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1 RBTS PAPER

160572 The velocity $v$ of a particle depends upon the time $t$ according to the equation $v = a + b t + \frac{d}{c + t}$ . Write the dimensions of $a, b, c$ and $d$ :

1

[2 L T^{- 1}], [L T^{- 2}], [L] & [T]

2

[L T^{- 1}], [2 L T^{- 2}], [L] & [T]

3

[L T^{- 1}], [L T^{- 2}], [L] & [T]

4

[L T^{- 1}], [L T^{- 2}], [T] & [L]

Explanation:

$\begin{aligned} V = a + b t + \frac{d}{c + t} \\ a = [L T^{- 1}], b = [L T^{- 2}], d = [L], c = [T] \end{aligned}$

NCERT-I-32

1 RBTS PAPER

160573 Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) :
The error in the measurement of radius of the sphere is $0.3 %$ . The permissible error in its surface area is $0.6 %$ .
Reason (R) :
The permissible error is calculated by the formula
$\frac{Δ A}{A} = \frac{4 Δ r}{r} .$
In the light of the above statements, choose the most appropriate answer from the options given below:

1 Both (A) and (R) are correct and (R) is the correct explanation of

(A)

2 Both (A) and (R) are correct but (R) is not the correct exaplanation of

(A)

3 (A) is correct but (R) is not correct

4 (A) is not correct but (R) is correct

Explanation:

$A = 4 π r^{2}$
$\begin{aligned} \frac{Δ A}{A} \times 100 = \frac{Δ r}{r} \times 100 \\ \frac{Δ A}{A} \times 100 = 2 \times 0.3 \end{aligned}$
$100 \times \frac{Δ A}{A} = 0.6 %$

NCERT-I-27

1 RBTS PAPER

160574 If the unit of force is $1$ kilonewton, the length is $1 km$ and time $100 s$ , what will be the unit of mass?

1

1, 000 kg

2

10, 000 kg

3

100 kg

4

1 kg

Explanation:

As $[F] = [{MLT}^{- 2}]$
$∴ 1000 = [x kg]^{1} [1000 m]^{1} [100 s]^{- 2}$
or $x = 10, 000 kg$

NCERT-I-25

1 RBTS PAPER

160577 Two cars $P$ and $Q$ start from a point at the same time in a straight line and their positions are represented by $x_{p} (t) =$ at $+ b t^{2}$ and $x_{q} (t) = f t - t^{2}$ . At what time do the cars have the same velocity :

1

\frac{a - f}{1 + b}

2

\frac{2 a + f}{2 (b - 1)}

3

\frac{a + f}{2 (1 + b)}

4

\frac{f - a}{2 (1 + b)}

Explanation:

$x_{p} = a t + b t^{2} \Rightarrow \frac{d x_{p}}{d t} = a + 2 b t$
$x_{Q} = f t - t^{2} \Rightarrow f - 2 t = \frac{d x_{Q}}{d t}$
If velocities are equal
$\begin{aligned} \frac{d x_{p}}{d t} & = \frac{d x_{Q}}{d t} \\ a + 2 b t & = f - 2 t \end{aligned}$ then, $t = \frac{f - a}{2 (b + 1)}$

NCERT -73

1 RBTS PAPER

160572 The velocity $v$ of a particle depends upon the time $t$ according to the equation $v = a + b t + \frac{d}{c + t}$ . Write the dimensions of $a, b, c$ and $d$ :

1

[2 L T^{- 1}], [L T^{- 2}], [L] & [T]

2

[L T^{- 1}], [2 L T^{- 2}], [L] & [T]

3

[L T^{- 1}], [L T^{- 2}], [L] & [T]

4

[L T^{- 1}], [L T^{- 2}], [T] & [L]

Explanation:

$\begin{aligned} V = a + b t + \frac{d}{c + t} \\ a = [L T^{- 1}], b = [L T^{- 2}], d = [L], c = [T] \end{aligned}$

NCERT-I-32

1 RBTS PAPER

160573 Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) :
The error in the measurement of radius of the sphere is $0.3 %$ . The permissible error in its surface area is $0.6 %$ .
Reason (R) :
The permissible error is calculated by the formula
$\frac{Δ A}{A} = \frac{4 Δ r}{r} .$
In the light of the above statements, choose the most appropriate answer from the options given below:

