Special instructions:-
विशेष निर्देश:
1: You must write question paper series in the circle at top left side of title page of your answer sheet.
2: While answering your questions you must indicate on your answer book the same question number as appears in your question paper.
3: Don't leave blank pages/pages in your answer book.
4: All questions are compulsory.
5: Internal choices are given in some questions.
6: Question no 1-10 are MCQ carrying 1 Mark each. Question no 11-14 are short answer type carrying 2 Mark each. Question no 15-26 are short answer type questions carrying 3.5 marks each and question no 27-31 are long answer type carrying 5 marks each.
7: Use of calculator is not permitted,however you ask for log table. If required from superintendent of examination.
8: Try to answer the questions in serial order as far as possible.
9: attach the graph properly.
Q11: constructor 3 into two Matrix whose elements are given by Aij=|i-3j|
OR
Using elementary transformation find the inverse of the matrix
[2 5]
A= [1 3]
Q12: find all points of discontinuity of f where f is Defined by
f( x)= {x+1 if x≥1
x²+1 if x<1
Q13 find the intervals in which the function f is given by
f(x)= -2x³-9x²-12x+1 is strictly decreasing.
Q14: form a differential equation representing the family of curves Y = MX where M is arbitrary constant
Q15: find gof and fog if
f(x)= 8x³ and g(x)=x⅓
Q16 prove that
sin-¹ 3/5 – sin-¹ 8/17 = cos-¹ 84/85
OR
tan-¹(cos x - sin x/ cos x + sin x), x<π
Q17 using properties of determinants show that
|x+y+2z x y|
|z y+z+2x y| =2(x+y+z)²
|z x z+x+2y|
Q18 find dy/dx for function
(Cos x)power y = (cos y)power x
OR
If y=( tan-¹x)² then show that
(x²+1)²y2 + 2x ( x² +1) y1 = 2
Q19: integrate 5 x + 3 /√ x² + 4 x + 10 with respect to x
Q20: integrate 5x/ (x + 1 )(x – 4) with respect to x
Q21 integrate | x–5|dx within limits 2 to 8
Q22 show that the family of curves for which the slope of the tangent at any point (x y) on it is x²+y²/2xy is given by x²–y² = cx
OR
(x+y)dy/dx= 1
Q23. Show that the vectors a→ = i^ – 2j^+3 k^, b→ = 2i^ + 3j^ – 4k^ and c→ = i^ – 3 j^ + t k^ are coplanar
Q24. Find the angles between the pair of lines
x–2/2 = y–1/5 = z+3/–3
and.
x+2/–1 = y–4/8 = z–5/4
Q25. A dice is tossed thrice find the probability of getting an odd number at least once.
Q26: from a lot of 30 bulbs which include 6 defectives a sample of 4 bulbs is drawn at random with replacement find the probability distribution of the number of defective bulbs
OR
if a fair coin is tossed 10 times find the probability of
1)exactly 6 heads
2)at least 6 heads
3) at most 6 heads
Q27. Solve system of linear equations using Matrix method
2x + 3y +3z = 5
x – 2y +z = –4
3x – y –2z= 3
Q28. Show that the right circular cone of least curved surface area and given volume has an altitude equal to √2 times of the radius of base
OR
find the equation of tangent and normal to the parabola y = 4 ax at point(at²,2at)
Q29. Find the area of the region bounded by ellipse x²/4 + y²/9 =1
OR
using integration find the area of bounded by triangle whose vertices are A(–1,0) B(1,3) and C(3,2)
Q30. Find the equation of plane through the line of intersection of plane X + Y + Z = 1 and 2 X + 3 Y + 4 Z = 5 which is perpendicular to plane x– y + Z = 0
Q31. Maximize z= 5x +10y
Subject to constraints
x + 2y ≤ 120
x + y ≥ 60
x – 2y ≥ 0
x,y ≥ 0
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