [2 – 12 + 2]
= \(\frac{1}{2}\) [-8]
= -4
∴ Area = 4 sq. units.

Question 20.
From the following table:

Classes	30 – 40	40 – 50	50 – 60	60 – 70	70 – 80	80 – 90	90 – 100
Frequency	3	7	12	15	8	3	2

Find
(i) Mean
(ii) Variance
(iii) Coefficient of Variation.
Answer: