# Solved papers for JEE Main & Advanced AIEEE Solved Paper-2004

### done AIEEE Solved Paper-2004 Total Questions - 75

• question_answer1) Let$R=\{(1,3),(4,2),(2,4),(2,3),(3,1)\}$be a relation on the set$A=\{1,2,3,4\}$. The relation R is

A)
a function

B)
transitive

C)
not symmetric

D)
reflexive

• question_answer2) The range of the function$f(x){{=}^{7-x}}{{P}_{x-3}}$is

A)
{1, 2, 3}

B)
{1, 2, 3, 4, 5, 6}

C)
{1, 2, 3, 4}

D)
{1, 2, 3, 4, 5}

• question_answer3) Let$z,w$be complex numbers such that $\overline{z}=i\overline{w}=0$ and $arg(zw)=\pi$. Then, $\arg (z)$ equals

A)
$\frac{\pi }{4}$

B)
$\frac{\pi }{2}$

C)
$\frac{3\pi }{4}$

D)
$\frac{5\pi }{4}$

• question_answer4) If$z=x-2y$and${{z}^{1/3}}=p+iq,$. Then ${\left( \frac{x}{p}+\frac{y}{q} \right)}/{({{p}^{2}}+{{q}^{2}})}\;$ is equal to

A)
1

B)
$-1$

C)
2

D)
$-2$

• question_answer5) If$|{{z}^{2}}-1|=|z{{|}^{2}}+1,$then z lies on

A)
the real axis

B)
the imaginary axis

C)
a circle

D)
an ellipse

• question_answer6) Let$A=\left[ \begin{matrix} 0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0 \\ \end{matrix} \right].$The only correct statement about the matrix A is

A)
A is a zero matrix

B)
$A=(-\text{ }1)l,$where$l$is a unit matrix

C)
${{A}^{-1}}$does not exist

D)
${{A}^{2}}=l$

• question_answer7) Let$A=\left[ \begin{matrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \\ \end{matrix} \right]$and$10B=\left[ \begin{matrix} 4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3 \\ \end{matrix} \right].$If B is the inverse of matrix A, then a is

A)
-2

B)
1

C)
2

D)
5

• question_answer8) If${{a}_{1}},{{a}_{2}},{{a}_{3}}....,{{a}_{n}},...$are in GP, then the value of the determinant $\left| \begin{matrix} \log {{a}_{n}} & \log {{a}_{n+1}} & \log {{a}_{n+2}} \\ \log \,\,{{a}_{n+3}} & \log {{a}_{n+4}} & \log {{a}_{n+5}} \\ \log {{a}_{n+6}} & \log {{a}_{n+7}} & \log {{a}_{n+8}} \\ \end{matrix} \right|,$ is

A)
0

B)
1

C)
2

D)
$-2$

• question_answer9) Let two numbers have arithmetic mean 9 and geometric mean 4. Then, these numbers are the roots of the quadratic equation

A)
${{x}^{2}}+18x+16=0$

B)
${{x}^{2}}-18x+16=0$

C)
${{x}^{2}}+18x-16=0$

D)
${{x}^{2}}+18x-16=0$

• question_answer10) If$(1-p)$is a root of quadratic equation${{x}^{2}}+px$ $+(1-p)=0,$then its roots are

A)
$0,1$

B)
$-1,1$

C)
$0,-1$

D)
$-1,2$

• question_answer11) Let$S(K)=1+3+5+...+(2K-1)=3+{{K}^{2}}.$Then, which of the following is true?

A)
S(1) is correct

B)
$S(K)\Rightarrow S(K+1)$

C)
$S(K)S(K+1)$

D)
Principle of mathematical induction can be used to prove the formula

• question_answer12) How many ways are there to arrange the letters in the word GARDEN with the vowels in alphabetical order?

