Three pipes A, B and C are installed to fill a tank. Pipes A and B opened together can fill the tank in the same time in which \(C\) can alone fill the tank. If pipe \(B\) can fill the tank 15 minutes faster than pipe \(A\) and 5 minutes slower than pipe \(C\), then the time required by pipe \(A\) to fill the tank alone is:

The function \(Z=\alpha x+\beta y(\alpha, \beta>0)\) corresponds to the objective function of an LPP that needs to be maximized subject to \(x+y \leq 1, x, y \geq 0\).
Then the set of optimal solutions is:

A card is selected at random from a pack of 52 playing cards.The selected card is a queen.The probability that this card is a card of spade is :

The solution of the differential equation \(\frac{d y}{d x}=\frac{3 e^{2 x}+3 e^{4 x}}{e^x+e^{-x}}\) is:

A and B invested ₹ 10,000 and ₹ ₹ 12,000 in a business two years ago. After 1 year their net loss was ₹ 880 . And during the 2 nd year their net profit was ₹ 2,530. So the presen

The value/s of \(\lambda\) for which the given system of equations will have infinitely many solutions \(x+y-6 z=0 ; \lambda x-y+2 z=0 ;-3 x+\lambda y+2 z=0\), is/are:

If the lines \(\frac{x+3}{k-5}=\frac{y-1}{1}=\frac{5-z}{-2 k-1}\) and \(\frac{x+2}{-1}=\frac{2-y}{-k}=\frac{z}{5}\) are perpendicular, then the value of \(k\) is

If 100 J of work is done to move electric charge equal to 4 C from a place where potential difference is \( -10 \text{ V} \) to another place where potential is V volt, then the value of V would be:

The radius of the first orbit in Bohr's hydrogen atom is 0.53\(\text{\AA}\). The radius of fourth orbit of this atom will be:

If \(A=\left[\begin{array}{lll}1 & 2 & 1 \\ 2 & 3 & 1 \\ 0 & 0 & 1\end{array}\right]\), then \(\left|\operatorname{adj}\left(3 A^T\right)\right|^2\) is equal to

A point object is placed at a distance of 20 cm from a spherical lens of refractive index n=3/2 and the radius of curvature of each surface 10 cm. The distance of the image formed from the lens is

Which one of the following is not an example of alien species invasion?

Read the passage carefully and answer the Questions
Aldehydes and ketones are important organic compounds prepared mainly by oxidation of alcohols. Primary alcohols give aldehyde and secondary alcohols yield ketones. Aldehydes can also be formed by partial reduction of acid chlorides, reduction of esters or by Gattermann-Koch reaction. Ketones are prepared by Friedel-Craft's acylation, hydration of alkyne and reaction of Grignard's reagent with nitriles. Chemically, aldehydes and ketones are reactive in nature due to the carbonyl group and undergo nucleophilic addition reactions. Aldehydes are more reactive than ketones and can be oxidized to carboxylic acids, while both can be reduced to alcohols or hydrocarbons and exhibit condensation reaction.
When two moles of benzaldehyde are heated with concentrated NaOH solution, the product/s obtained is/are: