Solved papers for JEE Main & Advanced AIEEE Solved Paper-2002

AIEEE Solved Paper-2002 Total Questions - 75

1) If \[\alpha \ne \beta ,\,{{\alpha }^{2}}=5\alpha -3\] and \[{{\beta }^{2}}=5\beta -3\], then the equation having \[\alpha /\beta \] and \[\beta /\alpha \] as its roots, is AIEEE Solved Paper-2002

A)

\[3{{x}^{2}}+19x+3=0\]

B)

\[3{{x}^{2}}-19x+3=0\]

C)

     \[3{{x}^{2}}-19x-3=0\]

D)

     \[{{x}^{2}}-16x+1=0\]

View Answer
2) If \[y={{(x+\sqrt{1+{{x}^{2}}})}^{n}}\] , then \[(1+{{x}^{2}})\frac{{{d}^{2}}y}{d{{x}^{2}}}+\frac{dy}{dx}\] is AIEEE Solved Paper-2002

A)

                     \[{{n}^{2}}y\]

B)

             \[-{{n}^{2}}y\]

C)

             \[-y\]

D)

                       \[2{{x}^{2}}y\]

View Answer
3) If 1, \[{{\log }_{3}}\sqrt{({{3}^{1-x}}+2)},\,{{\log }_{3}}\,({{4.3}^{x}}-1)\] are in AP, then x equals AIEEE Solved Paper-2002

A)

\[{{\log }_{3}}4\]

B)

          \[1-{{\log }_{3}}4\]

C)

          \[1-{{\log }_{4}}3\]

D)

          \[{{\log }_{4}}3\]

View Answer
4) A problem in Mathematics is given to three students A, B, C and their respective probability of solving the problem is \[\frac{1}{2},\frac{1}{3}\] and \[\frac{1}{4}\]. Probability that the problem is solved, is AIEEE Solved Paper-2002

A)

3/4

B)

          1/2

C)

2/3

D)

          1/3

View Answer
5) The period of \[{{\sin }^{2}}\theta \] is AIEEE Solved Paper-2002

A)

\[{{\pi }^{2}}\]

B)

                                         \[\pi \]

C)

          \[2\pi \]

D)

          \[\pi /2\]

View Answer
6) \[l,\,m,\,n\] are the pth, qth and rth terms of a GP and all positive, then \[\left| \begin{matrix}    \log \,\,l & p & 1 \\    \log \,\,m & q & 1 \\    \log \,\,n & r & 1 \\ \end{matrix} \right|\] equals AIEEE Solved Paper-2002

A)

3

B)

          2

C)

1

D)

          zero

View Answer
7) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\sqrt{1-\cos 2x}}{\sqrt{2}x}\] is AIEEE Solved Paper-2002

A)

\[\lambda \]

B)

                                          \[-1\]

C)

          zero

D)

          does not exist

View Answer
8) A triangle with vertices (4, 0), (-1, -1), (3, 5) is

A)

isosceles and right angled

B)

isosceles but not right angled

C)

right angled but not isosceles

D)

neither right angled nor isosceles

View Answer
9) In a class of 100 students, there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average marks of the girls? AIEEE Solved Paper-2002

A)

73

B)

                                          65

C)

          68

D)

          74

View Answer
10) If \[{{\cot }^{-1}}(\sqrt{\cos \alpha })-{{\tan }^{-1}}(\sqrt{\cos \alpha })=x\], then \[\sin x\] is equal to AIEEE Solved Paper-2002

A)

\[{{\tan }^{2}}\left( \frac{\alpha }{2} \right)\]

B)

\[{{\cot }^{2}}\left( \frac{\alpha }{2} \right)\]

C)

          \[\tan \alpha \]

D)

          \[\cot \left( \frac{\alpha }{2} \right)\]

View Answer
11) The order and degree of the differential equation \[{{\left( 1+3\frac{dy}{dx} \right)}^{2/3}}\] are AIEEE Solved Paper-2002

A)

\[\left( 1,\frac{2}{3} \right)\]

B)

                          (3, 1)

C)

          (3, 3)

D)

          (1, 2)

View Answer
12) A plane which passes through the point (3, 2, 0) and the line \[\frac{x-4}{1}=\frac{y-7}{5}\frac{z-4}{4}\] is AIEEE Solved Paper-2002

A)

\[x-y+z=1\]

B)

\[x+y+z=5\]

C)

\[x+2y-z=1\]

D)

          \[2x-y+z=5\]

View Answer
13) The solution of the equation \[\frac{{{d}^{2}}y}{d{{x}^{2}}}={{e}^{-2x}}\] is AIEEE Solved Paper-2002

A)

     \[\frac{{{e}^{-2x}}}{4}\]

B)

                    \[\frac{{{e}^{-2x}}}{4}\,+cx+d\]

C)

\[\frac{1}{4}{{e}^{-2x}}+c\,{{x}^{2}}+d\]

D)

        \[\frac{1}{4}{{e}^{-2x}}+c\,+d\]

View Answer
14) \[\underset{x\to \infty }{\mathop{\lim }}\,{{\left( \frac{{{x}^{2}}+5x+3}{{{x}^{2}}+x+2} \right)}^{x}}\] is equal to AIEEE Solved Paper-2002

A)

\[{{e}^{4}}\]

B)

                                        \[{{e}^{2}}\]

C)

\[{{e}^{3}}\]

D)

          e

View Answer
15) The domain of \[{{\sin }^{-1}}[{{\log }_{3}}(x/3)]\] is AIEEE Solved Paper-2002

A)

[1, 9]

B)

                          [-1, 9]

C)

          [-9, 1]

D)

          [-9,-1]

View Answer
16) The value of \[{{2}^{1/4}}.\,{{4}^{1/8}}.\,\,{{8}^{1/16}}.....\,\,\infty \] is AIEEE Solved Paper-2002

A)

1

B)

                                          2

C)

3/2

D)

4

View Answer
17) Fifth term of a GP is 2, then the product of its 9 terms is AIEEE Solved Paper-2002

A)

256

B)

          512

C)

          1024

D)

          None of these

View Answer
18) \[\int{{{_{0}}^{10\pi }}}\left| \sin x \right|dx\] is AIEEE Solved Paper-2002

A)

20

B)

          8

C)

          10

D)

          18

View Answer
19) \[{{I}_{n}}=\int_{0}^{\pi /4}{{{\tan }^{n}}\,x\,dx,}\] , then    \[\underset{x\to \infty }{\mathop{\lim }}\,n\,[{{I}_{n}}+{{I}_{n+2}}]\] equals AIEEE Solved Paper-2002

A)

\[\frac{1}{2}\]

B)

                                          1

C)

          \[\infty \]

D)

                          zero

View Answer
20) \[\int_{0}^{2}{[{{x}^{2}}]}\,dx\] is AIEEE Solved Paper-2002

A)

\[2-\sqrt{2}\]

B)

          \[2+\sqrt{2}\]

C)

          \[\sqrt{2}-1\]

D)

          \[-\sqrt{2}-\sqrt{3}+5\]

View Answer
21) \[\int{_{-\pi }^{\pi }}\frac{2\pi (1+\sin x)}{1+{{\cos }^{2}}x}dx\] is AIEEE Solved Paper-2002

A)

\[\frac{{{\pi }^{2}}}{4}\]

B)

                          \[{{\pi }^{2}}\]

C)

          zero

D)

          \[\frac{\pi }{2}\]

View Answer
22) The    period    of   the    function \[f(x)={{\sin }^{4}}x+{{\cos }^{4}}x\] is AIEEE Solved Paper-2002

A)

\[\pi \]

B)

                          \[\frac{\pi }{2}\]

C)

          \[2\pi \]

D)

          None of these

View Answer
23) The domain of definition of the function\[f(x)=\sqrt{{{\log }_{10}}\left( \frac{5x-{{x}^{2}}}{4} \right)}\] is AIEEE Solved Paper-2002

A)

[1, 4]

B)

                          [1, 0]

C)

          [0, 5]

D)

          [5, 0]

View Answer
24) If \[\sin y=x\sin (a+y)\], then-,-is AIEEE Solved Paper-2002

A)

\[\frac{\sin a}{{{\sin }^{2}}(a+y)}\]

