Plus One Maths Model Question Papers Paper 3 are part of Plus One Maths Previous Year Question Papers and Answers. Here we have given Plus One Maths Model Question Papers Paper 3.

Board |
SCERT |

Class |
Plus One |

Subject |
Maths |

Category |
Plus One Previous Year Question Papers |

## Plus One Maths Model Question Papers 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.

**Questions 1 to 7 carry 3 score each. Answer any 6.**

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}

Question 2.

In any triangle ABC, prove that

a(SinB- sinC) + b(sinC- sinA) +c(sinA- sinB) = 0

Question 3.

**a.** Solve x^{2} + 2 = 0

**b.** Find the multiplicative inverse of 2-3i

**a.** x^{2} + 2 = 0

Question 4.

**a.** Solve

**b.** Find the graphical solution of the above inequality.

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 ^{2n}C_{3}: ^{n}C_{3} = 12 : 1

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^{2 }+ xy – 3y^{2}– y + 2 = 0 becomes when the origin is shifted to the point (1,1)?

Question 7.

Evaluate :

**Questions from 8 to 17 carry 4 score each. Answer any 8.**

Question 8.

Question 9.

Consider the statement 1.3 + 2.3^{2} + 3.3^{3}

**a.** Verify whether the statement is true for n =1.

**b.** Prove the result by using principle of mathematical induction.

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.

Question 11.

solve the following linear inequalities graphically:

Question 12.

**a.** “P_{r }=

**b.** The letters of the word FATHER be permuted and arranged in a dictionary, find the rank of the word FATHER?

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^{2 }+ y^{2 }+ 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)

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.

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.

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

**Questions from 18 to 24 carry 6 score each. Answer any 5.**

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?

Question 19.

**a.** Write the number of terms in the expansion of (a – b)^{2n}

**b.** Find the general term in the expansion of (x^{2}– yx)^{12}, x ≠ 0

**c.** Find the coefficient of x^{6 }y^{3} in the expansion of (x + 2y)^{9}

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:

**c.** Find the sum of first n terms of the series : 0.6+0.66+0.666+…….to n terms.

Question 21.

**a.** Find the derivative of x^{n} from first principles.

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.

Question 23.

**a.** Find the Mean deviation of the data 3, 10, 10, 4, 7, 10, 5 from mean is ………

**b.** Calculate mean, variance and standard deviation of the following distribution:

Question 24.

**a.** In aleap year the probability of having 53 Sundays is ……..

**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.

**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.

Answer 4.

Answer 5.

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

⇒ X^{2}+2X + 1 + XY + X+ Y+ 1-3 (P + 27 + 1) – (7+ 1) + 2 – 0

⇒ X^{2} – 3Y^{2} + XY + 3X- 6Y = 0

∴ Equation in new system is

X^{2 }– 3Y^{2} + XY + 3X -6Y = 0

Answer 7.

Answer 8.

Answer 9.

Answer 10.

Answer 11.

Answer 12.

**a.** D

**b.** The alphabetical order of the word ‘ FATHER are A, E, F, H, R, T No. of words beginning with

Answer 13.

Answer 14.

a. D

b. Comparing x^{2} + y^{1} – 8x +10 y – 12 = 0 with

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

Answer 16.

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^{2 }– a^{2} ⇒ 7 divides a.

∴ there exists an integer ‘k’ such that a = 7k

a^{2 }= 49k^{2} ⇒ 7b^{2 }= 49k^{2}⇒b^{2}= 7k^{2} 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}

Answer 19.

**a.** Number of terms in expansion can be given by 2n + 1

**b.** General term can be given by

Answer 20.

Answer 21.

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

**b.** Slope of the required line, m = \(-\frac { 3 }{ 4 } \)

|| slope of the parallel line Equation of the line is y – y = m (x – x_{1})

Answer 23.

**a.** b

**c.** The parallel lines 15x + 20y – 57 = 0 and

3x + 4y – 7 = 0 ⇒15x + 20y – 35=0 x ing by 5

Parallel distance

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

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