List of practice Questions

\( \frac{d}{dx} \left[ a \tan^{-1} x + b \log\left(\frac{x-1}{x+1}\right) \right] = \frac{1}{x^{4} - 1} \implies a - 2b \) is equal to

\( y = e^{a \sin^{-1}(x)} \implies (1 - x^{2}) y_{n+2} - (2n+1)x y_{n+1} \) is equal to

The maximum value of \( \frac{\log x}{x}, \; 0 < x < \infty \) is

\( z = \tan(y + ax) + \sqrt{y - ax} \implies z_{xx} - a^{2} z_{yy} \) is equal to

\( \int \frac{dx}{(x+1)\sqrt{4x+3}} \) is equal to

\( \int \left(\frac{2 - \sin 2x}{1 - \cos 2x}\right) e^{x} \, dx \) is equal to

If \( I_{n} = \int \sin^{n} x \, dx \), then \( n I_{n} - (n-1) I_{n-2} \) equals

The line \( x = \frac{\pi}{4} \) divides the area of the region bounded by \( y = \sin x \), \( y = \cos x \) and the x-axis \( (0 \le x \le \frac{\pi}{2}) \) into areas \( A_{1} \) and \( A_{2} \). Then \( A_{1} : A_{2} \) equals

The solution of the differential equation \( \frac{dy}{dx} = \sin(x+y)\tan(x+y) - 1 \) is

The differential equation of the family \( y = a e^{x} + b x e^{x} + c x^{2} e^{x} \) is

The headquarter of International Labour Organisation is located at

The first Indian woman to receive Bharat Ratna was

‘Kip’ is the currency of

The charter of the United Nations was signed on June 26, 1945 in

The National Remote Sensing Agency is located at

The term Gambit is used in

World’s fastest missileship ‘INS Prahar’ was commissioned in

Nati is the classical dance of

Look at this series: 7, 10, 8, 11, 9, 12, ... What number should come next?

Magazine : Story : Article (Choose the group with the same relationship)

Juice : Orange : Banana (Choose the group with the same relationship)

Carnivorous : Tiger : Wolf (Choose the group with the same relationship)

Rain : Cloud : Evaporation (Choose the group with the same relationship)

Dog : Squirrel : Tail (Choose the group with the same relationship)

I wish I was with him. (Identify improvement for "was")