B)

          \[\frac{{{\sin }^{2}}\,(a+y)}{\sin \,\,a}\]

C)

          \[\sin \,a\,{{\sin }^{2}}(a+y)\]

D)

          \[\frac{{{\sin }^{2}}(a-y)}{\sin a}\]

View Answer
25) If \[{{x}^{y}}={{e}^{x-y}}\], then \[\frac{dy}{dx}\] is AIEEE Solved Paper-2002

A)

\[\frac{1+x}{1+\log x}\]

B)

                          \[\frac{1-\log x}{{{(1+\log x)}^{2}}}\]

C)

          not defined

D)

          \[\frac{\log x}{{{(1+\log x)}^{2}}}\]

View Answer
26) The two curves \[{{x}^{3}}-3x{{y}^{2}}+2=0\] and \[3\,{{x}^{2}}y-{{y}^{3}}-2=0\] AIEEE Solved Paper-2002

A)

cut at right angle

B)

touch each other

C)

cut at an angle \[\frac{\pi }{3}\]

D)

cut at an angle \[\frac{\pi }{4}\]

View Answer
27) The function \[f(x)={{\cot }^{-1}}x+x\] increases in the interval AIEEE Solved Paper-2002

A)

\[(1,\infty )\]

B)

                          \[(-1,\infty )\]

C)

          \[(-\infty ,\infty )\]

D)

\[(0,\infty )\]

View Answer
28) The greatest value of \[f(x)={{(x+1)}^{1/3}}-{{(x-1)}^{1/3}}\] on [0, 1] is AIEEE Solved Paper-2002

A)

1

B)

                          2

C)

          3

D)

1/3

View Answer
29) Evaluate \[\int{{{_{0}}^{\pi /2}}\frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}}dx}\] AIEEE Solved Paper-2002

A)

\[\frac{\pi }{4}\]

B)

\[\frac{\pi }{2}\]

C)

          0

D)

          1

View Answer
30) \[\int{\frac{dx}{x({{x}^{n}}+1)}}\] is equal to AIEEE Solved Paper-2002

A)

\[\frac{1}{n}\log \left( \frac{{{x}^{n}}}{{{x}^{n}}+1} \right)+C\]

B)

\[\frac{1}{n}\log \left( \frac{{{x}^{n}}+1}{{{x}^{n}}} \right)+C\]

C)

          \[\log \left( \frac{{{x}^{n}}}{{{x}^{n}}+1} \right)+C\]

D)

         None of these

View Answer
31) The area bounded by the curve \[y=2x-{{x}^{2}}\] and the straight line \[y=-x\] is given by AIEEE Solved Paper-2002

A)

\[\frac{9}{2}\] sq units

B)

          \[\frac{43}{6}\] sq units

C)

\[\frac{35}{6}\] sq units

D)

          None of these

View Answer
32) The differential equation of all non-vertical lines in a plane is AIEEE Solved Paper-2002

A)

\[\frac{{{d}^{2}}y}{d{{x}^{2}}}=0\]

B)

          \[\frac{{{d}^{2}}x}{d{{y}^{2}}}=0\]

C)

          \[\frac{dy}{dx}=0\]

D)

          \[\frac{dx}{dy}=0\]

View Answer
33) Given two vectors are \[\hat{i}-\hat{j}\] and \[\hat{i}+2\hat{j}\], the unit vector coplanar with the two vectors and perpendicular to first is AIEEE Solved Paper-2002

A)

\[\frac{1}{\sqrt{2}}(\hat{i}+\hat{j})\]

B)

          \[\frac{1}{\sqrt{5}}(2\hat{i}-\hat{j})\]

C)

          \[\pm \frac{1}{\sqrt{2}}(\hat{i}-\hat{k})\]

D)

          None of these

View Answer
34) The vector \[\hat{i}+x\hat{j}+3\hat{k}\] is rotated through an angle \[\theta \] and doubled in magnitude, then it becomes \[4\hat{i}+(4x-2)\hat{j}+2\hat{k}\]. The values of \[x\] are AIEEE Solved Paper-2002

