Differential equation of a parabola with vertex at origin and symmetric about \(x\)-axis is :

The greatest integer function \(f(x)=\lfloor x\rfloor\) is differentiable for all values of

Consider the differential equation, \(x \frac{d y}{d x}=y\left(\log _e y-\log _e x+1\right)\), then which of the following are true?
(A) It is a linear differential equation
(B) It is a homogenous differential equation
(C) Its general solution is \(\log _e\left(\frac{y}{x}\right)=C x\), where \(C\) is constant of integration
(D) Its general solution is \(\log _e\left(\frac{x}{y}\right)=C_y\), where \(C\) is constant of integration
(E) If \(y(1)=1\), then its particular solution is \(y=x\)
Choose the correct answer from the options given below:

If a fair coin is tossed 10 times the probability of atleast 6 heads is:

Two cards are drawn simultaneously from a well shuffled pack of 52 cards. Then variance of the number of kings is:

Which of the following is a correct statement?

The probabilities of occurrence of two events A and B are 0.45 and 0.20 respectively.
The probability of their simultaneous occurrence is 0.06.
The probability that neither A nor B occurs is

Three bad eggs are mixed with 7 good ones
If two eggs are drawn one by one without replacement
then the probability distribution of the number X of bad eggs drawn is

Identify the statements which are not true for the natural ecosystem.
(A) Grassland and desert are examples of terrestrial ecosystem.
(B) Oceans and rivers are man-made ecosystems.
(C) Wetland and estuary are examples of aquatic ecosystem.
(D) Crop fields and aquarium are natural ecosystems
Choose the correct answer from the options given below:

The enzyme used to treat a plant cell for isolation of DNA is:

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 elevation in boiling point will be maximum in

Read the passage carefully and answer the following questions
There are mainly four series of the transition metals, 3d series (Sc to Zn), 4d series (Y to Cd), 5d series (La and Hf to Hg) and 6d series which has Ac and elements from Rf to Cn. The two series of the inner transition metals; 4f (Ce to Lu) and 5f (Th to Lr) are known as lanthanoids and actinoids respectively. Their chemical properties are transitional between those of s and p-block elements. The transition metals (with the exception of Zn, Cd and Hg) are very hard and have low volatility. Their melting and boiling points are high. Transition metals have incomplete d subshell either in neutral atom or in their ions. With partly filled d orbitals these elements exhibit certain characteristic properties such as display of a variety of oxidation states, formation of coloured ions and entering into complex formation with a variety of ligands. The transition metals and their compounds are known for their catalytic activity.
Which of the following statements is correct?