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The length, breadth and thickness of a rectangular sheet of metal are 4.234 m, 1.005 m, and 2.01 cm respectively. Give the volume of the sheet to correct significant figures.
Population of a town is reported as 157,900 . Which of the following statements correct?
The product of energy and time is called action. The dimensional formula for action is same as that for
The Van der Waal equation for 1 mole of a real gas is
where P is the pressure, V is the volume, T is the absolute temperature, R is the molar gas constant and a, b are Van dar Waal constants. The dimensions of a are the same as those of
A particle is projected with a velocity v, so that its range on a horizontal plane is twice the greatest height attained. If g is acceleration due to gravity, then its range is
The range R of projectile is same when its maximum height are h_{1} and h_{2}. What is the relation between R, h_{1} and h_{2}?
A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first 2 sec, it rotates through an angle q1; in the next 2 sec it rotates through an additional angle θ_{2}, the ratio θ_{2}/θ_{1} is
Two cars are moving in same direction with speed of 30 kmph. They are separated by a distance of 5 km. What is the speed of a car moving in opposite direction if it meets the two cars at an interval of 4 min?
A body starts from rest, the ratio of distances travelled by the body during 3^{rd} and 4^{th}seconds is :
An object is said to be in uniform motion in a straight line if its displacement
A man pulls a block heavier than himself with a light horizontal rope. The coefficient of friction is the same between the man and the ground, and between the block and the ground.
Adjoining figure shows a force of 40 N acting at 30° to the horizontal on a body of mass 5 kg resting on a smooth horizontal surface. Assuming that the acceleration of freefall is 10 ms^{_2}, which of the following statements A, B, C is (are) correct?
[1] The horizontal force acting on the body is 20 N
[2] The weight of the 5 kg mass acts vertically downwards
[3] The net vertical force acting on the body is 30 N
Two spheres A and B of masses m_{1} and m_{2} respectively collide. A is at rest initially and B is moving with velocity v along xaxis. After collision B has a velocity 2v in a directionperpendicular to the original direction. The mass A moves after collision in the direction.
A ring of mass 200 gram is attached to one end of a light spring of force constant 100 N/m and natural length 10 cm. The ring is constrained to move on a rough wire in the shape of the quarter ellipse of the major axis 24 cm and the minor axis 16 cm with its centre at the origin. The plane of the ellipse is vertical and wire is fixed at points A and B as shown in the figure. Initially, ring is at A with other end of the spring fixed at the origin. If normal reaction of wire on ring at A is zero and ring is given a horizontal velocity of 10 m/s towards right so that it just reaches point B, then select the correct alternative (s) (g = 10 m/s^{2})
Two spheres of masses m_{1 }and m_{2} (m_{1}>m_{2}) respectively are tied to the ends of a light, inextensible string which passes over a light frictionless pulley. When the masses are released from their initial state of rest, the acceleration of their centre of mass is:
Which of the following options are correct,
where i, j and k are unit vectors along the x, y and z axis?
A rod PQ of mass M and length L is hinged at end P. The rod is kept horizontal by a massless string tied to point Q as shown in the figure. When the string is cut, the initial angular acceleration of the rod is:
[2013]
A physical quantity Q is given by
The percentage error in A,B, C, D are 1%, 2%, 4%, 2% respectively. Find the percentage error in Q.
A bullet is fired from a gun at a speed of 5000 m/s. At what height should the gun be aimed above a goal if it has to strike the goal at a distance of 500 m? Take g=10m/s^{2}
A bullet of mass 20 g strikes a pendulum of mass 5 kg. The centre of mass of pendulum rises a vertical distance of 10 cm. If the bullet gets embedded into the pendulum, calculate its initial speed.
A disc has a speed of 1200 rpm and it is made to slow down at a uniform rate of 4 rad/s^{2}.Calculate the number of revolution it makes before coming to rest?
In the HCl molecule, the separation between the nuclei of the two atoms is about 1.27 Å (1 Å = 10^{–10} m). Find the approximate location of the CM of the molecule, given that a chlorine atom is about 35.5 times as massive as a hydrogen atom and nearly all the mass of an atom is concentrated in its nucleus.
Electromagnetic radiations having λ = 310 Å are subjected to a metal sheet having work function = 12.8 eV. What will be the velocity of photoelectrons with maximum Kinetic energy.
Consider the ground state of Cr atom (X = 24). The number of electrons with the azimuthal quantum numbers, ℓ = 1 and 2 are, respectively [2004]
Which of the following sets of quantum numbers is correct for an electron in 4f orbital ? [2004]
Radial probability density in the occupied orbital of a hydrogen atom in the ground state (1s) is given below
25.0 g of FeSO_{4}.7H_{2}O was dissolved in water containing dilute H_{2}SO_{4}, and the volume was made up to 1.0 L. 25.0 mL of this solution required 20 mL of an N/10 KMnO_{4} solution for complete oxidation. The percentage of FeSO_{4}^{.} 7H_{2}O in the acid solution is
If 6.3 g of NaHCO_{3} are added to 15.0 g CH_{3}COOH solution, the residue is found to weigh 18.0 g. What will be the mass of CO_{2} released in the reaction?
Suppose the elements X and Y combine to form two compounds XY_{2} and X_{3}Y_{2}. When 0.1 mole of XY_{2} weighs 10 g and 0.05 mole of X_{3}Y_{2} weighs 9 g, the atomic weights of X and Y are
The following equations are balanced atomwise and chargewise.
