JEE Main 2017 (Online) 9th April Morning Slot

If y = mx + c is the normal at a point on the parabola y2 = 8x whose focal distance is 8 units, then \(\left| c \right|\) is equal to :

The number of ways in which 5 boys and 3 girls can be seated on a round table if a
particular boy B1 and a particular girl G1 never sit adjacent to each other, is :

Let E and F be two independent events. The probability that both E and F happen is \({1 \over {12}}\) and the probability that neither E nor F happens is \({1 \over {2}}\), then a value of \({{P\left( E \right)} \over {P\left( F \right)}}\)...

From a group of 10 men and 5 women, four member committees are to be formed each of which must contain at least one woman. Then the probability for these committees to have more women than men, is :

The sum of all the real values of x satisfying the equation
2(x\(-\)1)(x2 + 5x \(-\) 50) = 1 is :

If three positive numbers a, b and c are in A.P. such that abc = 8, then the minimum possible value of b is :

Let
Sn = \({1 \over {{1^3}}}\)\(+ {{1 + 2} \over {{1^3} + {2^3}}} + {{1 + 2 + 3} \over {{1^3} + {2^3} + {3^3}}} + ......... + {{1 + 2 + ....... + n} \over {{1^3} + {2^3} + ...... + {n^3}}}.\)
If 100 Sn = n, then n is equal to :

The sum of 100 observations and the sum of their squares are 400 and 2475,
respectively. Later on, three observations, 3, 4 and 5, were found to be incorrect. If
the incorrect observations are omitted, then the variance of the remaining obs...

A square, of each side 2, lies above the x-axis and has one vertex at the origin. If
one of the sides passing through the origin makes an angle 30o with the positive direction of the x-axis, then the sum of the x-coordinates of the vertices...

If the vector \(\overrightarrow b = 3\widehat j + 4\widehat k\) is written as the
sum of a vector \(\overrightarrow {{b_1}} ,\) paralel to \(\overrightarrow a = \widehat i + \widehat j\) and a vector \(\overrightarrow {{b_2}} ,\) perpe...

A sinusoidal voltage of peak value 283 V and angular frequency 320/s is applied to a series LCR circuit. Given that R=5 \(\Omega\), L=25 mH and C=1000 \(\mu\)F. The total impedance, and phase difference between the voltage across the sour...

The acceleration of an electron in the first orbit of the hydrogen atom (n = 1) is :

Imagine that a reactor converts all given mass into energy and that it operates at a power level of 109 watt. The mass of the fuel consumed per hour in the reactor will be : (velocity of light, c is
3×108 m/s)

A combination of parallel plate capacitors is maintained at a certain potential difference.

When a 3 mm thick slab is introduced between all the plates, in order to maintain the same potential difference, the distance between the plates i...

Two particles A and B of equal mass M are moving with the same speed \(\upsilon\) as shown in the figure. They collide completely inelastically and move as a single particle C. The angle \(\theta\) that the path of C makes with the X-axis...

A conical pendulum of length 1 m makes an angle \(\theta\) = 45o w.r.t. Z-axis and moves in a circle in the XY plane. The radius of the circle is 0.4 m and its center is vertically below O. The speed of the pendulum, in its circular path, ...

A signal is to be transmitted through a wave of wavelength \(\lambda\), using a linear antenna. The length l of the antenna and effective power radiated Peff will be given respectively as :
(K is a constant of proportionality)

In a meter bridge experiment resistances are connected as shown in the figure. Initially resistance P = 4 \(\Omega\) and the neutral point N is at 60 cm from A. Now an unknown resistance R is connected in series to P and the new position o...

The figure shows three circuits I, II and III which are connected to a 3V battery. If the powers dissipated by the configurations I, II and III are P1 , P2 and P3 respectively, then :

A uniform wire of length 1 and radius r has a resistance of 100 \(\Omega\). It is recast into a wire of radius \({r \over 2}.\) The resistance of new wire will be :

A Laser light of wavelength 660 nm is used to weld Retina detachment. If a Laser pulse of width 60 ms and power 0.5 kW is used the approximate number of photons in the pulse are :
[Take Planck's constant h \(=\) 6.62 \(\times\) 10\(-\)34 ...

