JEE Main 2021 (Online) 31st August Morning Shift

The length of the latus rectum of a parabola, whose vertex and focus are on the positive x-axis at a distance R and S (> R) respectively from the origin, is :

The number of six letter words (with or without meaning), formed using all the letters of the word 'VOWELS', so that all the consonants never come together, is ___________.

An electric instrument consists of two units. Each unit must function independently for the instrument to operate. The probability that the first unit functions is 0.9 and that of the second unit is 0.8. The instrument is switched on and it...

cosec18\(^\circ\) is a root of the equation :

The sum of 10 terms of the series
\({3 \over {{1^2} \times {2^2}}} + {5 \over {{2^2} \times {3^2}}} + {7 \over {{3^2} \times {4^2}}} + ....\) is :

Three numbers are in an increasing geometric progression with common ratio r. If the middle number is doubled, then the new numbers are in an arithmetic progression with common difference d. If the fourth term of GP is 3 r2, then r2 \(-\) d...

Which of the following is not correct for relation R on the set of real numbers ?

The mean of 10 numbers 7 \(\times\) 8, 10 \(\times\) 10, 13 \(\times\) 12, 16 \(\times\) 14, ....... is ____________.

If p and q are the lengths of the perpendiculars from the origin on the lines,x cosec \(\alpha\) \(-\) y sec \(\alpha\) = k cot 2\(\alpha\) andx sin\(\alpha\) + y cos\(\alpha\) = k sin2\(\alpha\)respectively, then k2 is equal to :

Let \(\overrightarrow a\) and \(\overrightarrow b\) be two vectors such that \(\left| {2\overrightarrow a + 3\overrightarrow b } \right| = \left| {3\overrightarrow a + \overrightarrow b } \right|\) and the angle between $$\overrightarro...

In an ac circuit, an inductor, a capacitor and a resistor are connected in series with XL = R = XC. Impedance of this circuit is :

A sample of a radioactive nucleus A disintegrates to another radioactive nucleus B, which in turn disintegrates to some other stable nucleus C. Plot of a graph showing the variation of number of atoms of nucleus B versus time is :(Assume th...

A capacitor of 50 \(\mu\)F is connected in a circuit as shown in figure. The charge on the upper plate of the capacitor is ______________\(\mu\)C.

A body of mass M moving at speed V0 collides elastically with a mass 'm' at rest. After the collision, the two masses move at angles \(\theta\)1 and \(\theta\)2 with respect to the initial direction of motion of the body of mass M. The larg...

If the sum of the heights of transmitting and receiving antennas in the line of sight of communication is fixed at 160 m, then the maximum range of LOS communication is ___________ km. (Take radius of Earth = 6400 km)

Consider a galvanometer shunted with 5\(\Omega\) resistance and 2% of current passes through it. What is the resistance of the given galvanometer ?

A square shaped wire with resistance of each side 3\(\Omega\) is bent to form a complete circle. The resistance between two diametrically opposite points of the circle in unit of \(\Omega\) will be ___________.

The voltage drop across 15\(\Omega\) resistance in the given figure will be ______________ V.

A moving proton and electron have the same de-Broglie wavelength. If K and P denote the K.E. and momentum respectively. Then choose the correct option :

A small square loop of side 'a' and one turn is placed inside a larger square loop of side b and one turn (b >> a). The two loops are coplanar with their centres coinciding. If a current I is passed in the square loop of side 'b', then the ...

The electric field in an electromagnetic wave is given by E = (50 NC\(-\)1) sin\(\omega\) (t \(-\) x/c)The energy contained in a cylinder of volume V is 5.5 \(\times\) 10\(-\)12 J. The value of V is _____________ cm3. (given \(\in\)0 = 8.8 ...

In the following logic circuit the sequence of the inputs A, B are (0, 0), (0, 1), (1, 0) and (1, 1). The output Y for this sequence will be :

Choose the correct waveform that can represent the voltage across R of the following circuit, assuming the diode is ideal one :

Two particles A and B having charges 20\(\mu\)C and \(-\)5\(\mu\)C respectively are held fixed with a separation of 5 cm. At what position a third charged particle should be placed so that it does not experience a net electric force?

An object is placed at the focus of concave lens having focal length f. What is the magnification and distance of the image from the optical centre of the lens?

Two plane mirrors M1 and M2 are at right angle to each other shown. A point source 'P' is placed at 'a' and '2a' meter away from M1 and M2 respectively. The shortest distance between the images thus formed is : (Take \(\sqrt 5\) = 2.3)

The masses and radii of the earth and moon are (M1, R1) and (M2, R2) respectively. Their centres are at a distance 'r' apart. Find the minimum escape velocity for a particle of mass 'm' to be projected from the middle of these two masses :

A reversible engine has an efficiency of \({1 \over 4}\). If the temperature of the sink is reduced by 58\(^\circ\)C, its efficiency becomes double. Calculate the temperature of the sink :

For an ideal gas the instantaneous change in pressure 'p' with volume 'v' is given by the equation \({{dp} \over {dv}} = - ap\). If p = p0 at v =0 is the given boundary condition, then the maximum temperature one mole of gas can attain is...

A car is moving on a plane inclined at 30\(^\circ\) to the horizontal with an acceleration of 10 ms\(-\)2 parallel to the plane upward. A bob is suspended by a string from the roof of the car. The angle in degrees which the string makes wit...

A coil having N turns is wound tightly in the form of a spiral with inner and outer radii 'a' and 'b' respectively. Find the magnetic field at centre, when a current I passes through coil:

A helicopter is flying horizontally with a speed 'v' at an altitude 'h' has to drop a food packet for a man on the ground. What is the distance of helicopter from the man when the food packet is dropped?

A uniform heavy rod of weight 10 kg ms\(-\)2, cross-sectional area 100 cm2 and length 20 cm is hanging from a fixed support. Young modulus of the material of the rod is 2 \(\times\) 1011 Nm\(-\)2. Neglecting the lateral contraction, find th...

When a rubber ball is taken to a depth of __________m in deep sea, its volume decreases by 0.5%. (The bulk modulus of rubber = 9.8 \(\times\) 108 Nm\(-\)2, Density of sea water = 103 kgm\(-\)3, g = 9.8 m/s2)

Angular momentum of a single particle moving with constant speed along circular path :

A particle of mass 1 kg is hanging from a spring of force constant 100 Nm\(-\)1. The mass is pulled slightly downward and released so that it executes free simple harmonic motion with time period T. The time when the kinetic energy and pote...

Match List - I with List - II.



List - I

List - II




(a)
Torque
(i)
MLT\(^{ - 1}\)


(b)
Impulse
(ii)
MT\(^{ - 2}\)


(c)
Tension
(iii)
ML\(^{ 2}\)T$$^{ - 2}...

Which of the following equations is dimensionally incorrect?Where t = time, h = height, s = surface tension, \(\theta\) = angle, \(\rho\) = density, a, r = radius, g = acceleration due to gravity, v = volume, p = pressure, W = work done, T ...

A wire having a linear mass density 9.0 \(\times\) 10\(-\)4 kg/m is stretched between two rigid supports with a tension of 900 N. The wire resonates at a frequency of 500 Hz. The next higher frequency at which the same wire resonates is 550...

A block moving horizontally on a smooth surface with a speed of 40 ms\(-\)1 splits into two equal parts. If one of the parts moves at 60 ms\(-\)1 in the same direction, then the fractional change in the kinetic energy will be x : 4 where x ...