1 Both (A) and (R) are correct and (R) is the correct explanation of

(A)

2 Both (A) and (R) are correct but (R) is not the correct exaplanation of

(A)

3 (A) is correct but (R) is not correct

4 (A) is not correct but (R) is correct

Explanation:

$A = 4 π r^{2}$
$\begin{aligned} \frac{Δ A}{A} \times 100 = \frac{Δ r}{r} \times 100 \\ \frac{Δ A}{A} \times 100 = 2 \times 0.3 \end{aligned}$
$100 \times \frac{Δ A}{A} = 0.6 %$

NCERT-I-27

1 RBTS PAPER

160574 If the unit of force is $1$ kilonewton, the length is $1 km$ and time $100 s$ , what will be the unit of mass?

1

1, 000 kg

2

10, 000 kg

3

100 kg

4

1 kg

Explanation:

As $[F] = [{MLT}^{- 2}]$
$∴ 1000 = [x kg]^{1} [1000 m]^{1} [100 s]^{- 2}$
or $x = 10, 000 kg$

NCERT-I-25

1 RBTS PAPER

160577 Two cars $P$ and $Q$ start from a point at the same time in a straight line and their positions are represented by $x_{p} (t) =$ at $+ b t^{2}$ and $x_{q} (t) = f t - t^{2}$ . At what time do the cars have the same velocity :

1

\frac{a - f}{1 + b}

2

\frac{2 a + f}{2 (b - 1)}

3

\frac{a + f}{2 (1 + b)}

4

\frac{f - a}{2 (1 + b)}

Explanation:

$x_{p} = a t + b t^{2} \Rightarrow \frac{d x_{p}}{d t} = a + 2 b t$
$x_{Q} = f t - t^{2} \Rightarrow f - 2 t = \frac{d x_{Q}}{d t}$
If velocities are equal
$\begin{aligned} \frac{d x_{p}}{d t} & = \frac{d x_{Q}}{d t} \\ a + 2 b t & = f - 2 t \end{aligned}$ then, $t = \frac{f - a}{2 (b + 1)}$

NCERT -73

1 RBTS PAPER

160572 The velocity $v$ of a particle depends upon the time $t$ according to the equation $v = a + b t + \frac{d}{c + t}$ . Write the dimensions of $a, b, c$ and $d$ :

1

[2 L T^{- 1}], [L T^{- 2}], [L] & [T]

2

[L T^{- 1}], [2 L T^{- 2}], [L] & [T]

3

[L T^{- 1}], [L T^{- 2}], [L] & [T]

4

[L T^{- 1}], [L T^{- 2}], [T] & [L]

Explanation:

$\begin{aligned} V = a + b t + \frac{d}{c + t} \\ a = [L T^{- 1}], b = [L T^{- 2}], d = [L], c = [T] \end{aligned}$

NCERT-I-32

1 RBTS PAPER

160573 Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) :
The error in the measurement of radius of the sphere is $0.3 %$ . The permissible error in its surface area is $0.6 %$ .
Reason (R) :
The permissible error is calculated by the formula
$\frac{Δ A}{A} = \frac{4 Δ r}{r} .$
In the light of the above statements, choose the most appropriate answer from the options given below:

1 Both (A) and (R) are correct and (R) is the correct explanation of

(A)

2 Both (A) and (R) are correct but (R) is not the correct exaplanation of

(A)

3 (A) is correct but (R) is not correct

4 (A) is not correct but (R) is correct

Explanation:

$A = 4 π r^{2}$
$\begin{aligned} \frac{Δ A}{A} \times 100 = \frac{Δ r}{r} \times 100 \\ \frac{Δ A}{A} \times 100 = 2 \times 0.3 \end{aligned}$
$100 \times \frac{Δ A}{A} = 0.6 %$

NCERT-I-27

1 RBTS PAPER

160574 If the unit of force is $1$ kilonewton, the length is $1 km$ and time $100 s$ , what will be the unit of mass?

1

1, 000 kg

2

10, 000 kg

3

100 kg

4

1 kg

Explanation:

As $[F] = [{MLT}^{- 2}]$
$∴ 1000 = [x kg]^{1} [1000 m]^{1} [100 s]^{- 2}$
or $x = 10, 000 kg$