A)
120

B)
240

C)
360

D)
480

• question_answer13) The number of ways of distributing 8 identical balls in 3 distinct boxes, so that none of the boxes is empty, is

A)
5

B)
21

C)
${{3}^{8}}$

D)
$^{8}{{C}_{3}}$

• question_answer14) If one root of the equation${{x}^{2}}+px+12=0$is 4, while the equation${{x}^{2}}+px+q=0$has equal roots, then the value of 'q' is

A)
$\frac{49}{4}$

B)
12

C)
3

D)
4

• question_answer15) The coefficient of the middle term in the binomial expansion in powers of$x$of${{(1+\alpha x)}^{4}}$ and of${{(1-ax)}^{6}}$is the same, if a equals

A)
$-\frac{5}{3}$

B)
$\frac{10}{3}$

C)
$-\frac{3}{10}$

D)
$\frac{3}{5}$

• question_answer16) The coefficient of${{x}^{n}}$in the expansion of $(1+x){{(1-x)}^{n}}$is

A)
$(n-1)$

B)
${{(-1)}^{n}}(1-n)$

C)
${{(-1)}^{n-1}}{{(n-1)}^{2}}$

D)
${{(-1)}^{n-1}}n$

• question_answer17) If${{S}_{n}}=\sum\limits_{r=0}^{n}{\frac{1}{^{n}{{C}_{r}}}}$and${{t}_{n}}=\sum\limits_{r=0}^{n}{\frac{r}{^{n}{{C}_{r}}}}$then$\frac{{{t}_{n}}}{{{S}_{n}}}$is equal to

A)
$\frac{n}{2}$

B)
$\frac{n}{2}-1$

C)
$n-1$

D)
$\frac{2n-1}{2}$

• question_answer18) Let${{T}_{r}}$be the rth term of an AP whose first term is a and common difference is d. If for some positive integers $m,n,m\ne n,{{T}_{m}}=\frac{1}{n}$and${{T}_{n}}=\frac{1}{m},$then$a-d$equals

A)
0

B)
1

C)
$\frac{1}{mn}$

D)
$\frac{1}{m}+\frac{1}{n}$

• question_answer19) The sum of the first$n$terms of the series ${{1}^{2}}+{{2.2}^{2}}+{{3}^{2}}+{{2.4}^{2}}+{{5}^{2}}+{{2.6}^{2}}+....$is $\frac{n{{(n+1)}^{2}}}{2},$ when n is even. When n is odd, the sum is

A)
$\frac{3n(n+1)}{2}$

B)
$\frac{{{n}^{2}}(n+1)}{2}$

C)
$\frac{n{{(n+1)}^{2}}}{4}$

D)
${{\left[ \frac{n(n+1)}{4} \right]}^{2}}$

• question_answer20) The sum of series$\frac{1}{2!}+\frac{1}{4!}+\frac{1}{6!}+.....$is

A)
$\frac{({{e}^{2}}-1)}{2}$

B)
$\frac{{{(e-1)}^{2}}}{2e}$

C)
$\frac{({{e}^{2}}-1)}{2e}$

D)
$\frac{({{e}^{2}}-2)}{e}$

• question_answer21) Let$\alpha ,\beta$be such that$\pi <\alpha -\beta <3\pi .$.If$\sin \alpha +\sin \beta =-\frac{21}{65}$and$\cos \alpha +\cos \beta =-\frac{27}{65},$then the value of$\cos \left( \frac{\alpha -\beta }{2} \right)$is

A)
$-\frac{3}{\sqrt{130}}$

B)
$\frac{3}{\sqrt{130}}$

C)
$\frac{6}{65}$

D)
$-\frac{6}{65}$

• question_answer22) If$u=\sqrt{{{a}^{2}}{{\cos }^{2}}\theta +{{b}^{2}}{{\sin }^{2}}\theta }$ $+\sqrt{{{a}^{2}}{{\sin }^{2}}\theta +{{b}^{2}}{{\cos }^{2}}\theta },$ then the difference between the maximum and minimum values of${{u}^{2}}$is given by

A)
$2({{a}^{2}}+{{b}^{2}})$

B)
$2\sqrt{{{a}^{2}}+{{b}^{2}}}$

C)
${{(a+b)}^{2}}$

D)
${{(a-b)}^{2}}$

• question_answer23) The sides of a triangle are$\sin \alpha ,\text{ }\cos \alpha$and$\sqrt{1+\sin \alpha \cos \alpha }$for some$0<\alpha <\frac{\pi }{2}$. Then, the greatest angle of the triangle is

