1 Marks Question - Maths STD 12 Science Questions - Vidyadip

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1 Marks Question

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21 questions · self-marked practice — reveal the answer and mark yourself.

Question 11 Mark

Classify the following measures as scalar and vector:
10 meters south-east.

Answer

10 meters south-east is a vector quantity as it involve direction.

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Question 21 Mark

If $\vec{\text{a}}$ ia a non-zero vector of modulus a and m is a non-zero scalar such that $\text{m}\vec{\text{a}}$ is the unit vector, write the value of m.

Answer

Given $\vec{\text{a}}$ is a non-zero vector of modulus a. Also, $\text{m}\vec{\text{a}}$ is the unit vector. Therefore,$|\text{m}\vec{\text{a}}|=1$
$\Rightarrow\ |\text{m}||\vec{\text{a}}|=1$
$\Rightarrow\ |\text{m}|\text{a}=1$
$\Rightarrow\ |\text{m}|=\frac{1}{\text{a}}$
$\Rightarrow\ \text{m}=\pm\frac{1}{\text{a}}$

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Question 31 Mark

Classify the following as scalar and vector quantities:
Acceleration.

Answer

Acceleration is a vector quantity because it involves both magnitude as well as direction.

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Question 41 Mark

Write $\overrightarrow{\text{PQ}}+\overrightarrow{\text{RP}}+\overrightarrow{\text{QR}}$ in the simplified form.

Answer

We have, $\overrightarrow{\text{PQ}}+\overrightarrow{\text{RP}}+\overrightarrow{\text{QR}}=\overrightarrow{\text{PQ}}+\overrightarrow{\text{QR}}+\overrightarrow{\text{RP}}$$=\overrightarrow{\text{PR}}+\overrightarrow{\text{RP}}$ $\Big[\therefore\ \overrightarrow{\text{PQ}}+\overrightarrow{\text{QR}}=\overrightarrow{\text{PR}}\Big]$
$=\vec0$

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Question 51 Mark

Define 'zero vector'.

Answer

A vector whose initial and terminal point are coincident is called a zero vector or null vector. The null vector is denoted by $\vec0$. The magnitude of null vectors is zero.

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Question 61 Mark

Classify the following as scalar and vector quantities:
Displacement.

Answer

Displacement is a vector quantity as it involves both magnitude and direction.

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Question 71 Mark

Classify the following as scalar and vector quantities:
Time period.

Answer

Time period is a scalar quantity as it involves only magnitude.

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Question 81 Mark

Find the direction cosines of the following vector: $2\hat{\text{i}}+2\hat{\text{j}}-\hat{\text{k}}$

Answer

We have, $2\hat{\text{i}}+2\hat{\text{j}}-\hat{\text{k}}$ The direction cosines are $\frac{2}{\sqrt{2^2+2^2+(-1)^2}},\frac{2}{\sqrt{2^2+2^2+(-1)^2}},\frac{1}{\sqrt{2^2+2^2+(-1)^2}}$ or, $\frac{2}{3},\frac{2}{3},\frac{-1}{3}$

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Question 91 Mark

Classify the following measures as scalar and vector:
45º

Answer

45º is a scalar quantity as it involves only magnitude.

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Question 101 Mark

Define unit vector.

Answer

A vector whose modulus is unity is called a unit vector. The unit vector in the direction of a vector $\vec{\text{a}}$ is denoted by $\hat{\text{a}}$.
Thus, $|\hat{\text{a}}|=1$

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Question 111 Mark

Classify the following as scalar and vector quantities:
Work.

Answer

Work done is a scalar quantity as it involves only magnitude.

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Question 121 Mark

Classify the following measures as scalar and vector:
20kg weight.

Answer

20kg weight is a vector quantity as it involves both magnitude and direction.

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Question 131 Mark

Find the direction cosines of the following vectors:
$3\hat{\text{i}}-4\hat{\text{k}}$

Answer

We have, $3\hat{\text{i}}-4\hat{\text{k}}$
The direction cosines are $\frac{3}{\sqrt{3^2+0+(-4)^2}},\frac{0}{\sqrt{3^2+0+(-4)^2}},\frac{-4}{\sqrt{3^2+0+(-4)^2}}$ or, $\frac{3}{5},0,\frac{-4}{5}$

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Question 141 Mark

Classify the following as scalar and vector quantities:
Force.

Answer

Force is a vector quantity as it involves both magnitude and direction.

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Question 151 Mark

Classify the following measures as scalar and vector:
15kg.

Answer

15kg is a scalar quantity because it involves only mass.

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Question 161 Mark

Define position vector of a point.

Answer

A point O is fixed as origin in space (or plane) and P is any point, then $\overrightarrow{\text{OP}}$ is called a position vector of P with reespect to O.

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Question 171 Mark

If $\vec{\text{a}}\text{ and }\vec{\text{b}}$ are two non-collinear vectors such that $\text{x}\vec{\text{a}}+\text{y}\vec{\text{b}}=\vec0$, Then write the values of x and y.

Answer

We have, $\text{x}\vec{\text{a}}+\text{y}\vec{\text{b}}=\vec0$$\Rightarrow\ \text{x}=0$$$ and $\text{y}=0$ $[\because\ \vec{\text{a}}$ and $\vec{\text{b}}$ are non-collinear vectors$]$

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Question 181 Mark

Find the direction cosines of the following vector:$6\hat{\text{i}}-2\hat{\text{j}}-3\hat{\text{k}}$

Answer

We have, $6\hat{\text{i}}-2\hat{\text{j}}-3\hat{\text{k}}$
The direction cosines are $\frac{6}{\sqrt{6^2+(-2)^2+(-3)^2}},\frac{2}{\sqrt{6^2+(-2)^2+(-3)^2}},\frac{-3}{\sqrt{6^2+(-2)^2+(-3)^2}}$ or, $\frac{6}{7},\frac{-2}{7},\frac{-3}{7}$

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Question 191 Mark

Classify the following as scalar and vector quantities:
Distance.

Answer

Distance is a scalar quantity as it involves only magnitude.

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Question 201 Mark

Classify the following as scalar and vector quantities:
Velocity.

Answer

Velocity is a vector quantity as it involves both magnitude as well as direction.

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Question 211 Mark

Classify the following measures as scalar and vector:
$50m/ sec^2$.

Answer

$50m/s^2$ is a scalar quantity as it involves magnitude of acceleration.

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