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Q. No.If \(x=\int_{0}^{3}t^2dt, \) then what is the value of \(x\text{?}\)
1. \(0\)
2. \(3\)
3. \(9\)
4. \(27\)
Subtopic: Integration |
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Level 1: 80%+
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Two forces of magnitude \(A\) and \({A\over 2}\) act perpendicular to each other. The magnitude of the resultant force is equal to:
| 1. | \(\dfrac A2\) | 2. | \(\dfrac {\sqrt {5}A} { 2}\) |
| 3. | \(\dfrac {3A} {2}\) | 4. | \(\dfrac {5A} {2}\) |
Subtopic: Resultant of Vectors |
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Level 1: 80%+
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The angle (in degrees ) between the resultant of \(2 \overrightarrow{q}-2 \overrightarrow{p}\) and \(2 \overrightarrow{q}+2 \overrightarrow{p}\) with \(\overrightarrow{q} \) is:
1. \(0^\circ\)
2. \(30^\circ\)
3. \(45^\circ\)
4. \(60^\circ\)
1. \(0^\circ\)
2. \(30^\circ\)
3. \(45^\circ\)
4. \(60^\circ\)
Subtopic: Scalar Product |
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Level 2: 60%+
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The magnitudes of forces \(\vec F_A\) and \(\vec F_B\) are \(400~\text{N}\) and \(300~\text{N},\) respectively, as shown in the diagram. What is the magnitude of the net force in each of the three given cases?
| 1. | In Case \(1\), the net force is \(100~\text{N}\); Case \(2\), \(700~\text{N}\); and Case \(3\), \(500~\text{N}.\) |
| 2. | In Case \(1\), the net force is \(700~\text{N}\); Case \(2\), \(100~\text{N}\); and Case \(3\), \(500~\text{N}.\) |
| 3. | In Case \(1\), the net force is \(350~\text{N}\); Case \(2\), \(50~\text{N}\); and Case \(3\), \(450~\text{N}.\) |
| 4. | In Case \(1\), the net force is \(350~\text{N}\); Case \(2\), \(50~\text{N}\), and Case \(3\), \(550~\text{N}.\) |
Subtopic: Resultant of Vectors |
91%
Level 1: 80%+
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The following diagram shows three vectors in a plane, each with equal magnitudes and separated by angles of \(120^\circ\) from each other.
What arrow best represents the direction of their vector sum?
1. \(\downarrow\)
2. \(\uparrow\)
3. The sum is zero.
4. The diagram is invalid.
What arrow best represents the direction of their vector sum?
1. \(\downarrow\)
2. \(\uparrow\)
3. The sum is zero.
4. The diagram is invalid.
Subtopic: Resultant of Vectors |
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Level 1: 80%+
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The following diagram represents three vectors of equal magnitudes in a plane.
What arrow best represents the direction of the sum of three vectors?
What arrow best represents the direction of the sum of three vectors?
| 1. | \(\rightarrow\) | 2. | \(\leftarrow\) |
| 3. | \(\uparrow\) | 4. | \(\downarrow\) |
Subtopic: Resultant of Vectors |
85%
Level 1: 80%+
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Consider the quantities, pressure, power, energy, impulse, gravitational potential, electrical charge, temperature, area. Out of these, the only vector quantities are
1. Impulse, pressure and area
2. Impulse and area
3. Area and gravitational potential
4. Impulse and pressure
1. Impulse, pressure and area
2. Impulse and area
3. Area and gravitational potential
4. Impulse and pressure
Subtopic: Scalars & Vectors |
74%
Level 2: 60%+
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Two vectors, each of magnitude \(A,\) are inclined at an angle \( \theta \) to each other. The magnitude of their resultant vector is:
| 1. | \(A \cos ^2 \dfrac{\theta}{2}\) | 2. | \(2 A \cos \dfrac{\theta}{2}\) |
| 3. | \(2 A \cos \theta\) | 4. | \(A \cos \dfrac{\theta}{2}\) |
Subtopic: Resultant of Vectors |
85%
Level 1: 80%+
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If a vector has a magnitude equal to that of \(\vec{A}=4 \hat{i}+3\hat{j}\) and is parallel to \(\vec{B}=4 \hat{i}+3\hat{j},\) then the \(x\) and \(y\) components of this vector in the first quadrant are \(x\) and \(3\) respectively. Then the value of \(x\) is:
1. \(3\)
2. \(4\)
3. \(5\)
4. \(2\)
1. \(3\)
2. \(4\)
3. \(5\)
4. \(2\)
Subtopic: Resultant of Vectors |
84%
Level 1: 80%+
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Column-I shows some vector equations that match Column-II (in which the values of the angles between \(\vec A\) and \(\vec B\) are given).
Codes:
| Column-I | Column-II | ||
| (A) | \(|\vec A+\vec B|=|\vec A-\vec B|\) | (P) | \(45^\circ\) |
| (B) | \(|\vec A\times\vec B|=\vec A\cdot\vec B\) | (Q) | \(30^\circ\) |
| (C) | \(\vec A\cdot\vec B=\dfrac{AB}{2}\) | (R) | \(90^\circ\) |
| (D) | \(|\vec A\times\vec B|=\dfrac{AB}{2}\) | (S) | \(60^\circ\) |
| 1. | \(\mathrm {A \rightarrow R, B \rightarrow S, C \rightarrow P, D \rightarrow Q }\) |
| 2. | \(\mathrm {A \rightarrow P, B \rightarrow Q, C \rightarrow R, D \rightarrow S }\) |
| 3. | \(\mathrm {A \rightarrow R, B \rightarrow P, C \rightarrow S, D \rightarrow Q }\) |
| 4. | \(\mathrm {A \rightarrow S, B \rightarrow P, C \rightarrow Q, D \rightarrow R}\) |
Subtopic: Vector Product |
84%
Level 1: 80%+
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