List of top Questions asked in CBSE Class XI

Fill in the blanks 

1. The volume of a cube of side 1 cm is equal to________\(m^3\).
2. The surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is equal to__________\(\text(mm)^2\).
3. A vehicle moving with a speed of 18 km \(h^{-1}\) covers ________m in 1 s.
4. The relative density of lead is 11.3. Its density is ....g \(\text {cm}^{-3}\) or ________kg \(\text m^{-3}\).

A car moving along a straight highway with speed of 126 \(\text{km}\;\text h^{-1}\) is brought to a stop within a distance of 200 \(\text m\). What is the retardation of the car (assumed uniform), and how long does it take for the car to stop ?

A drunkard walking in a narrow lane takes 5 steps forward and 3 steps backward, followed again by 5 steps forward and 3 steps backward, and so on. Each step is 1 m long and requires 1 s. Plot the x-t graph of his motion. Determine graphically and otherwise how long the drunkard takes to fall in a pit 13 m away from the start.

A woman starts from her home at 9.00 am, walks with a speed of 5 km \(\text{h}^{-1}\)on a straight road up to her office 2.5 km away, stays at the office up to 5.00 pm, and returns home by an auto with a speed of 25 \(\text {km}\) \(\text{h}^{-1}\). Choose suitable scales and plot the x-t graph of her motion.

The position-time (x-t) graphs for two children A and B returning from their school O to their homes P and Q respectively are shown in Fig. 2.9. Choose the correct entries in the brackets below ; 

1. (A/B) lives closer to the school than (B/A) 
2. (A/B) starts from the school earlier than (B/A) 
3. (A/B) walks faster than (B/A) 
4. A and B reach home at the (same/different) time 
5. (A/B) overtakes (B/A) on the road (once/twice).
    

In which of the following examples of motion, can the body be considered approximately a point object:

One mole of an ideal gas at standard temperature and pressure occupies 22.4 L (molar volume). What is the ratio of molar volume to the atomic volume of a mole of hydrogen ? (Take the size of hydrogen molecule to be about 1 \(\text\AA\) ). Why is this ratio so large ?

The unit of length convenient on the atomic scale is known as an angstrom and is denoted by \(\AA\) : 1 \(\AA\) = \(10^{-10}\;\text m\). The size of a hydrogen atom is about 0.5\(\AA .\) What is the total atomic volume in m3 of a mole of hydrogen atoms ?

The photograph of a house occupies an area of 1.75 \(\text{cm}^2\) on a 35 mm slide. The slide is projected on to a screen, and the area of the house on the screen is 1.55 \(\text m^2\). What is the linear magnification of the projector-screen arrangement.

The slope of a line is double of the slope of another line. If tangent of the angle between them is \(\frac{1}{3}\) , find the slopes of he lines.

A student measures the thickness of a human hair by looking at it through a microscope of magnification 100. He makes 20 observations and finds that the average width of the hair in the field of view of the microscope is 3.5 mm. What is the estimate on the thickness of hair ?

Which of the following is the most precise device for measuring length : 

a vernier calipers with 20 divisions on the sliding scale  
a screw gauge of pitch 1 mm and 100 divisions on the circular scale
an optical instrument that can measure length to within a wavelength of light ?

A new unit of length is chosen such that the speed of light in vacuum is unity. What is the distance between the Sun and the Earth in terms of the new unit if light takes 8 min and 20 s to cover this distance ?

Find the equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.

Explain this statement clearly : “To call a dimensional quantity ‘large’ or ‘small’ is meaningless without specifying a standard for comparison”. In view of this, reframe the following statements wherever necessary : 

1. atoms are very small objects 
2. a jet plane moves with great speed 
3. the mass of Jupiter is very large 
4. the air inside this room contains a large number of molecules 
5. a proton is much more massive than an electron 
6. the speed of sound is much smaller than the speed of light.

A calorie is a unit of heat (energy in transit) and it equals about 4.2 J where 1J = 1 \(\text {kg} \;\text m^2\; \text s^{-2}.\) Suppose we employ a system of units in which the unit of mass equals \(\alpha\) kg, the unit of length equals \(\beta\) m, the unit of time is \(\gamma\) s. Show that a calorie has a magnitude 4.2 \(\alpha^{-1}\; \beta^{-2}\; \gamma^{2}\) in terms of the new units.

A line passes through (x₁, y₁) and (h, k). If slope of the line is m, show that k-y₁=m(h-x₁)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): \(\frac{sin(x+a)}{cos\,a}\)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): \(\frac{sin\,x+cos\,x}{sin\,x-cos\,x}\)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): \(\frac{cos\,x}{1+sin\,x}\)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): cosec x cot x

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): sin (x + a)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): (ax +b)ⁿ (cx + d)^m

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): (ax +b)ⁿ

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): \(\frac{px^2+qx+r}{ax+b}\)