A)

\[\left\{ -\frac{2}{3},2 \right\}\]

B)

          \[\left\{ \frac{1}{3},2 \right\}\]

C)

          \[\left\{ \frac{2}{3},0 \right\}\]

D)

          \[\left\{ 2,7 \right\}\]

View Answer
35) A parallelepiped is formed by planes drawn through the points (2, 3, 5) and (5, 9, 7), parallel to the coordinate planes. The length of a diagonal of the parallelopiped is AIEEE Solved Paper-2002

A)

7 units

B)

                          \[\sqrt{38}\] units

C)

          \[\sqrt{155}\] units

D)

          None of these

View Answer
36) The equation of the plane containing the line \[\frac{x-{{x}_{1}}}{l}=\frac{y-{{y}_{1}}}{m}=\frac{z-{{z}_{1}}}{n}\] is \[a(x-{{x}_{1}})+b(y-{{y}_{1}})+c(z-{{z}_{1}})=0\]              where AIEEE Solved Paper-2002

A)

\[a{{x}_{1}}+b{{y}_{1}}+c{{z}_{1}}=0\]

B)

\[al+bm+cn=0\]

C)

          \[\frac{a}{l}=\frac{b}{m}=\frac{c}{n}\]

D)

          \[l\,{{x}_{1}}+m{{y}_{1}}+n{{z}_{1}}=0\]

View Answer
37) A and B play a game where each is asked to select a number from 1 to 25. If the two numbers match, both of them win a prize. The probability that they will not win a prize in a single trial, is AIEEE Solved Paper-2002

A)

\[\frac{1}{25}\]

B)

                          \[\frac{24}{25}\]

C)

\[\frac{2}{25}\]

D)

          None of these

View Answer
38) If A and B are two mutually exclusive events, then AIEEE Solved Paper-2002

A)

\[P(A)<P(\overline{B})\]

B)

         \[P(A)>P(\overline{B})\]

C)

          \[P(A)<P(B)\]

D)

         None of these

View Answer
39) The equation of the directrix of the parabola \[{{y}^{2}}+4y+4x+2=0\] is AIEEE Solved Paper-2002

A)

\[x=-1\]

B)

                                       \[x=1\]

C)

\[x=-3/2\]

D)

\[x=3/2\]

View Answer
40) Let \[{{T}_{n}}\] denotes the number of triangles which can be formed using the vertices of a regular polygon of n sides. If \[{{T}_{n\,+1}}-{{T}_{n}}=21\], then n equals AIEEE Solved Paper-2002

A)

5

B)

                                        7

C)

          6

D)

          4

View Answer
41) In a \[\Delta ABC,\,\,2ca\,\sin \,\left( \frac{A-B+C}{2} \right)\] is equal to AIEEE Solved Paper-2002

A)

\[{{a}^{2}}+{{b}^{2}}-{{c}^{2}}\]

B)

         \[{{c}^{2}}+{{a}^{2}}-{{b}^{2}}\]

C)

\[{{b}^{2}}-{{c}^{2}}-{{a}^{2}}\]

D)

          \[{{c}^{2}}-{{a}^{2}}-{{b}^{2}}\]

View Answer
42) For \[x\in R\underset{x\to \infty }{\mathop{\lim }}\,{{\left( \frac{x-3}{x+2} \right)}^{x}}\] is equal to AIEEE Solved Paper-2002

A)

e

B)

                                          \[{{e}^{-1}}\]

C)

          \[{{e}^{-5}}\]

D)

          \[{{e}^{5}}\]

View Answer
43) The incentre of the triangle with vertices              \[(1,\sqrt{3})\], (0, 0) and (2,0) is AIEEE Solved Paper-2002

A)

\[\left( 1,\frac{\sqrt{3}}{2} \right)\]

B)

                         \[\left( \frac{2}{3},\frac{1}{\sqrt{3}} \right)\]

C)

          \[\left( \frac{2}{3},\frac{\sqrt{3}}{2} \right)\]

D)

          \[\left( 1,\frac{1}{\sqrt{3}} \right)\]

