Plus Two Maths Model Question Paper 4

Kerala Plus Two Maths Model Question Paper 4

Time : 2 1/2 Hours
Cool off time : 15 Minutes
Maximum : 80 Score

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 questions and to plan your answers.
  • Read questions carefully before you answering.
  • Read the instructions careully.
  • When you select a question, all the sub-questions must be answered from the same question itself.
  • 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 Two Maths Previous Year Question Papers and Answers 2018 1

QUESTIONS

Question 1 to 7 carry 3 scores each. Answer any six questions only
Plus Two Maths Model Question Papers Paper 4 1

Question 1.
a. The slope of the tangent to the curve given by
x = 1- cos θ , y = θ – sin θ at θ = \(\frac { \pi }{ 2 }\) is
(i) 0
(ii) -1
(iii) 1
(iv) Not defined

b. Find the intervals in which the function f (x) = x2 – 4x + 6 is strictly decreasing.
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Question 2.
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Question 3.
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Question 4.
a. Write the Cartesian equation of the straight line through the point (1, 2, 3) and along the vector 3\(\widehat { i }\) + \(\widehat { j }\) + 2\(\widehat { k }\).
b. Write a general point on this straight line.
c. Find the distance from (1, 2, 3) to the plane 2x + 3y – z + 2 = 0.
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Question 5.
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Question 6.
Solve the system of linear equations :
x + 2y + z = 8
2x + y – z = 1
x – y + z = 2
x + 2y + z = 8
2x + y – z = 1
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Question 7.
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Question 8 to 17 carry 4 scores each. Answer any eight questions only
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Question 8.
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Question 9.
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Question 10.
i. Find the equation of the plane through the points (3,-1,2), (5,2,4) and (-1,-1,6).
ii. Find the perpendicular distance from the point (6,5,9) to this plane.
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Question 11.
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a. Express the euqations of the lines into vector form.
b. Find the shortest distance between the lines.
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Question 12.
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Question 13.
a. Find the equation of a plane with intercepts 2, 3 and 4 on X, Y and Z axes respectively.
b. Find the distance of the point (-1,-2, 3) from the plane r.(2\(\widehat { i }\) – \(\widehat { j }\)) + 4 \(\widehat { k }\)  = 4.
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Question 14.
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Question 15.
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Question 16.
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Question 17.
a. For two independent events A and B, which of the following pair of events need not be independent?
i. A’, B’
ii. A, B’
iii. A’, B
iv. A-B, B-A
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Question 18 to 24 carry 6 scores each. Answer any 5 questions only
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Question 18.
Consider the following L.P.P.
Maximize Z = 3x+2y
Subject to the constraints
x+2y < 10
3x+y < 15
x, y > 0
a. Draw its feasible region.
b. Find the comer points of the feasible region.
c. Find the maximum value of Z.
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Question 19.
a. y=a cos x+b sin x is the solution of the differential equation
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Question 20.
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Question 21.
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Question 22.
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Question 23.
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Question 24.
a. If \(\overline { a } \),\(\overline { b } \),\(\overline { c } \),\(\overline { d } \) respectively are the position vectors representing the vertices A, B, C, D of a parallelogram, then write \(\overline { d } \) in terms of \(\overline { a } \), \(\overline { b } \) and \(\overline { c } \) .

b. Find the projection vector of \(\overline { b } \) = \(\widehat { i }\) + 2 \(\widehat { j }\) + \(\widehat { k }\) along the vector \(\overline { a } \) = 2i +j + 2k. Also write \(\overline { b } \) as the sum of a vector along \(\overline { a } \) and a vector perpendicular to \(\overline { a } \) .

c. Find the area of a parallelogram for which the vectors 2 \(\widehat { i }\) + \(\widehat { j }\) and 3 \(\widehat { i }\) + \(\widehat { j }\) + 4 \(\widehat { k }\) are adjacent sides.
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ANSWERS

Answer 1.
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The point x = 2 divides the real line into two disjoint intervals namly (-∞, 2) and (2,∞). In the interval(-∞,2), f'(x)=2x-4 < 0
∴ f is strictly decreasing in this interval.

Answer 2.
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Answer 3.
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Answer 4.
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Answer 5.
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Answer 6.
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Answer 7.
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Answer 8.
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Answer 9.
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Answer 10.
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Answer 11.
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Answer 12.
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Answer 13.
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Answer 14.
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Answer 15.
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Answer 16.
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Answer 17.
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Answer 18.
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Answer 19.
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Answer 20.
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Answer 21.
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Answer 22.
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Answer 23.
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Answer 24.
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Plus Two Maths Previous Year Question Papers and Answers

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