Other Maths · JEE Main previous year questions

2005 10 questions

1. Q32005 · 28 Apr 2005 · Shift 1

   If $\omega =\frac{z}{z-\frac{1}{3}i}$ and $|\omega |=1$, then $z$ lies on :

   1. A.an ellipse
   2. B.a circle
   3. C.a straight line
   4. D.a parabola
   Show answer

   Answer: C

2. Q112005 · 28 Apr 2005 · Shift 1

   The line parallel to the $x$ - axis and passing through the intersection of the lines $ax+2by+3b=0$ and $bx-2ay-3a=0$, where $(a,b)\ne (0,0)$ is :

   1. A.below the $x$ - axis at a distance of $\frac{3}{2}$ from it
   2. B.below the $x$ - axis at a distance of $\frac{2}{3}$ from it
   3. C.above the $x$ - axis at a distance of $\frac{3}{2}$ from it
   4. D.above the $x$ - axis at a distance of $\frac{2}{3}$ from it
   Show answer

   Answer: A

3. Q242005 · 28 Apr 2005 · Shift 1

   If $A^2-A+I=0$, then the inverse of $A$ is :

   1. A.$A+I$
   2. B.$A$
   3. C.$A-I$
   4. D.$I-A$
   Show answer

   Answer: D

4. Q292005 · 28 Apr 2005 · Shift 1

   If $I_1={\int }_0^1{2}^{x^2}dx$, $I_2={\int }_0^1{2}^{x^3}dx$, $I_3={\int }_1^2{2}^{x^2}dx$ and $I_4={\int }_1^2{2}^{x^3}dx$ then

   1. A.$I_2>I_1$
   2. B.$I_1>I_2$
   3. C.$I_3=I_4$
   4. D.$I_3>I_4$
   Show answer

   Answer: B

5. Q392005 · 28 Apr 2005 · Shift 1

   If $C$ is the mid point of $AB$ and $P$ is any point outside $AB$, then :

   1. A.$\overrightarrow{PA}+\overrightarrow{PB}=2\overrightarrow{PC}$
   2. B.$\overrightarrow{PA}+\overrightarrow{PB}=\overrightarrow{PC}$
   3. C.$\overrightarrow{PA}+\overrightarrow{PB}=2\overrightarrow{PC}=\vec{0}$
   4. D.$\overrightarrow{PA}+\overrightarrow{PB}=\overrightarrow{PC}=\vec{0}$
   Show answer

   Answer: A

6. Q562005 · 28 Apr 2005 · Shift 1

   The resultant $R$ of two forces acting on a particle is at right angles to one of them and its magnitude is one third of the other force. The ratio of larger force to smaller one is

   1. A.$2:1$
   2. B.$3:\sqrt{2}$
   3. C.$3:2$
   4. D.$3:2\sqrt{2}$
   Show answer

   Answer: D

7. Q572005 · 28 Apr 2005 · Shift 1

   A particle is projected from a point $O$ with velocity $u$ at an angle of $60^{\circ }$ with the horizontal. When it is moving in a direction at right angles to its direction at $O$, its velocity then is given by

   1. A.$\frac{u}{3}$
   2. B.$\frac{u}{2}$
   3. C.$\frac{2u}{3}$
   4. D.$\frac{u}{\sqrt{3}}$
   Show answer

   Answer: D

8. Q582005 · 28 Apr 2005 · Shift 1

   The value of ${}^{50}{C}_4+{\sum }_{r=1}^6{}^{56-r}{C}_3$ is

   1. A.${}^{55}{C}_4$
   2. B.${}^{55}{C}_3$
   3. C.${}^{56}{C}_3$
   4. D.${}^{56}{C}_4$
   Show answer

   Answer: D

9. Q662005 · 28 Apr 2005 · Shift 1

   If the equation $a_n{x}^n+a_{n-1}{x}^{n-1}+\dots \cdots +a_{1}x=0$, $a_1\ne 0,n\ge 2$, has a positive root $x=\alpha$, then the equation $n{a}_n{x}^{n-1}+(n-1)a_{n-1}{x}^{n-2}+\dots \cdots +a_1=0$ has a positive root, which is

   1. A.greater than $\alpha$
   2. B.smaller than $\alpha$
   3. C.greater than or equal to $\alpha$
   4. D.equal to $\alpha$
   Show answer

   Answer: B

10. Q712005 · 28 Apr 2005 · Shift 1

    Let $\vec{a}=\hat{i}-\hat{k}$, $\vec{b}=x\hat{i}+\hat{j}+(1-x)\hat{k}$ and $\vec{c}=y\hat{i}+x\hat{j}+(1+x-y)\hat{k}$. Then $\left[\vec{a},\vec{b},\vec{c}\right]$ depends on :

    1. A.only $y$
    2. B.only $x$
    3. C.both $x$ and $y$
    4. D.neither $x$ nor $y$
    Show answer

    Answer: D