3D Geometry · JEE Main previous year questions

2005 5 questions

1. Q402005 · 28 Apr 2005 · Shift 1

   Let $a,b$ and $c$ be distinct non-negative numbers. If the vectors $a\hat{i}+a\hat{j}+c\hat{k}$, $\hat{i}+\hat{k}$ and $c\hat{i}+c\hat{j}+b\hat{k}$ lie in a plane, then $c$ is :

   1. A.the Geometric Mean of $a$ and $b$
   2. B.the Arithmetic Mean of $a$ and $b$
   3. C.equal to zero
   4. D.the Harmonic Mean of $a$ and $b$
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   Answer: A

2. Q552005 · 28 Apr 2005 · Shift 1

   $A$ and $B$ are two like parallel forces. A couple of moment $H$ lies in the plane of $A$ and $B$ and is combined with them. The resultant of $A$ and $B$ after combining is displaced through a distance

   1. A.$\frac{2H}{A-B}$
   2. B.$\frac{H}{A+B}$
   3. C.$\frac{H}{2(A+B)}$
   4. D.$\frac{H}{A-B}$
   Show answer

   Answer: B

3. Q672005 · 28 Apr 2005 · Shift 1

   If the angle $\theta$ between the line $\frac{x+1}{1}=\frac{y-1}{2}=\frac{z-2}{2}$ and the plane $2x-y+\sqrt{\lambda }z+4=0$ is such that $\sin \theta =\frac{1}{3}$ then value of $\lambda$ is :

   1. A.$\frac{5}{3}$
   2. B.$\frac{-3}{5}$
   3. C.$\frac{3}{4}$
   4. D.$\frac{-4}{3}$
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   Answer: A

4. Q682005 · 28 Apr 2005 · Shift 1

   If the plane $2ax-3ay+4az+6=0$ passes through the midpoint of the line joining the centres of the spheres $$x^2+y^2+z^2+6x-8y-2z=13\text{ and}$$ $$x^2+y^2+z^2-10x+4y-2z=8\text{ then }a\text{ equals :}$$

   1. A.$-1$
   2. B.$1$
   3. C.$-2$
   4. D.$2$
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   Answer: C

5. Q692005 · 28 Apr 2005 · Shift 1

   The distance between the line $$\vec{r}=2\hat{i}-2\hat{j}+3\hat{k}+\lambda (i-j+4k),\text{ and the plane}$$ $$\vec{r}\cdot \left(\hat{i}+5\hat{j}+\hat{k}\right)=5\text{ is}$$

   1. A.$\frac{10}{9}$
   2. B.$\frac{10}{3\sqrt{3}}$
   3. C.$\frac{3}{10}$
   4. D.$\frac{10}{3}$
   Show answer

   Answer: B