M.C.Q (1 Marks)

MCQ 1511 Mark

Solve the following differential equation. $\frac{\text{dy}}{\text{dx}}=\text{x}-1$

A
$ y=x^2+x $
B
$ y=x^2 $
✓
$ y=x^2-x $
D
None of the above

Answer

Correct option: C.

$ y=x^2-x $

Given, $\frac{\text{dy}}{\text{dx}}=\text{x}-1$
Integrating on both sides
$\int\frac{\text{dy}}{\text{dx}}=\int\text{x}-1\text{ dx}$
$y = x^2- x + c$

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MCQ 1521 Mark

If $P(3, 2, -4), Q(5, 4, -6)$ and $R(9, 8, -10)$ are collinear, then $R$ divides $PQ$ in the ratio:

A
$3 : 2$ internally
✓
$3 : 2$ externally
C
$2 : 1$ internally
D
$2 : 1$ externally

Answer

Correct option: B.

$3 : 2$ externally

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MCQ 1531 Mark

Choose the correct answer. 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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MCQ 1541 Mark

In a three dimensional space the equation $x^2- 5x + 6 = 0$ represents

A
Points.
B
Planes.
✓
Curves.
D
Pair of straight lines.

Answer

Correct option: C.

Curves.

Since, there is only one variable in the given equation.
Also, it is quadratic equation.
Hence, It represents curves in $yz$ plane.

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MCQ 1551 Mark

The points $(-5, 12), (-2, -3), (9, -10), (6, 5)$ taken in order, form:

✓
Parallelogram
B
Rectangle
C
Rhombus
D
Square

Answer

Correct option: A.

Parallelogram

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MCQ 1561 Mark

The ratio in which the line joining $(2, 4, 5)$ and $(3, 5, -9)$ is divided by the $yz-$plane is

A
$2 : 3$
B
$3 : 2$
✓
$-2 : 3$
D
$4 : -3$

Answer

Correct option: C.

$-2 : 3$

Let $A ≡ (2, 4, 5)$ and $B ≡ (3, 5, 9)$
Let the line joining $A$ and $B$ be divided by the $yz-$plane at point $P$ in the ratio $\lambda:1.$
Then, we have,
$\text{P}\equiv\Big(\frac{3\lambda+2}{\lambda+1},\ \frac{5\lambda+4}{\lambda+1},\ \frac{-9\lambda+5}{\lambda+1}\Big)$
Since $P$ lies on the $yz-$plane, the $x-$coordinate of $P$ will be zero
$\therefore\frac{3\lambda+2}{\lambda+1}=0$
$\Rightarrow3\lambda+2=0$
$\Rightarrow\lambda=\frac{-2}{3}$
Hence, the $yz-$plane divides $AB$ in the ratio $-2 : 3$

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MCQ 1571 Mark

$A = (1, 1, 4)$ and $B = (5, -3, 4)$ are two points. If the points $P, Q$ are on the line $AB$ such that $\text{AP = PQ = QB}$ then $\text{PQ} =$

A
$2\sqrt{2}$
B
$4$
✓
$\sqrt{\frac{32}{9}}$
D
$\sqrt{2}$

Answer

Correct option: C.

$\sqrt{\frac{32}{9}}$

$\text{AB}=\sqrt{(1-5)^2+(1+3)^2+(4+4)^2}$
$\text{AB}=\sqrt{(-4)^2+4^2}$
$\text{AB}=\sqrt{32}$
$\text{AB}=3\times\text{PQ}$
$=\frac{\sqrt{132}}{3}$
$=\sqrt{\frac{32}{9}}$

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MCQ 1581 Mark

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

A
First octant
✓
Seventh octant
C
Second octant
D
Eight octant

Answer

Correct option: B.

Seventh octant

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MCQ 1591 Mark

The ratio in which the line joining the points $(1, 2, 3)$ and $(-3, 4, -5)$ is divided by the $xy-$plane is:

A
$2 : 5$
✓
$3 : 5$
C
$5 : 2$
D
$5 : 3$

Answer

Correct option: B.

$3 : 5$

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MATHS M.C.Q (1 Marks)