NCERT-I-25

1 RBTS PAPER

160577 Two cars $P$ and $Q$ start from a point at the same time in a straight line and their positions are represented by $x_{p} (t) =$ at $+ b t^{2}$ and $x_{q} (t) = f t - t^{2}$ . At what time do the cars have the same velocity :

1

\frac{a - f}{1 + b}

2

\frac{2 a + f}{2 (b - 1)}

3

\frac{a + f}{2 (1 + b)}

4

\frac{f - a}{2 (1 + b)}

Explanation:

$x_{p} = a t + b t^{2} \Rightarrow \frac{d x_{p}}{d t} = a + 2 b t$
$x_{Q} = f t - t^{2} \Rightarrow f - 2 t = \frac{d x_{Q}}{d t}$
If velocities are equal
$\begin{aligned} \frac{d x_{p}}{d t} & = \frac{d x_{Q}}{d t} \\ a + 2 b t & = f - 2 t \end{aligned}$ then, $t = \frac{f - a}{2 (b + 1)}$

NCERT -73

1 RBTS PAPER

160572 The velocity $v$ of a particle depends upon the time $t$ according to the equation $v = a + b t + \frac{d}{c + t}$ . Write the dimensions of $a, b, c$ and $d$ :

1

[2 L T^{- 1}], [L T^{- 2}], [L] & [T]

2

[L T^{- 1}], [2 L T^{- 2}], [L] & [T]

3

[L T^{- 1}], [L T^{- 2}], [L] & [T]

4

[L T^{- 1}], [L T^{- 2}], [T] & [L]

Explanation:

$\begin{aligned} V = a + b t + \frac{d}{c + t} \\ a = [L T^{- 1}], b = [L T^{- 2}], d = [L], c = [T] \end{aligned}$

NCERT-I-32

1 RBTS PAPER

160573 Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) :
The error in the measurement of radius of the sphere is $0.3 %$ . The permissible error in its surface area is $0.6 %$ .
Reason (R) :
The permissible error is calculated by the formula
$\frac{Δ A}{A} = \frac{4 Δ r}{r} .$
In the light of the above statements, choose the most appropriate answer from the options given below:

1 Both (A) and (R) are correct and (R) is the correct explanation of

(A)

2 Both (A) and (R) are correct but (R) is not the correct exaplanation of

(A)

3 (A) is correct but (R) is not correct

4 (A) is not correct but (R) is correct

Explanation:

$A = 4 π r^{2}$
$\begin{aligned} \frac{Δ A}{A} \times 100 = \frac{Δ r}{r} \times 100 \\ \frac{Δ A}{A} \times 100 = 2 \times 0.3 \end{aligned}$
$100 \times \frac{Δ A}{A} = 0.6 %$

NCERT-I-27

1 RBTS PAPER

160574 If the unit of force is $1$ kilonewton, the length is $1 km$ and time $100 s$ , what will be the unit of mass?

1

1, 000 kg

2

10, 000 kg

3

100 kg

4

1 kg

Explanation:

As $[F] = [{MLT}^{- 2}]$
$∴ 1000 = [x kg]^{1} [1000 m]^{1} [100 s]^{- 2}$
or $x = 10, 000 kg$

NCERT-I-25

1 RBTS PAPER

160577 Two cars $P$ and $Q$ start from a point at the same time in a straight line and their positions are represented by $x_{p} (t) =$ at $+ b t^{2}$ and $x_{q} (t) = f t - t^{2}$ . At what time do the cars have the same velocity :

1

\frac{a - f}{1 + b}

2

\frac{2 a + f}{2 (b - 1)}

3

\frac{a + f}{2 (1 + b)}

4

\frac{f - a}{2 (1 + b)}

Explanation:

$x_{p} = a t + b t^{2} \Rightarrow \frac{d x_{p}}{d t} = a + 2 b t$
$x_{Q} = f t - t^{2} \Rightarrow f - 2 t = \frac{d x_{Q}}{d t}$
If velocities are equal
$\begin{aligned} \frac{d x_{p}}{d t} & = \frac{d x_{Q}}{d t} \\ a + 2 b t & = f - 2 t \end{aligned}$ then, $t = \frac{f - a}{2 (b + 1)}$

NCERT -73

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