The function \(f(x)=x^3+1\) is:

The angle between the line \(\frac{x+1}{2}=\frac{y}{3}=\frac{z-3}{6}\) and the plane \(10 x+2 y-11 z=3\) is :

If \(y=(x+1)\left(x^2+1\right)\left(x^4+1\right)\left(x^8+1\right)\) then \(\frac{d y}{d x}\) at \(x = -1\) is

Consider the line \(\vec{r}=\hat{i}-2 \hat{j}+4 \hat{k}+\lambda(-\hat{i}+2 \hat{j}-4 \hat{k})\)
Match List-I with List-II

List-I	List-II
(A) A point on the given line	(I) \(\left(\frac{-1}{\sqrt{21}}, \frac{2}{\sqrt{21}}, \frac{-4}{\sqrt{21}}\right)\)
(B) direction ratios of the line	(II) \((4,-2,-2)\)
(C) direction cosines of the line	(III) \((1,-2,4)\)
(D) direction ratios of a line perpendicular to given line	(IV) \((-1,2,-4)\)

Choose the correct answer from the options given below:

For \(x \in R\), if \(f(x)=-(x-1)^2+2\), then
(A) f is an increasing function on \((-\infty, 1)\)
(B) ƒ has no critical points
(C) ƒ has a maximum value at x = 1
(D) ƒ has a minimum value at x = 1
Choose the correct answer from the options given below:

The value of the integral \(\int_2^4 \frac{x}{x^2+1} d x\) is :

A takes a loan of ₹ \(5,00,000\) at an interest rate for 5 years. The EMI paid by him is ₹ 10,000 . The effective interest rate for A is : (Under flat rate system)

Which of the following is correct about RNA ?
(A) Unstable and mutates slower
(B) Unstable and mutates faster
(C) Stable and mutates faster
(D) Stable and mutates slower
Choose the correct answer from the options given below :

If \(X\) is a random variable and \(a, b\) are real numbers, which statements are TRUE?
(A) \(\operatorname{Var}(a X+b)=a^2 \operatorname{Var}(X)\)
(B) \(E(a X+b)=a E(X)+b\)
(C) \(E(a X+b)=a E(X)-E(b)\)
(D) \(\operatorname{Var}(a X+b)=a \operatorname{Var}(X)+b\)
Choose the correct answer :

The area bounded by the curve \(|x|+y=1\) and the axis of \(x\) is :

Match List-I with List-II

List-I	List-II
(A) The maximum value of \(f(x)=\sin (3 x)+6\)	(I) 2
(B) The maximum value of \(f(x)=-|x+2|+4\)	(II) 5
(C) The maximum value of \(f(x)=(3 x+1)^2+5\)	(III) 7
(D) The maximum value of \(f(x)=2 \cos x+4\)	(IV) 4

Choose the correct answer from the options given below:

If \(\left[\begin{array}{cc}2 & 3 \\ 5 & 7\end{array}\right]\left[\begin{array}{cc}1 & -3 \\ -2 & 4\end{array}\right]=\left[\begin{array}{cc}-4 & 6 \\ -9 & x\end{array}\right]\), then the value of \(x\) is:

Read the passage carefully and answer the Questions
A homogeneous mixture of two or more than two components has uniform composition and properties. The binary solutions have two components, which may be solid, liquid or gas. The resultant solution has a larger amount of solvent and a smaller amount of solute. The amount of solute in a given amount of solvent decides the concentration of the resulting solution. The concentration can be expressed in various ways, like molarity, molality, normality and mole fraction. The molality of a 1 liter aqueous solution of \(93 \backslash \% H _2 SO _4\) (mass/volume) is:
(Given: density of the solution \(=1.84 g mL ^{-1}\), molar mass of \(\left.H _2 SO _4=98 g mol ^{-1}\right)\)