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Worksheetssunday
Total questions: 55
Worksheet time: 2hrs 50mins
In a situation, a board is moving with a velocity v with respect to earth, while a man A and man B are running with a velocity 2v with respect to earth and both men are running from the opposite ends of the board at the same time, as shown. Length of the board is L. If they meet after time T, then
value of T is L/4v
value of T is L/2v
Displacement of man B with respect to board in time T is 3L/4
Displacement of man A with respect to board in time T is L/4
An object is moving in the xy plane with the position vector is given by and velocity vector is . Consider a point O at origin .Distance of object from origin in decreasing, if
v > 0, v < 0 & x < 0, y > 0
v < 0, v > 0 & x > 0, y < 0
xv + yv < 0
– xv + yv < 0
Two refracting media are separated by a spherical interface as shown in the figure. PP′ is the principal axis, μ and μ are the refractive indices of medium of incidence and medium of refraction respectively. Then:
if μ > μ, then there cannot be a real image of real object
if μ > μ, then there cannot be a real image of virtual object
if μ > μ, then there cannot be a virtual image of virtual object
if μ > μ, then there cannot be a real image of real object
In the figure shown radius of curvature of either surface of equi convex half lens is 40 cm and refractive index 1.5. Its one side is silvered. A plane mirror is also placed. A small object O is placed such that there is no parallax between final image formed by lens and mirror. If transverse length of final image formed by lens system is twice that formed by mirror. Choose the correct options :
a = 2.5 cm
b = 5 cm
Distance of image from object is 15 cm
Image formed by lens system is virtual
A bead of mass m is kept at a distance a from the axis of rotation of a smooth massless tube. The tube is rotated on a smooth horizontal surface along a vertical axis perpendicular to the length L of the tube and passing through one of its end 'O' with constant angular velocity ω.
The speed of the bead relative to tube when it is at distance r from axis of rotation is ω
The speed of the bead relative to tube when it is at distance r from axis of rotation is ω
The work done by the centrifugal force in the frame of the tube when the bead reaches at distance r from the axis starting from radius a is mω(r – a)
The work done by the centrifugal force in the frame of the tube when the bead reaches at distance r from the axis starting from radius a is mω (r – a)
A car is accelerating on a horizontal road with acceleration = 20 m/s. A box that is placed inside the car, of mass m = 10 kg is put in contact with the vertical wall as shown. The friction coefficient between the box and the wall is μ = 0.6.
The acceleration (with respect to ground) of the box will be 20 m/sec
The friction force acting on the box will be 100 N
The contact force between the vertical wall and the box will be 100N
The net contact force between the vertical wall and the box is only of electromagnetic in nature.
A car is travelling in steady rain with constant acceleration in a straight line. When it begins to move the driver sees that the raindrops make an angle of 37° with the vertical. After 20 s, the driver observes that the raindrops make an angle of 53° with vertical in same direction. The acceleration of the car is x cm/s. Find the value of 2x. Rain is falling at 3 m/s relative to the ground.
A river is flowing with velocity 5 km/hr relative to the ground as shown in the figure. A boat starts from A and reaches the other bank by covering shortest possible distance. Velocity of boat in still water is 3 km/hr. The distance (in m) boat covers is s. The value of is
Two inclined planes OA and OB of inclinations to the horizontal α and β, each equal to 30° are placed as shown in the figure. A particle is projected at an angle of 90° with plane OA from point A and its strikes the plane OB at point B normally. If the speed of projection in m/s is x. Fill the value of 8x. (given that OA = OB = 20 cm and g = 10 m/s)
The backside of a truck is open and a box of 40 kg is placed 5 m away from the rear end. The coefficient of friction of the box with the surface of the truck is 0.15. The truck starts from rest with acceleration 2 m s. Calculate the distance (in m) covered by the truck when the box falls off.
A police car is travelling in a straight line with a constant speed, υ. A truck travelling in the same direction with constant velocity, passes the police car at, t = 0. The police car starts accelerating 10 s after passing the truck, at a constant rate of 3 m s, while the truck continues to move at a constant speed. If the police car takes 10 s further to catch the truck, find the value of υ (m/s)
If pulley is ideal and string is massless then reading of weighing machine is kg then calculate x. : (g = 10 m/s)
Consider the arrangement shown in figure. Pulleys and string are ideal. There is no friction between smaller and bigger block. Both blocks have same mass m. The minimum coefficient of friction between bigger block and ground for which both blocks remains in equilibrium is μ, then 70μ is :
As shown in the figure, water is filled inside a beaker and a point object ‘O’ is kept at the bottom. Find the distance of the image formed due to reflection from the mirror. Assume paraxial rays.
water is filled inside a beaker and a point object ‘O’ is kept at the bottom. Find the distance of the image formed due to reflection from the mirror. Assume paraxial rays.
