(1) n! (2) (n-1)! (3) -1n(n-1)! (4) -1nn! Solution: y = (1+1/x)(1+2/x)(1+3/x) ….(1+n/x) dy/dx = (-1/x2)(1+2/x)(1+3/x) ….(1+n/x) + (1+1/x)(-2/x2)(1+3/x) ….(1+n/x)... View Article
(1) 22 (2) 11 (3) 0 (4) 20 Solution: Given g’(x) = -f(x) and f’(x) = g(x) h(x) = {f(x)}2... View Article
If y = \(\begin{array}{l}x^{x^{x…\infty }}\end{array} \), then dy/dx is equal to (1) yxy-1 (2) y2/x(1- y log x) (3) y/x(1+y... View Article
(1) 5x (x5 log 5 – 5x4) (2) x5 log 5 – 5x4 (3) x5 log 5 + 5x4 (4)... View Article
(1) -1/e (2) -1/2e (3) 1/2e (4) 1/e Solution: y = cos-1[(1-log x)/(1+log x)] dy/dx = \(\begin{array}{l}\frac{-1}{\sqrt{1-\left ( \frac{1-\log x}{1+\log... View Article
1) 1 2) –1 3) 2 4) 0 Solution: log(x + y) = 2xy When x = 0, log y... View Article
(1) 1 (2) -1 (3) 0 (4) 2 Solution: y = sin-1(x/2) + cos-1(x/2) We know sin-1θ + cos-1θ =... View Article
(1) \(\begin{array}{l}e^{sin^{-1}x}\end{array} \) (2) 1/√(1-x2) (3) sin-1 x (4) 1/(1-x2) Solution: Given f(x) = ex g(x) = sin-1x h(x) =... View Article
(1) ax (2) a2x2 (3) x/a (4) x/2a Solution: Given x = 2at/(1+t3) y = 2at2/(1+t3)2….(i) y = x2/2a (substitute... View Article
(1) 2x2 loge 10 (2) log10e/2x2 (3) loge10/2x2 (4) x2 loge 10 Solution: Let u = log10x = log x/log... View Article
1) x/log x 2) (x log x)–1 3) (log x)/x 4) None of these Solution: Given f(x) = log x... View Article
Reversing the Carnot cycle changes the direction of the heat and the work interaction. The refrigerator is based on the... View Article
In alkane solvents, triethylamine is a Lewis base. It forms adducts with many Lewis acids like phenols and I2. Triethylamine... View Article
There is only one law on gravitation proposed by Newton. According to Newton’s law of gravitation, any two objects in... View Article
If the multimeter is set to measure the voltage it will have a high value of resistance. So if the... View Article
The presence of the dielectric between the plates of the capacitor reduces the electric field between the plates this in... View Article
Temperature is a measure of heat energy. There is no temperature equivalent of energy.
As we go up the mountains there is less air above us, therefore, the air pressure decreases. As there is... View Article
The heat is taken from the environment in order to melt the ice. Melting of ice requires energy to break... View Article
A pendulum wave is a device that has a series of pendulums with an increasing time period. When these pendulums... View Article