View Answer
44) If the vectors a, b and c from the sides BC, CA and AB respectively of a \[\Delta ABC\], then AIEEE Solved Paper-2002

A)

\[a.\,b=b.\,c=c.\,b=0\]

B)

\[a\times b=b\times c=c\times a\]

C)

\[a.\,b=b.\,c=c.\,a=0\]

D)

\[a\times a+a\times c+c\times a=0\]

View Answer
45) If \[\omega \] is an imaginary cube root of unity, then \[{{(1+\omega -{{\omega }^{2}})}^{7}}\] equals AIEEE Solved Paper-2002

A)

\[128\,\omega \]

B)

          \[-128\,\omega \]

C)

          \[128\,{{\omega }^{2}}\]

D)

          \[-128\,{{\omega }^{2}}\]

View Answer
46) If \[\left| \begin{matrix} 6\,i & -3\,i & 1 \\ 4 & 3\,i & -1 \\    20 & 3 & i \\ \end{matrix} \right|=x+iy\], then AIEEE Solved Paper-2002

A)

\[x=3,\,y=1\]

B)

                          \[x=1,\,y=3\]

C)

          \[x=0,\,y=3\]

D)

          \[x=0,\,y=0\]

View Answer
47) \[{{\sin }^{2}}\theta =\frac{4xy}{{{(x+y)}^{2}}}\] is true if and only if AIEEE Solved Paper-2002

A)

\[x-y\ne 0\]

B)

          \[x=-y\]

C)

          \[x=y\]

D)

          \[x\ne 0,y\ne 0\]

View Answer
48) The radius of the circle passing through the foci of the ellipse \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{9}\] and having its centre at (0, 3), is

A)

4 units

B)

          3 units

C)

          \[\sqrt{12}\] units

D)

          \[\frac{7}{2}\] units

View Answer
49) The probability of India winning a test match against West-Indies is \[1/2\] assuming independence from match to match. The probability that in a match series India's second win occurs at the third test is

A)

\[1/8\]

B)

\[1/4\]

C)

\[1/2\]

D)

          \[2/3\]

View Answer
50) If \[(\omega \ne 1)\] is a cubic root of unity, then \[\left| \begin{matrix}    1 & 1+i+{{\omega }^{2}} & {{\omega }^{2}} \\    1-i & -1 & {{\omega }^{2}}-1 \\    -i & -1+\omega -i & -1 \\ \end{matrix} \right|\] equals AIEEE Solved Paper-2002

A)

0

B)

          1

C)

          \[i\]

D)

          \[\omega \]

View Answer
51) A biased coin with probability \[p,0<p<1\], of heads is tossed until a head appears for the first time. If the probability that the number of tosses required is even, is \[2/5\], then p equals AIEEE Solved Paper-2002

A)

\[1/3\]

B)

                          \[2/3\]

C)

          \[2/5\]

D)

          \[3/5\]

View Answer
52) A fair die is tossed eight times. The probability that a third six is observed on the eighth throw, is AIEEE Solved Paper-2002

A)

\[\frac{^{7}{{C}_{2}}\times {{5}^{5}}}{{{6}^{7}}}\]

B)

\[\frac{^{7}{{C}_{2}}\times {{5}^{5}}}{{{6}^{8}}}\]

C)

\[\frac{^{7}{{C}_{2}}\times {{5}^{5}}}{{{6}^{6}}}\]

D)

          None of these

View Answer
53) Let \[f(2)=4\] and \[f'\,(2)=4\]. Then,\[\underset{x\to 2}{\mathop{\lim }}\,\frac{xf(2)-2f(x)}{x-2}\] is given by AIEEE Solved Paper-2002

A)

2

B)

\[-2\]

C)

                          \[-4\]

D)

                       3

View Answer
54) Three straight lines \[2x+11y-5=0\], \[24x+7y-20=0\] and \[4x-3y-2=0\] AIEEE Solved Paper-2002

A)

form a triangle

B)

are only concurrent

C)

are concurrent with one line bisecting the angle between the other two

D)

None of the above

View Answer
55) A straight line through the point (2, 2) intersects   the   lines   \[\sqrt{3}x+y=0\]   and \[\sqrt{3}x-y=0\] at the points A and B. The equation to the line AB so that the \[\Delta OAB\] is equilateral, is AIEEE Solved Paper-2002

