JEE Main 2023 01 Feb Shift 2

79 Questions • 180 Minutes • 2023

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$\mathrm{O-O}$ bond length in $\mathrm{H_2O_2}$ is $\underline{\mathrm{X}}$ than the $\mathrm{O-O}$ bond length in $\mathrm{F_2O_2}$. The $\mathrm{O-H}$ bond length in $\mathrm{H_2O_2}$ is $\underline{Y}$ than that of the $\mathrm{O-F}$ bond in $\mathrm{F_2O_2}$. Choose the correct option for $\underline{\mathrm{X}}$ and $\underline{\mathrm{Y}}$ from the given below.

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The starting material for convenient preparation of deuterated hydrogen peroxide $(\mathrm{D_2O_2})$ in laboratory is:

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Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). **Assertion (A):** Gypsum is used for making fireproof wall boards. **Reason (R):** Gypsum is unstable at high temperatures. In the light of the above statements, choose the most appropriate answer from the options given below:

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The correct order of bond enthalpy $(\mathrm{kJ\ \ mol^{-1}})$ is:

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Given below are two statements: Statement I: Sulphanilic acid gives esterification test for carboxyl group. Statement II: Sulphanilic acid gives red colour in Lassigne’s test for extra element detection. In the light of the above statements, choose the most appropriate answer from the options given below:

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The industrial activity held least responsible for global warming is :

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The graph which represents the following reaction is: $\mathrm{(C_6H_5)_3C-Cl \xrightarrow[Pyridine]{OH^-} (C_6H_5)_3C-OH}$

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Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : $\mathrm{Cu^{2+}}$ in water is more stable than $\mathrm{Cu^{+}}$. Reason (R) : Enthalpy of hydration for $\mathrm{Cu^{2+}}$ is much less than that of $\mathrm{Cu^{+}}$. In the light of the above statements, choose the correct answer from the options given below :

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Which element is not present in Nessler’s reagent?

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The complex cation which has two isomers is:

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All structures given below are of vitamin $\mathrm{C}$. Most stable of them is:

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Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). **Assertion (A):** $\alpha$-halocarboxylic acid on reaction with dil. $\mathrm{NH_3}$ gives good yield of $\alpha$-amino carboxylic acid whereas the yield of amines is very low when prepared from alkyl halides. **Reason (R):** Amino acids exist in zwitter ion form in aqueous medium. In the light of the above statements, choose the correct answer from the options given below :

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The number of integral values of $k$, for which one root of the equation $2x^2-8x+k=0$ lies in the interval $(1,2)$ and its other root lies in the interval $(2,3)$, is :

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Let $a, b$ be two real numbers such that $ab<0$. If the complex number $\frac{1+ai}{b+i}$ is of unit modulus and $a+ib$ lies on the circle $|z-1|=|2z|$, then a possible value of $\frac{1+[a]}{4b}$, where $[t]$ is greatest integer function, is :

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The sum $\sum_{n=1}^{\infty}\frac{2n^2+3n+4}{(2n)!}$ is equal to :

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Let $P(x_0, y_0)$ be the point on the hyperbola $3x^2-4y^2=36$, which is nearest to the line $3x+2y=1$. Then $\sqrt{2}(y_0-x_0)$ is equal to :

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Which of the following statements is a tautology?

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Let $9 = \mathrm{x_1} < \mathrm{x_2} < ... < \mathrm{x_7}$ be in an A.P. with common difference $d$. If the standard deviation of $x_1, x_2 ..., x_7$ is 4 and the mean is $\overline{x}$, then $\overline{x}+x_6$ is equal to :

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Let $P(\mathrm{S})$ denote the power set of $S=\{1,2,3, . . ., 10\}$. Define the relations $R_1$ and $R_2$ on $P(\mathrm{S})$ as $AR_1B$ if $(A \cap B^c) \cup (B \cap A^c)=\phi$ and $AR_2\ B$ if $A \cup B^c=B \cup A^c, \forall A, B \in P(S)$ . Then :

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If $A=\frac{1}{2}\begin{bmatrix}1 & \sqrt{3}\\ -\sqrt{3} & 1\end{bmatrix}$ then,

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Paper Info

Exam: JEE
Year: 2023
Questions: 79
Duration: 180 mins

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