Prove that $\vec{\text{A}}.(\vec{\text{A}}\times\vec{\text{B}})=0.$
View full solution →Question types
Physics and Mathematics question types
60 questions across 5 question groups — pick any mix to generate a Physics paper with step-by-step answer keys.
60
Questions
5
Question groups
5
Question types
01
2 Marks Questions
33 Q→023 Marks Question
10 Q→031 Marks Question
4 Q→04M.C.Q (1 Marks)
11 Q→055 Marks Questions
2 Q→Sample Questions
Physics and Mathematics questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
A metre scale is graduated at every millimetre. How many significant digits will be there in a length measurement with this scale?
The length and the radius of a cylinder measured with a slide callipers are found to be 4.54cm and 1.75cm respectively. Calculate the volume of the cylinder.
Find the area bounded under the curve y = 3x2 + 6x + 7 and the X-axis with the ordinates at x = 5 and x = 10.
A mosquito net over a 7ft × 4ft bed is 3ft high. The net has a hole at one corner of the bed through which a mosquito enters the net. It flies and sits at the diagonally opposite upper corner of the net.
- Find the magnitude of the displacement of the mosquito.
- Taking the hole as the origin, the length of the bed as the X-axis, its width as the Y-axis, and vertically up as the Z-axis, write the components of the displacement vector.
A spy report about a suspected car reads as follows. "The car moved 2.00km towards east, made a perpendicular left turn, ran for 500m, made a perpendicular right turn, ran for 4.00km and stopped". Find the displacement of the car.
A carrom board (4ft × 4ft square) has the queen at the centre. The queen, hit by the striker moves to the front edge, rebounds and goes in the hole behind the striking line. Find the magnitude of displacement of the queen:
- From the centre to the front edge.
- From the front edge to the hole.
- From the centre to the hole.
The momentum p of a particle changes with time t according to the relation $\frac{\text{dp}}{\text{dt}}=(10\text{N})+(2\text{N/s)t}.$ If the momentum is zero at t = 0, what will the momentum be at t = 10s?
View full solution →A rod of length L is placed along the X-axis between x = 0 and x = L. The linear density (mass/ length) $\rho$ of the rod varies with the distance x from the origin as $\rho=\text{a + bx.}$
View full solution →- Find the SI units of a and b.
- Find the mass of the rod in terms of a, b and L.
Let $\varepsilon_1$ and $\varepsilon_2$ be the angles made by $\overrightarrow{\text{A}}$ and $-\overrightarrow{\text{A}}$ with the positive X-axis. Show that $\tan\varepsilon_1=\tan\varepsilon_2.$ Thus, giving tane does not uniquely determine the direction of $\overrightarrow{\text{A}}.$
View full solution →Is a vector necessarily changed if it is rotated through an angle?
If $\vec{\text{A}}=2\vec{\text{i}}+3\vec{\text{j}}+4\vec{\text{k}}$ and $\vec{\text{B}}=4\vec{\text{i}}+3\vec{\text{j}}+2\vec{\text{k}},$ find $\vec{\text{A}}\times\vec{\text{B}}.$
View full solution →The length of the string of a simple pendulum is measured with a metre scale to be 90.0cm. The radius of the bob plus the length of the hook is calculated to be 2.13cm using measurements with a slide callipers. What is the effective length of the pendulum? (The effective length is defined as the distance between the point of suspension and the centre of the bob.)
Can we have physical quantities having magnitude and direction which are not vectors?
A vector $\overrightarrow{\text{A}}$ points vertically upward and $\overrightarrow{\text{B}}$ points towards north. The vector product $\overrightarrow{\text{A}}\times\overrightarrow{\text{B}}$ is:
View full solution →- Along west.
- Along east.
- Zero.
- Vertically downward.
The magnitude of the vector product of two vectors $\big|\overrightarrow{\text{A}}\big|$ and $\big|\overrightarrow{\text{B}}\big|$ may be:
View full solution →- Greater than AB.
- Equal to AB.
- Less than AB.
- Equal to zero.
A vector is not changed if:
- It is rotated through an arbitrary angle.
- It is multiplied by an arbitrary scalar.
- It is cross multiplied by a unit vector.
- It is slid parallel to itself.
The x-component of the resultant of several vectors:
- Is equal to the sum of the x-components of the vectors.
- May be smaller than the sum of the magnitudes of the vectors.
- May be greater than the sum of the magnitudes of the vectors.
- May be equal to the sum of the magnitudes of the vectors.
Which of the sets given below may represent the magnitudes of three vectors adding to zero?
- 2, 4, 8
- 4, 8, 16
- 1, 2, 1
- 0.5, 1, 2
Refer to figure. Find
View full solution →- The magnitude.
- x and y components
- The angle with the X-axis of the resultant of $\overrightarrow{\text{OA}},\overrightarrow{\text{BC}}$ and $\overrightarrow{\text{DE}}.$
Add vectors $\overrightarrow{\text{A}},\overrightarrow{\text{B}}$ and $\overrightarrow{\text{C}}$ each having magnitude of 100 unit and inclined to the X-axis at angles 45°, 135° and 315° respectively.
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