A uniform magnetic field B of 0.3 T is along the positive Z-direction. A rectangular loop (abcd) of sides 10 cm × 5 cm carries a current I of 12 A. Out of the following different orientations which one
corresponds to stable equilibrium ?

The electric field component of a monochromatic radiation is given by
\(\overrightarrow E\) = 2 E0 \(\widehat i\) cos kz cos \(\omega\)t
Its magnetic field \(\overrightarrow B\) is then given by :

The current gain of a common emitter amplifier is 69. If the emitter current is 7.0 mA, collector current is :

Four closed surfaces and corresponding charge distributions are shown below.

Let the respective electric fluxes through the surfaces be \({\Phi _1},\) \({\Phi _2},\) \({\Phi _3}\) and \({\Phi _4}\). Then :

In an experiment a convex lens of focal length 15 cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5 cm from it. It is found that an object and its image coincide, if the object is placed at a distance...

The mass density of a spherical body is given by
\(\rho\) (r) = \({k \over r}\) for r \(\le\) R and \(\rho\) (r) = 0 for r > R,
where r is the distance from the centre.
The correct graph that describes qualitatively the acceleration, a...

For the P-V diagram given for an ideal gas,

out of the following which one correctly represents the T-P diagram ?

N moles of a diatomic gas in a cylinder are at a temperature T. Heat is supplied to the cylinder such that the temperature remains constant but n moles of the diatomic gas get converted into monoatomic gas. What is the change in the total k...

A steel rail of length 5 m and area of cross section 40cm2
is prevented from expanding along its length while the temperature rises
by 10oC. If coefficient of linear expansion and Young’s modulus of steel are 1.2×10−5 K−1 and 2×1011 Nm−2...

A negative test charge is moving near a long straight wire carrying a current. The force acting on the test charge is parallel to the direction of the current. The motion of the charge is :

A car is standing 200 m behind a bus, which is also at rest. The two start moving at the same instant but with different forward accelerations. The bus has acceleration 2 m/s2 and the car has acceleration 4 m/s2 . The car will catch up wit...

Two tubes of radii r1 and r2, and lengths l1 and l2 , respectively, are connected in series
and a liquid flows through each of them in stream line conditions. P1 and P2 are pressure differences across the two tubes.
If P2 is 4P1 and l...

The machine as shown has 2 rods of length1 m connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and the end of the other rod has a roller that rolls along the floor in a slot. As the roller g...

A circular hole of radius \({R \over 4}\) is made in a thin uniform disc having mass M and radius R, as shown in figure. The moment of inertia of the remaining portion of the disc about an axis passing through the point O and perpendicular...

A block of mass 0.1 kg is connected to an elastic spring of spring constant 640 Nm−1 and oscillates in a damping medium of damping constant 10−2 kg s−1 . The system dissipates its energy gradually. The time taken for its mechanical energy...

A physical quantity P is described by the relation
P = a\(^{{\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}}\) b2 c3 d\(-\)4
If the relative errors in the measurement of a, b, c and d respe...

A single slit of width 0.1 mm is illuminated by a parallel beam of light of wavelength 6000 \(\mathop A\limits^ \circ\) and diffraction bands are observed on a screen 0.5 m from the slit. The distance of the third dark band from the centr...

In an experiment to determine the period of a simple pendulum of length 1 m, it is attached to different spherical bobs of radii r1
and r2 . The two spherical bobs have uniform mass distribution. If the relative difference in the periods, ...

A standing wave is formed by the superposition of two waves travelling in
opposite directions. The transverse displacement is given by
y(x, t) = 0.5 sin \(\left( {{{5\pi } \over 4}x} \right)\,\) cos(200 \(\pi\)t).
What is the speed of the ...