If the slope of one of the lines given by ax2 + 2hxy + by2 = 0 is two times the other, then
Give that f(x) =\(\frac {1-cos4x}{x^2}\) if x < 0 ,f(x) = a if x = 0 , f(x) =\(\frac {\sqrt {x}}{\sqrt {16 + \sqrt {x} }- 4}\) if x > 0, is continuous at x = 0, then a will be
In a triangle ABC, with usual notations ∠A = 60°, then (1 + \(\frac {a}{c}\) + \(\frac {b}{c}\))(1 + \(\frac {c}{b}\) - \(\frac {a}{b}\)) = ?
If y = 4x – 5 is tangent to the curve y2 =px3 +q at (2, 3), then
For the differential equation [1 + \((\frac {dy}{dx})^2\)]5/2 = 8 \((\frac {d^2y}{dx^2})\) has the order and degree_________respectively.
Aldol condensation between which of the following compounds followed by dehydration gives 4-Methylpent-3-en-2-one.
Two coils P and S have a mutual inductance of 5 x 10-3 H. If the current in the coil, P is I = 10 sin (100 πt), then the maximum value of the e.m.f. induced in coil S is
A metal wire of density ‘ρ’ floats on water surface horizontally. If it is NOT to sink in water, then maximum radius of wire is (T = surface tension of water, g = gravitational acceleration)
A photon of energy ‘E’ ejects photoelectrons from a metal surface whose work function is W0. If this electron enters into uniform magnetic field of induction ‘B’ in a direction perpendicular to field and describes a circular path of radius‘r’, then radius is given by
A liquid drop having surface energy ‘E’ is spread into 216 droplets of the same size. The final surface energy of the droplets is __.
Choose the false statement from following about SN1 reaction mechanism.
Which of the following compounds is likely to show both Frenkel and Schottky defects in its crystalline form?
How many carbon atoms present in n mole of citric acid?
What is standard reduction potential of Cu2+ | Cu(s) if E° of following cell is 0.46V ? Cu(s) | Cu2+(aqs) || Ag+(aq) | Ag(s) ( Eo = 0.80V)
Which among the following is an actinoid element?
Which from following pair of elements have one electron in 5d-subshell in observed electronic configuration?
Ammonia and oxygen react at high temperature as in reaction, 4HN3(g) + 5O2(g) → 4NO(g) + 6H2O(g) If rate of formation of NO is 3.6 x 10–3 mol L–1 .sec–1 . Calculate the rate of formation of water.
If the position vectors of the points A and B are 3\(\hat {i}\) + \(\hat {j}\) + 2\(\hat {k}\) and \(\hat {i}\) -2\(\hat {j}\) -4\(\hat {k}\) respectively, then the equation of the plane through B and perpendicular to AB is
A random variable X has the following probability distribution then P (X ≥ 2) =?
If matrix A =\(\begin{bmatrix} 1 & 2 \\ 4 & 3 \end{bmatrix}\) is such that AX = I, where I is 2 x 2 unit matrix, then X =
\(\int_{-π/2}^{π/2} f(x) \,dx\) =?Where f(x) = sin |x| + cos |x|, x ∈ \((-\frac {π}{2}, \frac {π}{2})\)
If \(\int \frac {2e^x + e^x}{3e^x + 4e^{-x}} \,dx\) = Ax + Blog( 3e2x + 4) + C, then values of A and B are respectively (where C is a constant of integration.)
The ratio in which the plane r.(\(\hat i\) -2\(\hat j\) + 3\(\hat k\) ) =17 divides the line joining the points -2\(\hat i\)+4\(\hat j\)+7\(\hat k\) and 3\(\hat i\)-5\(\hat j\)+8\(\hat k\) is
The angle between two lines x +1 =y + 3 =z - 4 and \(\frac {x-4}{1}\) = \(\frac {y+2}{2}\) = \(\frac {z+1}{2}\) is
The area of the region bounded by the y-axis, y = cos x, y = sin x, when 0 ≤ x ≤\(\frac {π}{4}\), is
