The value of \(\tan \left\{2 \tan ^{-1}\left(\frac{1}{5}\right)+\pi / 4\right\}\) is :

The side of an equilateral triangle increases at the rate of \(3 cm / sec\), then the rate at which the area of the triangle increases when the side is 4 cm , is :

If the function \(f(x)=\left\{\begin{array}{ll}\frac{k c e s}{\pi-2 \pi} & : x \neq \frac{\pi}{2} \\ 3 & : x=\frac{\pi}{2}\end{array}\right.\) is continuous at \(x=\frac{\pi}{2}\), then \(k\) is equal to:

The function \(f(x)=6-6 x-2 x^2\)

The general solution of the differential equation \(y d x-\left(x+2 y^2\right) d y=0\) is:

If A and B are two events such that \(P(A)=\frac{1}{2}, P(B)=\frac{1}{3}\) and \(P(A \cap B)=\frac{1}{4}\), then which of the following statements are true?
(A) A and B are independent events
(B) \(P(A \mid B)=\frac{3}{4}\)
(C) \(P\left(A^{\prime} \mid B^{\prime}\right)=\frac{5}{8}\)
(D) \(P\left(A^{\prime} \mid B\right)=\frac{1}{4}\)
Choose the correct answer from the options given below:

If \(f(x)=\left\{\begin{array}{l}m x+1, x \geq \pi / 2 \\ \sin x+n, x \leq \pi / 2\end{array}\right.\) is continuous at \(x=\pi / 2\), where \(m \in Z\) (set of integers), then \(\sin 2 n=\)

Ultraviolet radiations of 6.2 eV are incident on an aluminum surface of work function 4.2 eV. The maximum kinetic energy of the emitted electrons is

The product obtained from catalytic reduction of propanal is:

If order of matrices \(A, B\) and \(C\) are \(4 \times 3,5 \times 4\) and \(3 \times 7\) respectively, then order of \(C^{\prime} \times\left(A^{\prime} \times B^{\prime}\right)\) is :

Arrange the stages of embryo development in a dicot plant.
(A) Heart shaped embryo
(B) Globular embryo
(C) Zygote
(D) Mature embryo
Choose the correct answer from the options given below:

MONOHYBRID CROSS
The inheritance of flower color in the dog flower (Snapdragon or Antirrhinum sp.) can be understood by crossbreeding between true-breeding red-flowered (RR) and true-breeding white-flowered plants (rr). When they were crossed, F₁ (Rr) was pink. When F₁ was self-pollinated, the F₂ results were Red, Pink and White. Here the genotype ratios were exactly as expected, but the phenotype ratios have been changed. What happened was that R was not completely dominant over r and this made it possible to distinguish Rr as pink from RR (Red) and rr (White).
What will be the phenotypic ratio in F₂ generation when F₁ (Rr) was self-pollinated?

The marks obtained by five students in a test of Applied Mathematics carrying 100 marks are 49,58,67,92,99. Then the point estimate of the population mean is