(i) Cr_{2}O_{7}^{2} + 8H+ + 2H_{2}O_{2} → 2Cr^{3}+ + 7H_{2}O + 2O_{2}
(ii) Cr_{2}O_{7}^{2} + 8H+ + 5H_{2}O_{2}→ 2Cr^{3+} + 9H_{2}O + 4O_{2}
(iii) Cr_{2}O_{7}^{2} + 8H+ + 7H_{2}O_{2}→ 2Cr+ + 11H_{2}O + 5O_{2}
The precise equationl equations representing the oxidation of H_{2}O_{2} is/are
Elements which occupied position in the lother meyer curve, on the peaks, were 
In the general electronic configuration 
(n  2)f^{114} (n  1)d^{01} ns^{2}, if value of n = 7 the configuration will be 
In which group of the modern periodic table are halogens placed?
The symbol for element with atomic number 111 and name Unununium is
Azide ion [N_{3}^{}] exhibits an (N−N) bond order of 2 and may be represented by the resonance structures I,II and III given below:
The most stable resonance structure is
C—Cl bond in (vinyl chloride) is stabilised in the same way as in
Hydrogen bonds are formed in many compounds e.g., H_{2}O, HF, NH_{3}. The boiling point of such compounds depends to a large extent on the strength of hydrogen bond and the number of hydrogen bonds. The correct decreasing order of the boiling points of above compounds is :
Which of the following angle corresponds to sp_{2} hybridisation?
bond in between (C_{2}— C_{3}) vinyl acetylene is formed by ...... overlapping
Direction (Q. Nos. 111) This section contains 11 multiple choice questions. Each question has four choices (a), (b), (c) and (d), out of which ONLY ONE option is correct.
Q. Assuming that Hund's rule is violated, the bond order and magnetic nature of the diatomic molecule B_{2} is
In white phosphorous (P_{4}) if
x is total number of triangle
y is total number of plane of symmetry z is total number of P–P bond
then calculate value of (y + z)/x.
The energy of electron in the second and third Bohr orbit of the hydrogen atom is –5.42 x 10^{–12 }erg and –2.41 x 10^{–12}erg, respectively. Calculate the wavelengths of emitted radiation when the electron drops from third to second orbit.
29.2 % (w/w) HCl stock solution has density of 1.25 g mL^{1}. The molecular weight of HCl is 36.5 g mol^{1}. The volume (mL) of stock solution required to prepare a 200 mL solution of 0.4 M HCl is
How many spectral lines are emitted by atomic hydrogen excited to n^{th} energy level?
The domain of the function √(log1/3 log4 ([x]2  5)) is (where [x] denotes greatest integer function)
A real valued function f(x) satisfies the functional equation f(x – y) = f(x) f(y) – f(a – x) f(a + y) where a is a given constant and f(0) = 1, f(2a – x) is equal to
Let R be a relation defined on the set of N natural numbers as R = {(x, y): y is a factor of x, x, y∈ N} then,
If A = {x : x is a multiple of 3} and B = {x : x is a multiple of 5}, then A  B is
If z ≠ 1 and is real, then the point represented by the complex number z lies : [2012]
If b ≠ 1 be any n^{th} root of unity then 1 + 3β + 5β^{2} + ........n terms equals
Find the number of integral values of x for which
(5x  1) < (x + 1^{)2} < (7x – 3)
If (5x + 2) < (8x 1) and (7x  2) > 3(x + 6). What will be the solution set of x ( x ∈ N?
Calculate the least whole number, which when subtracted from both the terms of the ratio 5 : 6 gives a ratio less than 17 : 22.
The equations ax + 9y = 1 and 9y  x  1 = 0 represent the same line if a =
Given, 6x + 2(6  x) > 2x  2 < 5x/2  3x/4, then x can take which of the following values?
If ^{2n}C_{3} : ^{n}C_{2} = 12 : 1, then the value of n is ?
How many possible twodigit numbers can be formed by using the digits 3, 5 and 7 (repetition of digits is allowed)?
From a group of 7 men and 6 women, five persons are to be selected to form a committee so that atleast 3 men are there on the committee. In how many ways can it be done ?
In how many different ways can the letters of the word 'GEOGRAPHY' be arranged such that the vowels must always come together?
The number of ways of arrangements of 10 persons in four chairs is 
If the number of distinct positive rational numbers p/q smaller than 1, where p, q ∈ {1, 2, 3 ....., 6} is k then k is :
If the function ƒ(x) = 2 + x^{2} – e^{–x} and g(x) = ƒ^{–1}(x), then the value of equals
Let y = g(x) be the inverse of a bijective mapping f : R → R, f(x) = 3x^{3} + 2x. The area bounded by graph of g(x), the xaxis and the ordinate at x = 5 is 
If function ƒ(x) = x^{3} + ax^{2} + bx + c is monotonically increasing ∀ x ∈ R, where a & b are prime numbers less than 10, then number of possible ordered pairs (a,b) is
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JEE Main Part Test  2 Test  75 ques 
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357 docs148 tests

JEE Main Part Test  2 Test  75 ques 
JEE Main Part Test  3 Test  75 ques 
JEE Main Part Test  4 Test  75 ques 
JEE Main Part Test  5 Test  75 ques 
JEE Main Part Test  6 Test  75 ques 