Aieee mathematics -2011
- 1. AEEE –Past papersMATHEMATICS - UNSOLVED PAPER - 2011
- 2. SECTION – IStraight Objective TypeThis section contains multiple choice questions numbered 30 . Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.
- 3. 01ProblemThe lines L1 : y − x = 0 and L2 : 2x + y = 0 intersect the line L3 : y + 2 = 0 at P and Q respectively. Thebisector of the acute angle between L1 and L2 intersect L3 at R .Statement – 1 : The ratio PR :RQ equals 2 2: 5 .Statement – 2 : In any triangle, bisector of an angle divides the triangle into two similar triangles.Statement – 1 is true, Statement – 2 is true; Statement – 2 is not a correct explanation for Statement – 1Statement – 1 is true, Statement– 2 is false.Statement – 1 is false, Statement– 2 is true.Statement – 1 is true, Statement – 2 is true; Statement – 2 is a correct explanation for Statement – 1
- 4. Problem02If A = sin2 x + cos4 x , then for all real Xea.b.c.d.
- 5. Problem03The coefficient of xE in the expansion of (1−X− X2 + X3 ) 6 is-132 -144 132 144
- 6. Problem04equals √2 equals − √2 equals does not exist
- 7. Problem05Statement – 1 : The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is 9 C3Statement – 2 : The number of ways of choosing any 3 places from 9 different places is 9 C3 .Statement – 1 is true, Statement – 2 is true; Statement – 2 is not a correct explanation for Statement – 1Statement – 1 is true, Statement– 2 is false.Statement – 1 is false, Statement– 2 is true.Statement – 1 is true, Statement – 2 is true; Statement – 2 is a correct explanation for Statement – 1
- 8. Problem06 equalsa.b.c.d.
- 9. Problem07If y 3 0 = + > and y (0) = 2 , then y(ln2) is equal to5 13 -2 7
- 10. Problem08Let R be the set of real numbersStatement – 1 : A = {(x,y)∈R×R : y − x is an integer} is an equivalence relation on R .Statement – 2 : B = {(x,y)∈R×R : x = αy for some rational number α} is an equivalence relation on Statement – 1 is true, Statement – 2 is true; Statement – 2 is not a correct explanation for Statement – 1Statement – 1 is true, Statement– 2 is false.Statement – 1 is false, Statement– 2 is true.Statement – 1 is true, Statement – 2 is true; Statement – 2 is a correct explanation for Statement – 1
- 11. Problem09The value of ISa.b.c. Log 2d.πlog 2
- 12. Problem10Let α, β be real and z be a complex number. If z2 + αz + β = 0 has two distinct roots on the line Rez = 1, then it is necessary thatβ∈(−1, 0) |β| = 1 β∈(1, ∞)β∈(0, 1)
- 13. Problem11Consider 5 independent Bernoulli’s trials each with probability of success p. If the probability of at least one failure is greater than or equal to , then p lies in the intervala.b.c.d.
- 14. Problem12A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs. 11040 after19 months 20 months 21 months 18 months
- 15. Problem13The domain of the function f (x) is(0, ∞) (−∞, 0) (−∞, ∞) − {0} (−∞, ∞)
- 16. Problem14If the angle between the line and the planes cos 1then λ equalsa. b. ⅖c.d.⅔
- 17. Problem15If and then the value ofa.-3b.5c.3d.-5
- 18. Problem16Equation of the ellipse whose axes are the axes of coordinates and which passes through the point (−3, 1) and has eccentricity is5x2 + 3y2 − 48 = 0 3x2 + 5y2 −15 = 0 5x2 + 3y2 − 32 = 03x2 + 5y2 − 32 = 0
- 19. Problem17Let I be the purchase value of an equipment and V(t) be the value after it hasbeen used for t years. The value V(t) depreciates at a rate given by differentialequation , k > 0 is a constant and T is the total life in years of theequipment. Then the scrap value V(T) of the equipment isa.b.c.d.
- 20. Problem18The vector and are not perpendicular and andare two vectors satisfying: and a.d = 0 . Then the vector d is equal toa.b.c.d.
- 21. Problem19The two circles x2 + y2 = ax and x2 + y2 = c2 (c > 0) touch each other ifa = ca = 2c a = 2c 2 a = c
- 22. Problem20If C and D are two events such that C ⊂ D and P(D) ≠ 0 , then the correct statement among the following isP(C |D) ≥ P(C) P(C |D) < P(C) P(C |D) =P(C |D) = P(C)
- 23. Problem21The number of values of k for which the linear equations 4x + ky + 2z = 0 ; kx + 4y + z = 0 ; 2x + 2y + z = 0 possess a non-zero solution is2 1 zero 3
- 24. Problem22Consider the following statementsP : Suman is brilliantQ : Suman is richR : Suman is honestThe negation of the statement “Suman is brilliant and dishonest if and only if Suman is rich” can be expressed as~ (Q ↔ (P∧ ~ R)) ~ Q ↔~ P ∧R ~ (P∧ ~ R) ↔ Q~ P ∧ (Q ↔~ R)
- 25. Problem23The shortest distance between line y − x = 1 and curve x = y2 isa.b.c.d.
- 26. Problem24If the mean deviation about the median of the numbers a, 2a, …, 50a is 50, then a equals3 4 5 2
- 27. Problem25Statement – 1 : The point A(1, 0, 7) is the mirror image of the point B(1, 6, 3) in the line Statement – 2 : The line: x y 1 z 2bisects the line segment joining A(1, 0, 7) and B(1, 6, 3) .Statement – 1 is true, Statement–2 is true; Statement–2 is not a correct explanation for Statement – 1Statement – 1 is true, Statement– 2 is false.Statement – 1 is false, Statement– 2 is true.Statement – 1 is true, Statement – 2 is true; Statement – 2 is a correct explanation for Statement – 1
- 28. Problem26Let A and B be two symmetric matrices of order 3.Statement – 1 : A(BA) and (AB)A are symmetric matrices.Statement – 2 : AB is symmetric matrix if matrix multiplication of A and B is commutative. Statement – 1 is true, Statement – 2 is true; Statement – 2 is not a correct explanation for Statement – 1Statement – 1 is true, Statement– 2 is false.Statement – 1 is false, Statement– 2 is true.Statement – 1 is true, Statement – 2 is true; Statement – 2 is a correct explanation for Statement – 1
- 29. Problem27If ω(≠ 1) is a cube root of unity, and (1+ ω )7 = A + Bω . Then (A, B) equals(1, 1) (1, 0) (-1, 1) (4) (0, 1)
- 30. Problem28The value of p and q for which the function f is continuous for all x in R, isa.b.c.d.
- 31. Problem29The area of the region enclosed by the curves 1and the positive x-axis is1 square units square units square unitssquare units
- 32. Problem30For 5 x 0,2 define sintdt . Then f haslocal minimum at π and 2πlocal minimum at π and local maximum at 2πlocal maximum at π and local minimum at 2πlocal maximum at π and 2π
- 33. FOR SOLUTION VISIT WWW.VASISTA.NET
Editor's Notes
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