A)

\[x-2=0\]

B)

\[y-2=0\]

C)

          \[x+y-4=0\]

D)

          None of these

View Answer
56) The greatest distance of the point P(10,7) from the circle \[{{x}^{2}}+{{y}^{2}}-4x-2y-20=0\] is AIEEE Solved Paper-2002

A)

10 units

B)

          15 units

C)

          5 units

D)

          None of these

View Answer
57) The equation of the tangent to the circle \[{{x}^{2}}+{{y}^{2}}+4x-4y+4=0\] which make equal intercepts on the positive coordinate axes, is AIEEE Solved Paper-2002

A)

\[x+y=2\]

B)

                          \[x+y=2\sqrt{2}\]

C)

\[x+y=4\]

D)

          \[x+y=8\]

View Answer
58) The equation of the ellipse whose foci are \[(\pm \,2,0)\] and eccentricity is \[1/2\], is AIEEE Solved Paper-2002

A)

\[\frac{{{x}^{2}}}{12}+\frac{{{y}^{2}}}{16}=1\]

B)

\[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{12}=1\]

C)

          \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{8}=1\]

D)

          None of these

View Answer
59) The equation of the chord joining two points \[({{x}_{1}},{{y}_{1}})\] and \[({{x}_{2}},{{y}_{2}})\] on the rectangular hyperbola \[xy={{c}^{2}}\]is AIEEE Solved Paper-2002

A)

\[\frac{x}{{{x}_{1}}+{{x}_{2}}}+\frac{y}{{{y}_{1}}+{{y}_{2}}}=1\]

B)

\[\frac{x}{{{x}_{1}}-{{x}_{2}}}+\frac{y}{{{y}_{1}}-{{y}_{2}}}=1\]

C)

\[\frac{x}{{{y}_{1}}+{{y}_{2}}}+\frac{y}{{{x}_{1}}+{{x}_{2}}}=1\]

D)

\[\frac{x}{{{y}_{1}}-{{y}_{2}}}+\frac{y}{{{x}_{1}}-{{x}_{2}}}=1\]

View Answer
60) If the vectors \[c,a=x\,\hat{i}+y\hat{j}+z\hat{k}\] and \[b=\hat{j}\] are such that a, c and b form a right handed system, then c is AIEEE Solved Paper-2002

A)

\[z\hat{i}-x\hat{k}\]

B)

                          0

C)

          \[y\,\hat{i}\]

D)

          \[-z\,\hat{i}+x\,\hat{k}\]

View Answer
61) The centre of the circle given by \[r.\,(\hat{i}+2\hat{j}+2\hat{k})=15\] and \[\left| r-(\hat{j}+2\hat{k} \right|=4\]is

A)

(0, 1, 2)

B)

               (1, 3, 4)

C)

(-1, 3, 4)

D)

          None of these

View Answer
62) The value of \[\frac{1-{{\tan }^{2}}{{15}^{o}}}{1+{{\tan }^{2}}{{15}^{o}}}\] is AIEEE Solved Paper-2002

A)

1

B)

                          \[\sqrt{3}\]

C)

             \[\frac{\sqrt{3}}{2}\]

D)

                       2

View Answer
63) If \[\tan \theta =-\frac{4}{3}\] then sine is AIEEE Solved Paper-2002

A)

\[-\frac{4}{5}\] but not \[\frac{4}{5}\]

B)

          \[-\frac{4}{5}\] or \[\frac{4}{5}\]

C)

          \[\frac{4}{5}\] but not \[-\frac{4}{5}\]

D)

          None of these

View Answer
64) If \[\sin (\alpha +\beta )=1,\,\,\sin (\alpha -\beta )=\frac{1}{2}\] then \[\tan \,(a+2\beta )\tan \,(2\alpha +\beta )\] is equal to AIEEE Solved Paper-2002

A)

1

B)

- 1

C)

zero

D)

None of these

View Answer
65) If \[y={{\sin }^{2}}\theta +\cos e{{c}^{2}}\theta ,\,\,\theta \ne 0\], then AIEEE Solved Paper-2002

