M.C.Q (1 Marks)

MCQ 11 Mark

What is the length of foot of perpendicular drawn from the point $P(3, 4, 5)$ on $y-$axis.

A
$\sqrt{41}$
✓
$\sqrt{34}$
C
$5$
D
$\text{None of these.}$

Answer

Correct option: B.

$\sqrt{34}$

We know that, on the $y-$axis $x = 0$ and $z = 0.$
$\therefore$ Point $\text{A}\equiv(0,4,0)$
$\therefore\text{PA}=\sqrt{(0-3)^2+(4-4)^2+(0-5)^2}$
$=\sqrt{9+0+25}$
$=\sqrt{34}$

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MCQ 21 Mark

$L$ is the foot of the perpendicular drawn from a point $P(3, 4, 5)$ on the $xy-$plane. The coordinates of point $L$ are:

A
$(3, 0, 0).$
B
$(0, 4, 5).$
C
$(3, 0, 5).$
✓
None of these.

Answer

Correct option: D.

None of these.

We know that on the $xy-$plane, $z = 0.$
Hence, the coordinates of the points $L$ are $(3, 4, 0).$

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MCQ 31 Mark

$x-$axis is the intersection of two planes:

✓
$xy$ and $xz.$
B
$yz$ and $zx.$
C
$xy$ and $yz.$
D
None of these.

Answer

Correct option: A.

$xy$ and $xz.$

We know that on the $xy$ and $xz-$planes, the line of intersection is $x-$axis.
Hence, the correct option is $(a).$

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MCQ 41 Mark

The locus of a point for which $x = 0$ is:

A
$xy-$plane.
✓
$yz-$plane.
C
$zx-$plane.
D
None of these

Answer

Correct option: B.

$yz-$plane.

On the $yz-$plane, $x = 0$
Hence, the locus of the point is $yz-$plane.
So, the correct option is $(b).$

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MCQ 51 Mark

If a parallelopiped is formed by planes drawn through the points $(5, 8, 10)$ and $(3, 6, 8)$ parallel to the coordinate planes, then the length of diagonal of the parallelopiped is:

✓
$2\sqrt{3}$
B
$3\sqrt{2}$
C
$\sqrt{2}$
D
$\sqrt{3}$

Answer

Correct option: A.

$2\sqrt{3}$

Given parallelepiped passes through $A(5, 8, 10)$ and $B(3, 6, 8)$
$\therefore$ Length of the diagonal,
$\text{AB}=\sqrt{(5-3)^2+(8-6)^2+(10-8)^2}$
$=\sqrt{4+4+4}$
$=2\sqrt{3}$

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MCQ 61 Mark

The distance of point $P(3, 4, 5)$ from the $yz-$plane is:

✓
$3$ units.
B
$4$ units.
C
$5$ units.
D
$550.$

Answer

Correct option: A.

$3$ units.

Given point is $P(3, 4, 5)$
$\therefore$ Distance of from $yz-$plane
$=\sqrt{(0-3)^2+(4-4)^2+(5-5)^2}$
$=\sqrt{9}$
$=3\text{ units}$
Hence, the correct option is $(a).$

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MCQ 71 Mark

Distance of the point $(3, 4, 5)$ from the origin $(0, 0, 0)$ is:

✓
$\sqrt{50}$
B
$3$
C
$4$
D
$5$

Answer

Correct option: A.

$\sqrt{50}$

Given point $A(3, 4, 5)$ and the given $O(0, 0, 0)$
$\therefore\sqrt{(3-0)^2+(4-0)^2+(5-0)^2}$
$=\sqrt{9+16+25}$
$=\sqrt{50}$
Hence, the correct is $a.$

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MCQ 81 Mark

The point $(-2, -3, -4)$ lies in the:

A
First octant.
✓
Seventh octant.
C
Second octant.
D
Eighth octant.

Answer

Correct option: B.

Seventh octant.

The point $(-2, -3, -4)$ lies in seventh octant.
Hence the correct option is $(b).$

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MCQ 91 Mark

If the distance between the points $(a, 0, 1)$ and $(0, 1, 2)$ is $27,$ then the value of a is:

A
$5$
✓
$\pm5$
C
$-5$
D
None of these.

Answer

Correct option: B.

$\pm5$

Given points are $A(a, 0, 1)$ and $B(0, 1, 2).$
$\therefore\text{AB}=\sqrt{(\text{a}-0)^2+(0-1)^2+(1-2)^2}=\sqrt{27} ($Given$)$
$\Rightarrow27=\text{a}^2+2$
$\Rightarrow\text{a}^2=25$
$\Rightarrow\text{a}=\pm5$

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MCQ 101 Mark

$L$ is the foot of the perpendicular drawn from a point $(3, 4, 5)$ on $x-$axis. The coordinates of $L$ are:

✓
$(3, 0, 0).$
B
$(0, 4, 0).$
C
$(0, 0, 5).$
D
None of these.

Answer

Correct option: A.

$(3, 0, 0).$

On the $x-$axis, $y = 0$ and $z = 0.$
Hence, the required coordinates are $(3, 0, 0).$

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MCQ 111 Mark

A plane is parallel to $yz-$plane so it is perpendicular to:

✓
$x-$axis.
B
$y-$axis.
C
$z-$axis.
D
None of these.

Answer

Correct option: A.

$x-$axis.

Any plane parallel to $yz-$plane, so it is perpendicular to $x-$axis.
Hence, the correct option is $(a)$

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MCQ 121 Mark

Equation of $y-$axis is considered as:

A
$x = 0, y = 0.$
B
$y = 0, z = 0.$
✓
$z = 0, x = 0.$
D
None of these.

Answer

Correct option: C.

$z = 0, x = 0.$

On $y-$axis, $x = 0$ and $z = 0$
Hence, the correct option is $(c).$

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MCQ 131 Mark

The locus of a point for which $y = 0, z = 0$ is:

✓
Equation of $x-$axis.
B
Equation of $y-$axis.
C
Equation at $z-$axis.
D
None of these.

Answer

Correct option: A.

Equation of $x-$axis.

We know that one equation of $x-$axis, $y = 0, z = 0$
Hence, the locus of the point is equation of $x-$axis.
So, the correct option is $(a).$

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Maths M.C.Q (1 Marks)

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