A)
$60{}^\circ$

B)
$90{}^\circ$

C)
$120{}^\circ$

D)
$150{}^\circ$

• question_answer24) A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is $60{}^\circ$and when he retires 40 m away from the tree, the angle of elevation becomes$30{}^\circ$. The breadth of the river is

A)
20 m

B)
30 m

C)
40 m

D)
60 m

• question_answer25) If $f:R\to S,$ defined by $f(x)=\sin x-\sqrt{3}\cos x+1,$is onto, then the interval of S is

A)
$[0,\text{ }3]$

B)
$[-1,\text{ }1]$

C)
$[0,\,1]$

D)
$[-1,\text{ }3]$

• question_answer26) The graph of the function$y=f(x)$is symmetrical about the line$x=2,$then

A)
$f(x+2)=f(x-2)$

B)
$f(2+x)=f(2-x)$

C)
$f(x)=f(-x)$

D)
$f(x)=-f(-x)$

• question_answer27) The domain of the function $f(x)=\frac{si{{n}^{-1}}(x-3)}{\sqrt{9-{{x}^{2}}}}$is

A)
[2, 3]

B)
[2, 3)

C)
[1, 2]

D)
[1, 2)

• question_answer28) If$\underset{x\to \infty }{\mathop{\lim }}\,{{\left( 1+\frac{a}{x}+\frac{b}{{{x}^{2}}} \right)}^{2x}}={{e}^{2}},$then the values of a and b are

A)
$a\in R,b\in R$

B)
$a=1,b\in R$

C)
$a\in R,b=2$

D)
$a=1,b=2$

• question_answer29) Let$f(x)=\frac{1-\tan x}{4x-\pi },x\ne \frac{\pi }{4},x\in \left[ 0,\frac{\pi }{2} \right]$. If f(x) is continuous in$\left[ 0,\frac{\pi }{2} \right]$,then$f\left( \frac{\pi }{4} \right)$is

A)
1

B)
1/2

C)
$-1/2$

D)
$-1$

• question_answer30) If$x={{e}^{y+{{e}^{y+....\infty }}}},x>0,$then$\frac{dy}{dx}$is

A)
$\frac{x}{1+x}$

B)
$\frac{1}{x}$

C)
$\frac{1-x}{x}$

D)
$\frac{1+x}{x}$

• question_answer31) A point on the parabola${{y}^{2}}=18x$at which the ordinate increases at twice the rate of the abscissa, is

A)
(2, 4)

B)
(2, -4)

C)
$\left( -\frac{9}{8},\frac{9}{2} \right)$

D)
$\left( \frac{9}{8},\frac{9}{2} \right)$

• question_answer32) A function$y=f(x)$has a second order derivative$f'\,'=6(x-1)$. If its graph passes through the point (2, 1) and at that point, the tangent to the graph is$y=3x-5,$then the function is

A)
${{(x-1)}^{2}}$

B)
${{(x-1)}^{3}}$

C)
${{(x+1)}^{3}}$

D)
${{(x+1)}^{2}}$

• question_answer33) The normal to the curve$x=a(1+\cos \theta ),$ $y=a\sin \theta$at$'\theta '$always passes through the fixed point

A)
(a, 0)

B)
(0, a)

C)
(0, 0)

D)
(a, a)

• question_answer34) If$2a+3b+6c=0,$ then atleast one root of the equation$a{{x}^{2}}+bx+c=0$lies in the interval

A)
(0, 1)

B)
(1, 2)

C)
(2, 3)

D)
(1, 3)

• question_answer35) $\underset{n\to \infty }{\mathop{\lim }}\,\sum\limits_{r=1}^{n}{\frac{1}{n}{{e}^{r/n}}}$is