A)

\[y=0\]

B)

                          \[y\le 2\]

C)

          \[y\ge -2\]

D)

          \[y\ge 2\]

View Answer
66) In a \[\Delta ABC\], \[a=4,\,b=3,\,\,\angle A={{60}^{o}}\], then c is the root of the equation AIEEE Solved Paper-2002

A)

\[{{c}^{2}}-3c-7=0\]

B)

\[{{c}^{2}}+3c+7=0\]

C)

          \[{{c}^{2}}-3c+7=0\]

D)

          \[{{c}^{2}}+3c-7=0\]

View Answer
67) In a \[\Delta ABC,\,\tan \frac{A}{2}=\frac{5}{6},\tan \frac{C}{2}=\frac{2}{5}\], then AIEEE Solved Paper-2002

A)

a, c, b are in AP

B)

          a, b, c are in AP

C)

          b, a, c are in AP

D)

         a, b, care in GP

View Answer
68) The equation \[a\sin x+b\cos x=c\], where \[\left| c \right|>\sqrt{{{a}^{2}}+{{b}^{2}}}\] has AIEEE Solved Paper-2002

A)

a unique solution

B)

infinite number of solutions

C)

no solution

D)

None of the above

View Answer
69) If \[\alpha \] is a root of \[25{{\cos }^{2}}\theta +5\cos \theta -12=0\frac{\pi }{2}<a<\pi \], then \[\sin 2\alpha \] is equal to AIEEE Solved Paper-2002

A)

\[\frac{24}{25}\]

B)

                          \[-\frac{24}{25}\]

C)

          \[\frac{13}{18}\]

D)

          \[-\frac{13}{18}\]

View Answer
70) \[{{\tan }^{-1}}\left( \frac{1}{4} \right)+{{\tan }^{-1}}\left( \frac{2}{9} \right)\] is equal to AIEEE Solved Paper-2002

A)

\[\frac{1}{2}{{\cos }^{-1}}\left( \frac{3}{5} \right)\]

B)

\[\frac{1}{2}{{\sin }^{-1}}\left( \frac{3}{5} \right)\]

C)

\[\frac{1}{2}{{\tan }^{-1}}\left( \frac{3}{5} \right)\]

D)

\[{{\tan }^{-1}}\left( \frac{1}{2} \right)\]

View Answer
71) \[\sum\limits_{n=0}^{\infty }{\frac{{{({{\log }_{e}}x)}^{n}}}{n!}}\] is equal to AIEEE Solved Paper-2002

A)

                                        \[{{\log }_{e}}x\]

B)

                                          \[x\]

C)

          \[{{\log }_{x}}e\]

D)

          None of these

View Answer
72) \[{{x}^{(x-1)-\frac{1}{2}{{(x-1)}^{2}}+\frac{{{(x-1)}^{3}}}{3}-\frac{{{(x-1)}^{4}}}{4}+....}}\] is equal to AIEEE Solved Paper-2002

A)

\[\log \,(x-1)\]

B)

\[\log \,\,x\]

C)

\[x\]

D)

          None of these

View Answer
73) The     coefficient    of    \[{{x}^{5}}\] in \[{{(1+2x+3{{x}^{2}}+....)}^{-3/2}}\] is AIEEE Solved Paper-2002

A)

                                        21

B)

          25

C)

          26

D)

          None of these

View Answer
74) If \[\left| x \right|<1\], then the coefficient of \[{{x}^{n}}\] in expansion of \[{{(1+x+{{x}^{2}}+{{x}^{3}}+....)}^{2}}\] is AIEEE Solved Paper-2002

A)

n

B)

          \[n-1\]

C)

          \[n+2\]

D)

          \[n+1\]

View Answer
75) The number of real roots of \[{{3}^{2{{x}^{2}}-7x+7}}=9\] is AIEEE Solved Paper-2002

A)

zero

B)

          2

C)

          1

D)

          4

View Answer

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done AIEEE Solved Paper-2002 Total Questions - 75

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AIEEE Solved Paper-2002

AIEEE Solved Paper-2002 Total Questions - 75