Two concave refracting surfaces each with radius of curvature R = 35 cm and refractive indices μ and μ respectively, are placed facing each other in air as shown in figure. A point object 'O' is placed at a distance R/2 from one of the surface as shown. Answer the following : Distance of image after refraction from 1st surface (μ = 1.5) is equal to :
45 cm towards left of P
45 cm towards right of P
30 cm towards left of P
30 cm towards right of P
Two concave refracting surfaces each with radius of curvature R = 35 cm and refractive indices μ and μ respectively, are placed facing each other in air as shown in figure. A point object 'O' is placed at a distance R/2 from one of the surface as shown. Answer the following : Separation between the images of 'O' formed by each refracting surfaces is equal to : (μ = 1.5)
8 cm
4 cm
2 cm
cannot be determined
Two particles are projected horizontally in opposite direction from a point on a smooth inclined plane with velocity u and u as shown in figure. Angle of incline is θ with horizontal. Time when their velocities will become perpendicular is -
Two particles are projected horizontally in opposite direction from a point on a smooth inclined plane with velocity u and u as shown in figure. Angle of incline is θ with horizontal. The separation between the particles when their velocities become perpendicular to each other is :
Amongs the species given below which will have same mass?
0⋅1 mol of sulphur dioxide
0⋅1 mol of NO
0⋅1 mol of CO
Avogadro number of CO molecules
Which of the following contains same number of sulphur atoms as present in 1 g S ?
1g S
1g S
1g S
1 mol of SO
Which of the following is/are aromatic compounds :
Identify correct structure of 4-ethylidene-3,7-dimethyldeca-1,7-diene
Select the structure in which incorrect numbering has been done for IUPAC name of the compound :
A nonpolarmolecule AX have all bond angles equal then which of the following conclusions are correct?
Molecule may be tetrahedral.
Molecule may be square planar.
Central atom 'A' must have at least six valence electrons.
Central atom 'A' has either zero lone pair or two lone pairs
Calculate molecular diameter for a gas if its molar excluded volume is 3.2 π ml. (in nenometer). Give the answer by multiplying with 100. (Take N = 6.0 × 10)
If wave functions, ψ(r, θ, φ) of 2s and 2p electrons in a hydrogen atom are given by ψ(2s) = K and ψ(2p) = kcosθ, where a = 53 pm and let constants k = k . If the probability of finding the electron in 2s orbital in a small spherical volume of radius r(r << a) around r = a is P and of electron in 2p orbital in same spherical volume around r = a at θ = 30 is P then Find (P – P) × 15:
How many products (structural isomers) are formed by monochlorination of following compound ?
How many alkene on hydrogenation give 2,3-dimethyl pentane ?
In given pairs no. of pairs in which Ι compound is more stable than ΙΙ.
For one mole of a van der Waals gas when b = 0 and T = 300 K, the PV vs.1/V plot is shown below. The value of the vanderWaals constant a (atm.liter mol ), If your answer is x then what will be the value of 10x.
CN ion is oxidised by a powerful oxidising agent to NO and CO or CO depending on the acidity of the reaction mixture. CN ⎯→ CO + NO + H+ ne What is the number (n) of electrons per mole of CN involved in the process ?
1 g of dry green algae absorbs 4.7 × 10 mole of CO per hour by photosynthesis. If the fixed carbon atoms were all stored after photosynthesis as starch (CHO). Approximately how long (in hour) would it take for the algae to double their own weight assuming photosynthesis takes place at a constant rate?
(Q) gives positive iodoform test and also give red precipitate with fehling solution. Hydrogenation of (P) results benzenoid compound (S). Compound (S) gives three monochloro products (only structural) on monochlorination. The structure of the aromatic compound P is :
(Q) gives positive iodoform test and also give red precipitate with fehling solution. Hydrogenation of (P) results benzenoid compound (S). Compound (S) gives three monochloro products (only structural) on monochlorination. The structure of the product Q is :
One of the important approach to the study of real gases involves the analysis of a parameter Z called the compressibility factor Z = where P is pressure, V is molar volume, T is absolute temperature and R is the universal gas constant. Such a relation can also be expressed as Z = (where V and Vare the molar volume for ideal and real gas respectively). Gas corresponding Z > 1 have repulsive tendencies among constituent pa
One of the important approach to the study of real gases involves the analysis of a parameter Z called the compressibility factor Z = where P is pressure, V is molar volume, T is absolute temperature and R is the universal gas constant. Such a relation can also be expressed as Z = (where V and Vare the molar volume for ideal and real gas respectively). Gas corresponding Z > 1 have repulsive tendencies among constituent particles due to their size factor, whereas those corresponding to Z < 1 have attractive forces among constituent particles. As the pressure is lowered or temperature is increased the value of Z approaches 1. (reaching the ideal behaviour) For a real gas ‘G’ Z > 1 at STP Then for ‘G’ : Which of the following is true :
1 mole of the gas occupies 22.4 L at NTP
1 mole of the gas occupies 22.4 L at pressure higher than that at STP (keeping temperature constant)
1 mole of the gas occupies 22.4 L at pressure lower than that at STP (keeping temperature constant)
None of the above
Which of the following function are defined for all x
sin[x] + cos [x] ([x] denotes greatest integer x)
sec (1 + sin x)
tan (log x)
If f(x) = (h(x) –h(–x)) (h(x) – h(–x))...... (h(x) – h(–x)) where h(x), h(x), ....... h(x) are defined everywhere & f(200) = 0, then f(x) is
one-one
many one
odd
even
If f(x) = sin{[x + 5] + {x – {x –{x}}} for x ∈ is invertible, where {.} and [.] represent fractional part and greatest integer functions respectively, then f(x) is-
sinx
– cosx
sin{x}
cos{x}
Let then :
Maximum value of f() R is
Maximum value of f() R is
f(0) =
Number of principle solutions of f(θ) = 0 is 8
If the roots of 10x – cx – 54x – 27 = 0 are in harmonic progression, then
c = 9
one integral root
two positive roots
two negative roots
Let f(x) = ||x – 4x + 3| – 2| which of the following is / are correct
f(x) = m has exactly two real solution of different sign m > 2
f(x) = m has exactly two real solution m (2, ) {0}
f(x) = m has no solution m < 0
f(x) = m has four distinct real solution m (0, 1)
If both the given equations 2x + (λ – 1)x + 8 = 0 and x – 8x + λ + 4 = 0 have real roots, then find the greatest value of λ such that .
The absolute value of maximum possible integral value of a for which the equation x + ax – 4 = 0 has its smaller root in the interval (–1, 2) is
If sum of all solutions of the equation – – 2 = 0 is where a, b, c ∈N & a, b are prime numbers then a × b equals
In a class of 30 pupils 12 take geography, 16 take physics and 18 take history. If all the 30 students take at least one subject and no one takes all three, then the number of pupils taking 2 subjects is
Let N = . then the value of log N =
Let a is real number then minimum number of real roots of equation (x + ax + 1) (3x + ax – 3) = 0 can be
The maximum value of 12 sin θ – 9 sin θ is -
If the equation |2x – 15x + 36x – 30| = , R has 4 solution, for (), then the value of () is
Let f be a function from the set of positive integers to the set of real numbers {f : N → R} such that (i) f(1) = 1 (ii) f(1) + 2f(2) + 3f(3) .....+ nf (n) = n(n + 1) f(n) then Function f(x) forms-
A.P.
G.P.
H.P.
None of these
Let f be a function from the set of positive integers to the set of real numbers {f : N → R} such that (i) f(1) = 1 (ii) f(1) + 2f(2) + 3f(3) .....+ nf (n) = n(n + 1) f(n) then Function f(x) is-
2x + 1
x
None of these
Let graph of y = x + 6x + k (k R) cuts x-axis at two real and distinct points x and x, while graph of quadratic expression y = ax + bx + c (a,b,c R) neither touches nor cuts the x-axis, then answer the following questions : If x > 0 and a – 2b + 4c > 0, then product a.k is
positive
zero
negative
can't say
Let graph of y = x + 6x + k (k ∈ R) cuts x-axis at two real and distinct points x and x, while graph of quadratic expression y = ax + bx + c (a,b,c ∈ R) neither touches nor cuts the x-axis, then answer the following questions : Set of all possible values of k is
(–, 9]
(0, 9)
(–, 9)
[0, 9)
