JEE Main 2021 (Online) 17th March Morning Shift

The system of equations kx + y + z = 1, x + ky + z = k and x + y + zk = k2 has no solution if k is equal to :

Team 'A' consists of 7 boys and n girls and Team 'B' has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams when a boy plays against a boy and a girl plays against a girl, then n is equal to :

Let there be three independent events E1, E2 and E3. The probability that only E1 occurs is \(\alpha\), only E2 occurs is \(\beta\) and only E3 occurs is \(\gamma\). Let 'p' denote the probability of none of events occurs that satisfies the...

Two dies are rolled. If both dices have six faces numbered 1, 2, 3, 5, 7 and 11, then the probability that the sum of the numbers on the top faces is less than or equal to 8 is :

The value of \(4 + {1 \over {5 + {1 \over {4 + {1 \over {5 + {1 \over {4 + ......\infty }}}}}}}}\) is :

In a school, there are three types of games to be played. Some of the students play two types of games, but none play all the three games. Which Venn diagrams can justify the above statement?

In a triangle PQR, the co-ordinates of the points P and Q are (\(-\)2, 4) and (4, \(-\)2) respectively. If the equation of the perpendicular bisector of PR is 2x \(-\) y + 2 = 0, then the centre of the circumcircle of the \(\Delta\)PQR is :

The maximum value of z in the following equation z = 6xy + y2, where 3x + 4y \(\le\) 100 and 4x + 3y \(\le\) 75 for x \(\ge\) 0 and y \(\ge\) 0 is __________.

If \(\overrightarrow a = \alpha \widehat i + \beta \widehat j + 3\widehat k\),\(\overrightarrow b = - \beta \widehat i - \alpha \widehat j - \widehat k\) and \(\overrightarrow c = \widehat i - 2\widehat j - \widehat k\)such that $$\over...

Let \(\overrightarrow a\) = 2\(\widehat i\) \(-\) 3\(\widehat j\) + 4\(\widehat k\) and \(\overrightarrow b\) = 7\(\widehat i\) + \(\widehat j\) \(-\) 6\(\widehat k\).If \(\overrightarrow r\) \(\times\) \(\overrightarrow a\) = $$\overri...

An AC current is given by I = I1 sin\(\omega\)t + I2 cos\(\omega\)t. A hot wire ammeter will give a reading :

If an electron is moving in the nth orbit of the hydrogen atom, then its velocity (vn) for the nth orbit is given as :

Which level of the single ionized carbon has the same energy as the ground state energy of hydrogen atom?

A parallel plate capacitor whose capacitance C is 14 pF is charged by a battery to a potential difference V = 12 V between its plates. The charging battery is now disconnected and a porcelin plate with k = 7 is inserted between the plates, ...

Four identical rectangular plates with length, l = 2 cm and breadth, b = \({3 \over 2}\) cm are arranged as shown in figure. The equivalent capacitance between A and C is \({{x{\varepsilon _0}} \over d}\). The value of x is ______________. ...

A modern grand - prix racing car of mass m is travelling on a flat track in a circular arc of radius R with a speed v. If the coefficient of static friction between the tyres and the track is \(\mu\)s, then the magnitude of negative lift FL...

For VHF signal broadcasting, ___________ km2 of maximum service area will be covered by an antenna tower of height 30 m, if the receiving antenna is placed at ground. Let radius of the earth be 6400 km. (Round off to the Nearest Integer) (T...

The equivalent resistance of series combination of two resistors is 's'. When they are connected in parallel, the equivalent resistance is 'p'. If s = np, then the minimum value for n is ____________. (Round off to the Nearest Integer)

A current of 10A exists in a wire of cross-sectional area of 5 mm2 with a drift velocity of 2 \(\times\) 10\(-\)3 ms\(-\)1. The number of free electrons in each cubic meter of the wire is ___________.

An electron of mass m and a photon have same energy E. The ratio of wavelength of electron to that of photon is : (c being the velocity of light)

If 2.5 \(\times\) 10\(-\)6 N average force is exerted by a light wave on a non-reflecting surface of 30 cm2 area during 40 minutes of time span, the energy flux of light just before it falls on the surface is ___________ W/cm2. (Round off t...

The output of the given combination gates represents :

The thickness at the centre of a plane convex lens is 3 mm and the diameter is 6 cm. If the speed of light in the material of the lens is 2 \(\times\) 108 ms\(-\)1. The focal length of the lens is ____________.

The radius in kilometer to which the present radius of earth (R = 6400 km) to be compressed so that the escape velocity is increased 10 times is ___________.

A Carnot's engine working between 400 K and 800 K has a work output of 1200 J per cycle. The amount of heat energy supplied to the engine from the source in each cycle is :

Two identical metal wires of thermal conductivities K1 and K2 respectively are connected in series. The effective thermal conductivity of the combination is :

A polyatomic ideal gas has 24 vibrational modes. What is the value of \(\gamma\)?

Two ideal polyatomic gases at temperatures T1 and T2 are mixed so that there is no loss of energy. If F1 and F2, m1 and m2, n1 and n2 be the degrees of freedom, masses, number of molecules of the first and second gas respectively, the tempe...

Two blocks (m = 0.5 kg and M = 4.5 kg) are arranged on a horizontal frictionless table as shown in figure. The coefficient of static friction between the two blocks is \({3 \over 7}\). Then the maximum horizontal force that can be applied o...

A solenoid of 1000 turns per metre has a core with relative permeability 500. Insulated windings of the solenoid carry an electric current of 5A. The magnetic flux density produced by the solenoid is : (permeability of free space = 4\(\pi\)...

A car accelerates from rest at a constant rate \(\alpha\) for some time after which it decelerates at a constant rate \(\beta\) to come to rest. If the total time elapsed is t seconds, the total distance travelled is :

When two soap bubbles of radii a and b (b > a) coalesce, the radius of curvature of common surface is :

The angular speed of truck wheel is increased from 900 rpm to 2460 rpm in 26 seconds. The number of revolutions by the truck engine during this time is _____________. (Assuming the acceleration to be uniform).

The following bodies,(1) a ring(2) a disc(3) a solid cylinder(4) a solid sphere,of same mass 'm' and radius 'R' are allowed to roll down without slipping simultaneously from the top of the inclined plane. The body which will reach first at ...

A mass M hangs on a massless rod of length l which rotates at a constant angular frequency. The mass M moves with steady speed in a circular path of constant radius. Assume that the system is in steady circular motion with constant angular ...

A triangular plate is shown. A force \(\overrightarrow F\) = 4\(\widehat i\) \(-\) 3\(\widehat j\) is applied at point P. The torque at point P with respect to point 'O' and 'Q' are :

For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal ?

Consider two identical springs each of spring constant k and negligible mass compared to the mass M as shown. Fig. 1 shows one of them and Fig. 2 shows their series combination. The ratios of time period of oscillation of the two SHM is Tb/...

The vernier scale used for measurement has a positive zero error of 0.2 mm. If while taking a measurement it was noted that '0' on the vernier scale lies between 8.5 cm and 8.6 cm, vernier coincidence is 6, then the correct value of measure...

A boy is rolling a 0.5 kg ball on the frictionless floor with the speed of 20 ms-1. The ball gets deflected by an obstacle on the way. After deflection it moves with 5% of its initial kinetic energy. What is the speed of the ball now?