The equation of the plane which passes through the point (3, 2, -1) and is perpendicular to the line with direction ratios 2, 1, 2 is:

Let X be a random variable. Let E(X) and Var(X) denote the mean and the variance of X respectively.
Match List - I with List - II

List - I	List - II
(A) If \(\operatorname{Var}( X )=\alpha\), then \(\operatorname{Var}(2 X +3)\) is	(I) \(11 \alpha\)
(B) If \(E ( X )=\alpha\), then \(E (2 X )\) is	(II) \(6 \alpha\)
(C) If \(\operatorname{Var}( X )=\alpha\), then \(\operatorname{Var}(3 X -\alpha)+\operatorname{Var}(\sqrt{2} X +\beta)\) is	(III) \(4 \alpha\)
(D) If \(E(X) = 3\) \(\frac{5\alpha}{12}, \text{ then E(12X + } \alpha)\) is	(IV) \(2 \alpha\)

Choose the correct answer from the options given below:

An edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the volume of the cube increasing when the edge is 10 cm long?

Let \(\vec{a}=4 \hat{i}-\hat{j}+3 \hat{k}\) and \(\vec{b}=-2 \hat{i}+\hat{j}-2 \hat{k}\). Then
(A) \(\vec{a}\) is a unit vector
(B) \(\vec{a} \times \vec{b}=-\hat{i}+2 \hat{j}+2 \hat{k}\)
(C) \(\vec{a}\) and \(\vec{b}\) are parallel vectors
(D) \(\vec{a}\) and \(\vec{b}\) are neither parallel nor perpendicular vectors
Choose the \(\backslash\) textbf\{correct\} answer from the options given below :

Out of students in a school, it is known that \(65 \%\) reside in hostel and \(35 \%\) are day scholars. Previous year results report that \(40 \%\) of the students who reside in hostel attain A grade and \(20 \%\) of day scholars attain A grade in their annual examination.
At the end of the year, one student is chosen at random from the class.
Probability of the selected student attaining grade \(A\) is:

The interval where the function \(f(x)=2 x^3-9 x^2+12 x+15\) is decreasing, is :

A Bond has a coupon rate of 10\% per annum paid semi annually and the coupon payment made is ₹ 50 , so the face value of the bond 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).
In the above passage, the inheritance is an example of:

Degree of dissociation, when molar conductivity of X at its concentration C is 24.14 and its limiting molar conductivity is 48.28 will be :

Which one of the following options is incorrect?
For a square matrix \(A\) in the matrix equation \(A X=B\).

A wire of resistance \( 5 \, \Omega \) is drawn out so that its length is increased to thrice its original length. The new resistance would be :

The synthesis of alkyl fluoride is best accomplished by the following reaction:
\(CH_3Br + AgF\rightarrow CH_3F + AgBr\)
The reaction is termed as:

Match List - I with List - II

List - I	List - II
(A) \([Ni(CN)_4]^{2-}\)	(I) \(EDTA^{4-}\)
(B) bidentate	(II) paramagnetic
(C) chelate ligand	(III) diamagnetic
(D) \([Ni(Cl)_4]^{2-}\)	(IV) oxalate

Choose the correct answer from the options given below: