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Ionization potential of hydrogen atom is 13.6 eV. Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy 12.1 eV. the spectral lines emitted by hydrogen atoms according to Bohr's theory will be
An infinite number of identical capacitors, each of capacitance 1 μ F, are connected as in the figure. The equivalent capacitance between 'A' and 'B' is
If 4 * 1020 eV of energy is required to move a charge of 0•25 coluomb between two points, the p.d between them is
On a rough horizontal surface, a body of mass 2 kg is given a velocity of 10 m/s. If the coefficient of friction is 0.2 and g=10 m/s2, the body will stop after covering a distance of
The temperature of a body falls from 50oC to 40oC in 10 minutes. If the temperature of the surroundings is 20oC Then temperature of the body after another 10 minutes will be
A river water is flowing at 0.5 m-s⁻1. The shearing stress between horizontal layers at a distance of 10 cm of the river water is (Viscosity of water = 0.01 poise)
If an air-bubble of radius 0.4 mm at a depth h in water having surface tension of 72*10⁻3 N-m⁻1 and density 1000 kg-m⁻3 is in equilibrium then, the value of h is (Take g=10 m-s⁻2)
A stone projected with a velocity u at an angle θ with the horizontal reaches maximum height H₁. When it is projected with velocity u at an angle (π/2 -θ) with the horizontal, it reaches maximum height H₂. The relation between the horizontal range R of the projectile, H₁ and H₂ is
An impulse applied to a moving object with the force at an angle of 120 o with respect to the velocity vector. The angle between impulse vector and change in momentum vector is
The horizontal range is four times the maximum height attained by a projectile. The angle of projection is
The moment of inertia of a thin uniform circular disc about one of the diameters is I. Its moment of inertia about an axis perpendicular to the circular surface and passing through the centre is
A point object O is placed at 15 cm in front of a glass rod having spherical end of radius of curvature 30 cm. The image would be formed at
Here, μ1 = 1, μ2 = 1.5, u = - 15 cm,
R = + 30 cm, v = ?
Refraction from rearer to denser medium,
A fuse wire with radius 1 mm blows at 1.5 amp. The radius of the fuse wire of the same material to blow at 3A will be
A reversible engine converts one-sixth of the heat into work. When temperature of sink is reduced by 62oC, the efficiency of the engine is doubled. The temperature of source and sink are
If the two slits in Young's experiment have width ratio 1:4, the ratio of intensity at maxima and minima in the interference pattern in
If r is the radius of first orbit, the radius of nth orbit of the H atom will be
The no. of unpaired electrons in an element with electronic configuration 1s2,2s2,3p2 is
Which of the following does not have sp2-hybridised carbon?
1 dm3 of 2 M CH₃COOH is mixed with 1 dm3 of 3 M ethanol to form ester. The decrease in the initial rate if each solution is diluted with an equal volume of water would be
Which of the following has highest first ionization potential?
Nitrogen has highest first ionization potential. This is because N contains exactly half-filled p-orbitals which is extra stable. hence its first ionisation potential is high.
Electronic configuration of N:
The densities of graphite and diamond at 298 K are 2.25 and 3.31 g-cm-3 respectively. If the standard free energy difference (ΔGo)is equal to 1895 J-mol-1, then pressure at which graphite will be transformed into diamond at 298 K is
The aqueous solution containing which of the following ions will be colourless?
Atomic weight of bromine is 80,0.1 mole of ethylene absorbs following gram of bromine
The area bounded by the x-axis and the curve y = 4x - x2 - 3, is
The coordinates of a point from which tangents drawn to three circles x2+y2=1, x2+y2+8x+15=0, x2+y2+10y+24=0 are equal in length, are
The number of common tangents to the circles x2 + y2 = 4 and x2 + y2 - 8x + 12 = 0 is
The differential equation of the family of curves y2=4a (x+a) is
y = Aex + Be2x + Ce3 x
satisfies the diferential equation
A house subtends a right angle on the window of its opposite house and the angle of elevation of the window from the foot of the former houses is 60o. If the distance between houses is 6 metres, then the height of the former house is
The product of the perpendicular, drawn from any point on a hyperbola to its asymptotes is
The slope of the tangent at (x, y) to a curve passing through (2, 1) is (x2 + y2)/2xy, then the equation of the curve is
If each element of a 3 * 3 matrix is multiplie by 3, then the determinant of the newly formed matrix is
The angle between pair of lines represented by x2+2xy-y2=0 is
Two finite sets have m and n elements, the total number of subsets of the first set is 56 more than the total number of subsets of the second. The value of m and n are respectively
Let A denote the first set and B denote the second set
We have, n(A) = 2m and n(B) = 2n
As per the question, we have
n(A) = 56 + n(B)
⇒ n(A) - n(B) = 56
⇒ 2m - 2n = 56
⇒ 2n (2m - n - 1)
⇒ 2n (2m - n - 1) = 8 * 7
⇒ 2n = 8 = 23 or (2m - n - 1) = 7
⇒ n = 3 or 2m - n = 8 = 23 = 26 - 3
⇒ n = 3 or m - n = 3
⇒ n = 3 or m = 6
Hence, the required values of m and n are 6 and 3 respectively
The parabola (y + 1)2 = a x − 2 passes through the point 1, − 2 . The equation of its directrix is
In Δ A B C , if the line joining the circumcentre 'O' and the incentre I is parallel to BC ,then cosB + cosC =
If x, y, z are positive real numbers, then (x3/z) < (x3 + y3 + z3)/(x + y + z) < (z3/x) if
The 6th term of a G.P. is 32 and its 8th term is 128 ; then the common ratio of the G.P. is
The two curves x = y2, xy = a3 cut arthogonally at a point, then a2 =
All the values of x satisfying sin 2 x + sin 4 x = 2 sin 3 x are
Group the following figures into three classes on the basis of identical properties.
1,6,9, are all triangles.
3,4,7, are all four-sided figures.
2,5,8 are all five-sided figures.