TOSS Inter Model Question Paper Maths

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MODEL QUESTION PAPER

Intermediate (TOSS) MATHEMATICS 311 (E) (Set ʹ II)

Time: 3 hrs Max. Marks: 100

Instructions:-

1) All questions are Compulsory.
2) This question paper consists of two parts viz., A and B

3) All questions from Part A are to be attempted

4) Part-B has two options. Candidates are required to attempt questions from one option only.

(Part ʹ A)

SECTION ʹ 1
Each question carries 1 mark. (13 x 1 = 13 marks)

1) If Z1 = x + iy, and Z2 = a + ib then what is Z1 + Z2 ?
2) What are the roots of x2 + 5x + 6 = 0 ?
3) Show the region represented by the in-equations x ൑ 0 and y ൑ 0
4) /ĨƚŚĞ͙͙͙͙͙ƚǁŽƐƚƌĂŝŐŚƚůŝŶĞƐŽŶĞƉĞƌƉĞŶĚŝĐƵůĂƌ͕ƚŚĞŶǁŚĂƚŝƐƚŚĞƉƌŽĚƵĐt of their slopes?
5) Find the distance between the points (-1,2) and (0,-6) ?
6) Convert 2700 into Radians.
7) What is the domain of the function?
Ĩс΂;Ϭ͕ϭͿ͕;Ϯ͕ϯͿ͕;ϰ͕ϱͿ͕;ϲ͕ϳͿ͕͙͙͕͘͘;ϭϬϬ͕ϭϬϭͿ΃
8) Evaluate Lt ‫ݔ‬՜0 [ሺ2‫ ݔ‬+ 1ሻ3 െ 5]
9) What is the derivative of ‫ ݊ ݔ‬w.r.t x ?
10) tŚĂƚŝƐƚŚĞƐůŽƉĞŽĨƚŚĞ͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙сdž͘tƌŝƚĞƚŚĞ
formulae of slope of the tangent of the curve y = f (x) at (x1, y1)
11) What is ‫ ݔ ݁ ׬‬ሾ݂ ሺ‫ݔ‬ሻ + ݂ 1 ሺ‫ݔ‬ሻሿ݀ሺ‫ݔ‬ሻ? ǥ . . ] ݀‫ݔ‬
݀‫ݕ‬
12) Write the Integrating factor of ݀‫ ݔ‬нĨ;džͿLJсY;džͿ͙͙͙͙͙͙͙͙͙͙..

13) What is the principle of standard deviation for grouped data?

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Section ʹ 2
( Each question carries 2 marks)
1 2 2 1
14) If A = ቂ ቃ2x2 and B = ቂ ቃ2x2 then prove that AB ് BA
െ1 0 2 2
ܽ11 ܽ12 ܽ13
15) What is the expanded form of อܽ21 ܽ22 ܽ23อ
ܽ31 ܽ32 ܽ33

‫ ݔ ݏ݋ܥ‬െܵ݅݊ ‫ݔ‬
16) Find the inverse of the matrix ቂ ቃ
ܵ݅݊ ‫ݔ ݏ݋ܥ ݔ‬

17) Find the equation of the parabola whose focus is (2,3), directrix is 3x + 4y = 1.

18) tŚĂƚŝƐƚŚĞƐƵŵŽĨƚŚĞƐĞƌŝĞƐϯнϱнϳн͙͙͙͙͙͙н;ϮŶнϭͿ͙͙͘

19) Draw the Venn diagram for A ‫ ڂ‬B, when A and B are disjoint sets.

ξ3
20) What is the principle value of cos െ1 ( )
2

݀‫ݕ‬
21) If y = cos െ1 (4‫ ݔ‬3 െ 3‫ ) ݔ‬find .
݀‫ݔ‬

22) What is the Area bounded by the curve x = y, Y-axis and the line y = 0, y = 3.

23) A die is tossed twice. Find the probability of a number greater than 4 in each throw.

Section ± 3
(Each question carries 5 marks)

24) There are 5 Mathematics, 4 Physics and 5 Chemistry books. In how many ways can you arrange
4 Mathematics, 3 Physics and 4 Chemistry books, if the books on the same subjects are arranged
together?
25) If the 4th term and the 9th term of a G.P. are 8 and 256 respectively, then write the G.P.
26) Find the Maximum and Minimum value of the function f (x) = Sin x (1 + Cos x) in (0, ߨ )
27) The data below presents the earning of 50 labours of a factory. Calculate the Mean deviation.

Earning in Rs: 1200 1300 1400 1500 1600 1800
No. of Labors: 4 7 15 12 7 3

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Section ʹ 4
(Each question carries 8 marks)
28) Using Principle of Mathematical induction, prove the following
1 1 1 1 n
1.3
+ 3.5 + 5.7 + ‫ ڮ‬+ ሺ2݊െ1ሻ.ሺ2݊+1ሻ = ሺ2݊+1ሻ

29) Find the equation of the circle which passes through the points (0,2), (2,0) and (0,0)
ܾ c
30) In ο ‫ܥܤܣ‬, ݂݅ < ‫ = ܣ‬600 prove that ܿ+ܽ
+ ܽ+ܾ = 1
݀‫ݕ‬
31) If y = ( ܶܽ݊ ‫ ݔ ݐ݋ܥ)ݔ‬+ ( ‫ ݔ )ݔ ݐ݋ܥ‬then find ݀‫ ݔ‬.

Part ʹ B
Optional ʹ I (VECTORS and 3 ʹ D Geometry)

32) If ‫ݎ‬1 = ݅ - ݆ + ݇ and ‫ݎ‬2 = 2݅ - 4݆ - 3݇ , then the magnitude of ‫ݎ‬1 + ‫ݎ‬2 1 Mark
33) Write the position vector of the centroid of the triangle, whose vertices are A (ܽԦ), B (ܾሬԦ), C (ܿԦ) 4
Marks.
34) If the foot of the perpendicular drawn from the origin to the plane is (4, -2, -5), then find the
equation of the plane. (5 Marks)
2 2 2
35) Find the centre and radius of the circle x + y + z ʹ 6x ʹ 4y + 12z ʹ 36 = 0, x + 2y ʹ 2z = 1
(Optional ʹ II)

32) Define Share 1 Mark
33) Write any one use of Index numbers 1 Mark
34) Discuss the characteristics of VAT 5 Marks
35) For a new product a manufacturer spends Rupees 1,00,000 on the infrastructure and the
variable cost is estimated as Rs. 150 per unit of the product the sale price per unit fixed at Rs.
200.
Calculate (1) Cost function
(2) Revenue function
(3) Profit function and
(4) the breakeven point

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