A)
$e$

B)
$e-1$

C)
$1-e$

D)
$e+1$

• question_answer36) If $\int{\frac{\sin x}{\sin (x-\alpha )}}dx$ $=Ax+B\text{ }\log \text{ }\sin (x-\alpha )+C,$then value of $(A,\text{ }B)$is

A)
$(sin\text{ }\alpha ,\text{ }cos\text{ }\alpha )$

B)
(b)$(cos\text{ }\alpha ,\text{ }sin\text{ }\alpha \text{)}$

C)
$(-\sin \text{ }\alpha ,\text{ }\cos \text{ }\alpha )$

D)
$(-\cos \text{ }\alpha ,\text{ }\sin \text{ }\alpha )$

• question_answer37) $\int{\frac{dx}{\cos x-\sin x}}$is equal to

A)
$\frac{1}{\sqrt{2}}\log \left| \tan \left( \frac{x}{2}-\frac{\pi }{8} \right) \right|+C$

B)
$\frac{1}{\sqrt{2}}\log \left| \cot \left( \frac{x}{2} \right) \right|+C$

C)
$\frac{1}{\sqrt{2}}\log \left| \tan \left( \frac{x}{2}-\frac{3\pi }{8} \right) \right|+C$

D)
$\frac{1}{\sqrt{2}}\log \left| \tan \left( \frac{x}{2}+\frac{3\pi }{8} \right) \right|+C$

• question_answer38) The value of $\int_{-2}^{3}{|1-{{x}^{2}}|}dx$is

A)
$\frac{28}{3}$

B)
$\frac{14}{3}$

C)
$\frac{7}{3}$

D)
$\frac{1}{3}$

• question_answer39) The value of$\int_{0}^{\pi /2}{\frac{{{(\sin x+\cos x)}^{2}}}{\sqrt{1+\sin 2x}}}dx$is

A)

B)
1

C)
2

D)
3

• question_answer40) If$\int_{0}^{\pi }{x}f(\sin x)dx=A\int_{0}^{\pi /2}{f(\sin x)}dx,$then A is equal to

A)
0

B)
$\pi$

C)
$\frac{\pi }{4}$

D)
$2\,\pi$

• question_answer41) If$f(x)=\frac{{{e}^{x}}}{1+{{e}^{x}}},{{I}_{1}}=\int_{f(-a)}^{f(a)}{x}g\{x(1-x)\}dx$and${{I}_{2}}=\int_{f(-a)}^{f(a)}{g\{x(1-x)\}dx},$ then the value of$\frac{{{I}_{2}}}{{{I}_{1}}}$is

A)
2

B)
$-3$

C)
$-1$

D)
1

• question_answer42) The area of the region bounded by the curves $y=|x-2|,x=1,x=3$and the X-axis is

A)
1

B)
2

C)
3

D)
4

• question_answer43) The differential equation for the family of curves${{x}^{2}}+{{y}^{2}}-2\text{ }ay=0,$where a is an arbitrary constant, is

A)
$2({{x}^{2}}-{{y}^{2}})y'=xy$

B)
$2({{x}^{2}}+{{y}^{2}})y'=xy$

C)
$({{x}^{2}}-{{y}^{2}})y'=2xy$

D)
$({{x}^{2}}+{{y}^{2}})y'=2xy$

• question_answer44) The solution of the differential equation $ydx+(x+{{x}^{2}}y)dy=0$is

A)
$-\frac{1}{xy}=C$

B)
$-\frac{1}{xy}+\log y=C$

C)
$\frac{1}{xy}+\log y=C$

D)
$\log y=Cx$

• question_answer45) Let A (2, - 3) and B (- 2,1) be vertices of a$\Delta ABC$ If the centroid of this triangle moves on the line $2x+3y=1,$then the locus of the vertex C is the line

A)
$2x+3y=9$

B)
$2x-3y=7$

C)
$3x+2y=5$

D)
$3x-2y=3$

• question_answer46) The equation of the straight line passing through the point (4, 3) and making intercepts on the coordinate axes whose sum is -1, is

