If \(x=a(t-1 / t), y=b(t+1 / t)\), then \(d y / d x=\)

The value of the integral \(\int\left(x^6+x^4\right) d\left(x^2\right)\) is equal to:

Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards.
The probability distribution of number of aces is given by :

The effective rate of return equivalent to a nominal rate of 12% per annum compounded quarterly is:
[Given that \((1.03)^4=1.1255\) ]

The shortest distance between the lines \(\frac{x+3}{1}=\frac{y-2}{2}=\frac{z+4}{3}\) and \(\frac{x+3}{-3}=\frac{y+7}{2}=\frac{z-6}{4}\) is :

\(A\) and \(B\) take turns in throwing a pair of dice, the first to throw a sum of 9 wins the prize.
If \(A\) throws first, then the ratio of the probabilities of \(A\) and \(B\) winning is :

Two parallel plate capacitors of capacitances \(2 \mu F\) and \(3 \mu F\) are joined in series and connected to a battery of \(V\) volts. The values of potential across the two capacitors V1 and V2 and energy stored in them U1 and U2 are related as :

An ac source of variable angular frequency and constant amplitude is connected in series with a capacitance C and an electric bulb of resistance R. When angular frequency is increased then :

Which vector is used for introducing nematode specific genes into the tobacco host plant.

Read the passage carefully and answer the questions based on the passage:
Pollen pistil interaction involves all events from the landing of pollen grains on the stigma until the pollen tube enters the embryo sac (when the pollen is compatible). When a pollen tube grows through the style and enters into the ovules, it finally discharges two male gametes in one of the synergids. Syngamy and triple fusion are two fusion events occur in angiosperms. Thus, angiosperms exhibit double fertilization. The products of these fusions are the diploid zygote and triploid primary endosperm nucleus. Zygote develops into embryo and primary endosperm cell forms the endosperm tissue. The developing embryo passes through different stages before maturation.
The coconut water from tender coconut, a good source of nutrition is nothing but:

The corner points of the bounded feasible region for an LPP are (0, 20), (3, 12), (6,8), (0, 15).
The objective function is \(Z=a x+\beta y\), where \(a, \beta>0\).
If the maximum of Z occurs at the corner points (3, 12) and (6,8), then the relationship between \(a\) and \(\beta\) is:

The magnetic field in a plane electromagnetic wave is given by \( B = 3 \times 10^{-7} \sin(1.5z + 5 \times 10^{8}t) \text{ T} \), where \( z \) is in meter and \( t \) is in second. The wavelength of the wave is: (Take \( \pi = 3 \))

Chasmogamous flowers are -