For three simple statements p, q, and r, p → (q ˅ r) is logically equivalent to
Argument of \(\frac {1-i√3}{1+i√3}\) is
The second derivative of a sin 3t w.r.t. a cos 3t at t =π/4 is
Two numbers are selected at random from the first six positive integers. If X denotes the larger of two numbers, then Var (X) =?
If the lines 2x – 3y = 5 and 3x – 4y = 7 are the diameters of a circle of area 154 sq. units, then equation of the circle is (Taken π=\(\frac {22}{7}\))
A round table conference is to be held among 20 countries. If two particular delegates wish to sit together, then such arrangements can be done in __________ways.
If xy = e(x – y) , then \(\frac {dy}{dx}\) =?
The equation of the line perpendicular to 2x – 3y + 5 = 0 and making an intercept 3 with positive Y-axis is
If a, b, c are position vectors of points A, B, C respectively, with 2a + 3b -5c = 0 , then the ratio in which point C divides segment AB is
If a and b are two vectors such that I\(\vec {a}\)I + I\(\vec {b}\)I = \(\sqrt 2\) with \(\vec {a}\).\(\vec {b}\) = –1, then the angle between \(\vec {a}\) and \(\vec {b}\) is
Let cos (α + β) = \(\frac {4}{5}\) and sin (α - β) = \(\frac {5}{13}\), where 0 < α, β < \(\frac {π}{4}\) , then tan 2α=?
Which of the following reactions does not match correctly with its name?
What is IUPAC name of mesityl oxide?
Explain structure of polyacrylonitrile.
What is the Monomer of Neoprene?
An equation of a simple harmonic progressive wave is given by y = A sin (100πt-3x).The distance between two particles having a phase difference of \(\frac {π}{3}\) in metre is
Two satellites A and B rotate round a planet’s orbit having radius 4R and R respectively. If the speed of satellite A is 3 V then speed of satellite B is
Two thin lenses have a combined power of +9D. When they are separated by a distance of 20 cm, then their equivalent power becomes +27/5 D. Their individual power (in dioptre) is
In a p-type semiconductor
A diffraction pattern is obtained by making blue light incident on a narrow slit. If blue light is replaced by red light then
In metre bridge experiment, null point is obtained at 20 cm from left end of the wire, when resistance X is balanced against another resistance Y (X < Y). To balance a resistance 4 X against Y, the new position of the null point from the same end will be
Probability of getting odd numbers in first 100 numbers.
Polymers used for making toys are?
In which thermodynamic process, there is no exchange of heat between the system and surroundings?