Other Maths · JEE Main previous year questions

2006 7 questions

1. Q122006 · 29 Apr 2006 · Shift 1

   If $(a,a^2)$ falls inside the angle made by the lines $y=\frac{x}{2}$, $x>0$ and $y=3x$, $x>0$, then $a$ belong to :

   1. A.$(0,\frac{1}{2})$
   2. B.$(3,\infty )$
   3. C.$(\frac{1}{2},3)$
   4. D.$(-3,-\frac{1}{2})$
   Show answer

   Answer: C

2. Q182006 · 29 Apr 2006 · Shift 1

   If $x^m\cdot y^n=(x+y{)}^{m+n}$, then $\frac{dy}{dx}$ is

   1. A.$\frac{y}{x}$
   2. B.$\frac{x+y}{xy}$
   3. C.$xy$
   4. D.$\frac{x}{y}$
   Show answer

   Answer: A

3. Q222006 · 29 Apr 2006 · Shift 1

   Let $A=\left(\begin{array}{cc}1& 2\\ 3& 4\end{array}\right)$ and $B=\left(\begin{array}{cc}a& 0\\ 0& b\end{array}\right),a,b\in N$. Then

   1. A.there cannot exist any $B$ such that $AB=BA$
   2. B.there exist more then one but finite number of $B$'s such that $AB=BA$
   3. C.there exists exactly one $B$ such that $AB=BA$
   4. D.there exist infinitely many $B$'s such that $AB=BA$
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   Answer: D

4. Q302006 · 29 Apr 2006 · Shift 1

   The two lines $x=ay+b,z=cy+d$; and $x=a^{\prime }y+b^{\prime },z=c^{\prime }y+d^{\prime }$ are perpendicular to each other if :

   1. A.$a{a}^{\prime }+c{c}^{\prime }=-1$
   2. B.$a{a}^{\prime }+c{c}^{\prime }=1$
   3. C.$\frac{a}{a^{\prime }}+\frac{c}{c^{\prime }}=-1$
   4. D.$\frac{a}{a^{\prime }}+\frac{c}{c^{\prime }}=1$
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   Answer: A

5. Q342006 · 29 Apr 2006 · Shift 1

   A particle has two velocities of equal magnitude inclined to each other at an angle $\theta$. If one of them is halved, the angle between the other and the original resultant velocity is bisected by the new resultant. Then $\theta$ is

   1. A.$90^{\circ }$
   2. B.$120^{\circ }$
   3. C.$45^{\circ }$
   4. D.$60^{\circ }$
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   Answer: B

6. Q352006 · 29 Apr 2006 · Shift 1

   A body falling from rest under gravity passes a certain point P. It was at a distance of 400 m from P, 4 s prior to passing through P. If $g=10m/{\mathrm{s}}^2$, then the height above the point P from where the body began to fall is

   1. A.720 m
   2. B.900 m
   3. C.320 m
   4. D.680 m
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   Answer: A

7. Q372006 · 29 Apr 2006 · Shift 1

   For natural numbers $m,n$, if $(1-y{)}^m(1+y{)}^n=1+a_{1}y+a_2{y}^2+\dots$ and $a_1=a_2=10$, then $(m,n)$ is

   1. A.$(20,45)$
   2. B.$(35,20)$
   3. C.$(45,35)$
   4. D.$(35,45)$
   Show answer

   Answer: D