A)
$\frac{x}{2}+\frac{y}{3}=-1$and$\frac{x}{-2}+\frac{y}{1}=-1$

B)
$\frac{x}{2}-\frac{y}{3}=-1$and$\frac{x}{-2}+\frac{y}{1}=-1$

C)
$\frac{x}{2}+\frac{y}{3}=1$and$\frac{x}{-2}+\frac{y}{1}=1$

D)
$\frac{x}{2}-\frac{y}{3}\,=1$ and $\frac{x}{-2}\,+\frac{y}{1}\,=1$

• question_answer47) If the sum of the slopes of the lines given by ${{x}^{2}}-2cxy-7{{y}^{2}}=0$is four times their product, then c has the value

A)
1

B)
$-1$

C)
2

D)
$-2$

• question_answer48) If  one  of  the  lines   given  by$6{{x}^{2}}-xy+4c{{y}^{2}}=0$is$3x+4y=0,$then c equals

A)
1

B)
$-1$

C)
3

D)
$-3$

• question_answer49) If a circle passes through the point [a, b) and cuts the circle${{x}^{2}}+{{y}^{2}}=4$orthogonally, then the locus of its centre is

A)
$2ax+2by+({{a}^{2}}+{{b}^{2}}+4)=0$

B)
$2\,ax\,+2by-({{a}^{2}}+{{b}^{2}}\,+4)=0$

C)
$2ax-2by+({{a}^{2}}+{{b}^{2}}+4)=0$

D)
$2ax-2by-({{a}^{2}}+{{b}^{2}}+4)=0$

• question_answer50) A variable circle passes through the fixed point $A(p,\text{ }q)$and touches x-axis. The locus of the other end of the diameter through A is

A)
${{(x-p)}^{2}}=4qy$

B)
${{(x-q)}^{2}}=4qy$

C)
${{(y-p)}^{2}}=4qx$

D)
${{(y-q)}^{2}}=4px$

• question_answer51) If the lines$2x+3y+1=0$and$3x-y-4=0$lie along diameters of a circle of circumference$10\pi ,$then the equation of the circle is

A)
${{x}^{2}}+{{y}^{2}}-2x+2y-23=0$

B)
${{x}^{2}}+{{y}^{2}}-2x-2y-23=0$

C)
${{x}^{2}}+{{y}^{2}}+2x+2y-23=0$

D)
${{x}^{2}}+{{y}^{2}}+2x-2y-23=0$

• question_answer52) The intercept on the line$y=x$by the circle${{x}^{2}}+{{y}^{2}}-2x=0$is AB. Equation of the circle on AB as a diameter is

A)
${{x}^{2}}+{{y}^{2}}-x-y=0$

B)
${{x}^{2}}+{{y}^{2}}-x+y=0$

C)
${{x}^{2}}+{{y}^{2}}+x+y=0$

D)
${{x}^{2}}+{{y}^{2}}+x-y=0$

• question_answer53) If$a\ne 0$and the line$2bx+3cy+4d=0$passes through the points of intersection of the parabolas${{y}^{2}}=4\text{ }ax$and${{x}^{2}}=4\text{ }ay,$then

A)
${{d}^{2}}+{{(2b+3c)}^{2}}=0$

B)
${{d}^{2}}+{{(3b+2c)}^{2}}=0$

C)
${{d}^{2}}+{{(2b-3c)}^{2}}=0$

D)
${{d}^{2}}+{{(3b-2c)}^{2}}=0$

• question_answer54) The eccentricity of an ellipse with its centre at the origin, is$\frac{1}{2}$. If one of the directories is$x=4,$then the equation of the ellipse is

A)
$3{{x}^{2}}+4{{y}^{2}}=1$

B)
$3{{x}^{2}}+4{{y}^{2}}=12$

C)
$4{{x}^{2}}+3{{y}^{2}}=12$

D)
$4{{x}^{2}}+3{{y}^{2}}=1$

• question_answer55) A line makes the same angle$\theta$with each of the x and z-axes. If the angle$\beta ,$which it makes with y-axis, is such that${{\sin }^{2}}\beta =3{{\sin }^{2}}\theta ,$then$\cos \theta$equals

