If the two lines \(\frac{x-1}{2}=\frac{y-3}{4}=-z\) and \(\frac{x-4}{3}=\frac{y-1}{-2}=z-1\) are contained in a plane then the equation of the plane is :

The equation of tangent to the curve given by \(x=a \sin ^3 t, y=b \cos ^3 t\) at a point where \(t=\frac{\pi}{2}\) is :

If \(\left[\begin{array}{lll}1 & 2 & 3\end{array}\right] A=\left[\begin{array}{ll}4 & 5\end{array}\right]\), then the order of matrix \(A\) is:

Let \(A=\left[a_{i j}\right]_{n \times n}\) and \(B=\left[b_{i j}\right]_{n \times n}\).
Then which of the following is/are true?
(A) \(A B=B A\)
(B) \((A B)^{-1}=B^{-1} A^{-1}\)
(C) \((A B)^T=B^T A^T\)
(D) \(A B=0 \Rightarrow A=0\) or \(B=0\)
Choose the correct answer from the options given below :

Difference between the maximum and minimum value of the objective function \(Z=5 x+3 y\), subject to the constraints: \(3 x+5 y \leq 15 ; 5 x+2 y \leq 10 ; x, y \geq 0\) is:

The maximum value of \(\frac{\log x}{x}\) for \(x\) in \([2, \infty)\) is :

Match List I with List II with regard to degree of the Differential Equation.

List - I	List - II
(A) \(\frac{d^3 y}{d x^3}+\sin y=0\)	(I) 4
(B) \(\left(\frac{d y}{d x}\right)^4+\cos \left(\frac{d y}{d x}\right)-1=0\)	(II) 1
(C) \(\left(\frac{d^2 y}{d x^2}\right)^2+\left(\frac{d y}{d x}\right)^4=0\)	(III) Not defined
(D) \(\left(\frac{d^2 y}{d x^2}\right)^5+2\left(\frac{d^3 y}{d x^3}\right)^4+7=0\)	(IV) 2

If \(y=\tan ^{-1} x\) then \(\frac{d y}{d x}\) at \(y=\frac{\pi}{3}\) is equal to :

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 percentage of progeny in F₁ generation when RR (red flowered plant) is crossed with rr (white flowered plant) in the above passage?

Intermolecular hydrogen bonding is observed between chloroform and acetone.
Therefore, their binary solution will_
(A) Show positive deviation from Raoult's law
(B) Show negative deviation from Raoult's law
(C) Obey Raoult's law
(D) Show decrease in vapor pressure
Choose the correct answer from the options given below:

Magnetic moment values for \([\text{Fe}(\text{H}_2\text{O})_6]^{3+}\) and \([\text{Fe}(\text{CN})_6]^{3-}\) are

The device that regulates change in intensity of illumination into change in electric current is :

The general solution of the differential equation \(\frac{x d y}{d x}+4 y=x^3,(x \neq 0)\) is :