Consider a closed cylinder of radius \(r\) with a fixed surface area. The volume of the cylinder is maximum when its height is :

Which of the following are correct about equated monthly installments (EMI)?
(A) The EMI depends on principal borrowed, rate of interest and tenure of the loan.
(B) It is a fixed amount made by borrower to the lender every month.
(C) The interest remains constant for every EMI in reducing balance method.
(D) As we pay off our loan, the outstanding principal amount decreases with every EMI in reducing balance method.
Choose the correct answer from the options given below :

Which of the following statements are true?
(A) The vector equation of the line through the point (5, 2, -4) and parallel to the vector \(3 \hat{i}+2 \hat{j}-8 \hat{k}\) is \(\vec{r}=(5 \hat{i}+2 \hat{j}-4 \hat{k})+\lambda(3 \hat{i}+2 \hat{j}-8 \hat{k})\)
(B) Vector form of the equation of line \(\frac{x-5}{3}=\frac{y+4}{7}=\frac{z-6}{2}\) is \(\vec{r}=(5 \hat{i}-4 \hat{j}+6 \hat{k})+\lambda(3 \hat{i}+7 \hat{j}+2 \hat{k})\)
(C) The direction cosines of z-axis are (1, 1, 0).
(D) If a line has direction ratios 2, -1, -2, then its direction cosines are \(-2 / 3,-1 / 3,-2 / 3\).
Choose the correct answer from the options given below:

If \(A=\left[\begin{array}{ccc}2 & -1 & 0 \\ 1 & 2 & 1 \\ -1 & 0 & 1\end{array}\right]\), then which of the following statement(s) is/are correct?
(A) A is singular matrix
(B) |3A |= 135
(C) |adj A| = 125
(D) \(\left|A^{-1}\right|=\frac{1}{5}\)
Choose the correct answer from the options given below:

The values of \(x\) which satisfy the inequality \(|x-3|<2\) lie in :

If \(e^y(x+1)=1\), then

If \(y=\sqrt{2024 x+2025}\), then which of the following is correct?

The type of pollination in which genetically different pollen grains fall on the stigma is known as:

A point source of light is placed at a distance twice the focal length of a converging lens. If the focal length of the lens is f, the intensity of the image of light source on the other side of the lens will be maximum at

A slab of material of dielectric constant K has the same area as the plates of a parallel-plate capacitor but has a thickness \( \frac{1}{4}d \), where d is the separation between the plates. If the slab is inserted between the plates, the potential difference becomes:
(Given: Potential difference across the capacitor without dielectric is \( V_0 \))

If \(f(x) = \begin{vmatrix} 0 & x-a & x-b \\ x+a & 0 & x-c \\ x+b & x+c & 0 \end{vmatrix}\), then \(f(0)\) is:

The time required for a 50 Hz alternating current to reach the peak value starting from zero

Let \(R =\left\{\left(L_1, L_2\right) : L_1 \perp L_2\right.\) where \(L_1, L_2 \in L\) (set of straight line in a plane), then