A)
$\frac{2}{3}$

B)
$\frac{1}{5}$

C)
$\frac{3}{5}$

D)
$\frac{2}{5}$

• question_answer56) Distance between two parallel planes $2x+y+2z=8$and$4x+2y+4z+5=0$is

A)
$\frac{3}{2}$

B)
$\frac{5}{2}$

C)
$\frac{7}{2}$

D)
$\frac{9}{2}$

• question_answer57) A line with direction cosines proportional to 2,1,2 meets each of the lines$x=y+a=z$and $x+a=2y=2z$. The coordinates of each of the points of intersection are given by

A)
(3a, 3a, 3a), (a, a, a)

B)
(3a, 2a, 3a), (a, a, a)

C)
(3a, 2a, 3a), (a, a, 2a)

D)
(2a, 3a, 3a), (2a, a, a)

• question_answer58) If the straight lines $x=1+s,y=-3-\lambda s,$ $z=1+\lambda \,s$and$x=\frac{t}{2},y=1+t,z=2-t,$with parameters s and t respectively, are coplanar, then$\lambda ,$equals

A)
$-2$

B)
$-1$

C)
$-\frac{1}{2}$

D)
0

• question_answer59) The intersection of the spheres ${{x}^{2}}+{{y}^{2}}+{{z}^{2}}+7x-2y-z=13$ and ${{x}^{2}}+{{y}^{2}}+{{z}^{2}}-3x+3y+4z=8$ is the same as the intersection of one of the sphere and the plane

A)
$x-y-z=1$

B)
$x-2y-z=1$

C)
$x-y-2z=1$

D)
$2x-y-z=1$

• question_answer60) Let a, b and c be three non-zero vectors such that no two of these are collinear. If the vector $a+2b$is collinear with c and$b+3c$is collinear with a$(\lambda$being some non-zero scalar), then $a+2b+6c$equals

A)
$\lambda a$

B)
$\lambda b$

C)
$\lambda c$

D)
0

• question_answer61) A particle is acted upon by constant forces $4\hat{i}+\hat{j}-3\hat{k}$and$3\hat{i}+\hat{j}-\hat{k}$which displace it from a point$\hat{i}+2\hat{j}-3\hat{k}$to the point $5\hat{i}+4\hat{j}+\hat{k}$. The work done in standard units by the forces is given by

A)
40

B)
30

C)
25

D)
15

• question_answer62) If a, b, c are non-coplanar vectors and$\lambda$is a real number, then the vectors$a+2b+3c,\lambda b+4c$and$(2\lambda -1)c$are non-coplanar for

A)
all values of$\lambda$

B)
all except one value of $\lambda$

C)
all except two values of $\lambda$

D)
no value of$\lambda$

• question_answer63) Let$u,v,w$be such that$|u|=1,|v|=2,$$|w|=3.$If the projection v along u is equal to that of w along u and$v,w$are perpendicular to each other, then$|u-v+w|$equals

A)
2

B)
$\sqrt{7}$

C)
$\sqrt{14}$

D)
14

• question_answer64) Let a,b and c be non-zero vectors such that $(a\times b)\times c=\frac{1}{3}|b||c|a.$If$\theta$is the acute angle between the vectors b and c, then$\sin \theta$equals

A)
$\frac{1}{3}$

B)
$\frac{\sqrt{2}}{3}$

C)
$\frac{2}{3}$

D)
$\frac{2\sqrt{2}}{3}$

• question_answer65) Consider the following statements (1) Mode can be computed from histogram. (2) Median is not independent of change of scale. (3) Variance is independent of change of origin and scale. (4) Which of these is/are correct?

A)
Only (1)

B)
Only (2)

C)
Only (1) and (2)

D)
(1), (2) and (3)

• question_answer66) In a series of$2n$observations, half of them equal$a$and remaining half equal$-a$. If the standard deviation of the observations is 2, then $|a|$ equals

A)
$\frac{1}{n}$

B)
$\sqrt{2}$

C)
$2$

D)
$\frac{\sqrt{2}}{n}$

• question_answer67) The probability that A speaks truth is 4/5 while this probability for B is 3/4. The probability that they contradict each other when asked to speak on a fact, is

A)
$\frac{3}{20}$

B)
$\frac{1}{5}$

C)
$\frac{7}{20}$

D)
$\frac{4}{5}$

• question_answer68) A random variable X has the probability distribution  $x$ 1 2 3 4 5 6 7 8 $p(x)$ 0.15 0.23 0.12 0.1 0.2 0.08 0.07 0.05
For the events E = {X is a prime number} and$F=\{X<4\},$the probability$P(E\cup F)$is

A)
0.87

B)
0.77

C)
0.35

D)
0.50

• question_answer69) The mean and the variance of a binomial distribution are 4 and 2, respectively. Then, the probability of 2 successes is

A)
$\frac{37}{256}$

B)
$\frac{219}{256}$

C)
$\frac{128}{256}$

D)
$\frac{28}{256}$

• question_answer70) With two forces acting at a point, the maximum effect is obtained when their resultant is 4N. If they act at right angles, then their resultant is 3N. Then, the forces are

A)
$(2+\sqrt{2})N$and$(2-\sqrt{2})N$

B)
$(2+\sqrt{3})N$and$(2-\sqrt{3})N$

C)
$\left( 2+\frac{1}{2}\sqrt{2} \right)N$and $\left( 2-\frac{1}{2}\sqrt{2} \right)N$

D)
$\left( 2+\frac{1}{2}\sqrt{3} \right)N$and$\left( 2-\frac{1}{2}\sqrt{3} \right)N$

• question_answer71) In a right angled $\Delta ABC,\,\,\angle A={{90}^{\text{o}}}$ and sides a,b,c are respectively, 5 cm, 4 cm and 3 cm. If a force F has moments 0, 9 and 16 (in N cm) units respectively about vertices A, B and C, the magnitude of F is

A)
3

B)
4

C)
5

D)
9

• question_answer72) Three forces P, Q and R acting along$IA,IB$and $IC,$where$I$is the incentre of a$\Delta ABC,$are in equilibrium. Then, P : Q : R is

A)
$\cos \frac{A}{2}:\cos \frac{B}{2}:\cos \frac{C}{2}$

B)
$\sin \frac{A}{2}:\sin \frac{B}{2}:\sin \frac{C}{2}$

C)
$\sec \frac{A}{2}:\sec \frac{B}{2}:\sec \frac{C}{2}$

D)
$\cos ec\,\frac{A}{2}:\,\,\cos ec\,\frac{B}{2}\,:\,\cos ec\,\frac{C}{2}$

• question_answer73) A particle moves towards East from a point A to a point B at the rate of 4 km/h and then towards North from B to C at rate of 5 km/h. If AB = 12 km and BC = 5 km, then its average speed for its journey from A to C and resultant average velocity direct from A to C are respectively

A)
$\frac{17}{14}km/h\text{ }and\frac{13}{4}km/h$

B)
$\frac{13}{4}km/h\text{ }and\frac{17}{4}km/h$

C)
$\frac{17}{9}km/h\text{ }and\frac{13}{9}km/h$

D)
$\frac{13}{9}km/h\text{ }and\frac{17}{9}km/h$

• question_answer74) A velocity 1/4 m/s is resolved into two components along OA and OB making angles $30{}^\circ$and$45{}^\circ$respectively with the given velocity, Then, the component along OB is

A)
$\frac{1}{8}m/s$

B)
$\frac{1}{4}(\sqrt{3}-1)m/s$

C)
$\frac{1}{4}m/s$

D)
$\frac{1}{8}(\sqrt{6}-\sqrt{2})m/s$

• question_answer75) If${{t}_{1}}$and${{t}_{2}}$are the times of flight of two particles having the same initial velocity u and range R on the horizontal, then$t_{1}^{2}+t_{2}^{2}$is equal to

A)
${{u}^{2}}/g$

B)
$4{{u}^{2}}/{{g}^{2}}$

C)
${{u}^{2}}/2g$

D)
1