In the chemical reactions
Question: In the chemical reactions Fluorobenzene and phenolBenzene diazonium chloride and benzonitrileNitrobenzene and chlorobenzenePhenol and bromobenzeneCorrect Option: , 2 Solution: Solution not required...
Read More →The sum of the co-efficients of all odd degree terms in the expansion of
Question: The sum of the co-efficients of all odd degree terms in the expansion of $\left(x+\sqrt{x^{3}-1}\right)^{5}+$ $\left(x-\sqrt{x^{3}-1}\right)^{5},(x1)$ is-0125Correct Option: , 3 Solution:...
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Question: Let $f: R \rightarrow R$ be defined by $f(x)=\left\{\begin{array}{lll}k-2 x, \text { if } x \leq-1 \\ 2 x+3, \text { if } x-1\end{array}\right.$ If $\mathrm{f}$ has a local minimum at $x=-1$, then a possible value of $\mathrm{k}$ is : 10$-\frac{1}{2}$$-1$Correct Option: , 4 Solution:...
Read More →In the chemical reactions,
Question: In the chemical reactions, the compounds 'A' and 'B' respectively are :-Nitrobenzene and chlorobenzeneNitrobenzene and fluorobenzenePhenol and benzeneBenzene diazonium chloride and fluorobenzeneCorrect Option: 4, Solution: Solution not required...
Read More →The value of
Question: The value of $\left({ }^{21} C_{1}-{ }^{10} C_{1}\right)+\left({ }^{21} C_{2}-{ }^{10} C_{2}\right)+$ $\left({ }^{21} \mathrm{C}_{3}-{ }^{10} \mathrm{C}_{3}\right)+\left({ }^{21} \mathrm{C}_{4}-{ }^{10} \mathrm{C}_{4}\right)+\ldots .+$ $\left({ }^{21} \mathrm{C}_{10}-{ }^{10} \mathrm{C}_{10}\right)$ is :-$2^{20}-2^{10}$$2^{21}-2^{11}$$2^{21}-2^{10}$$2^{20}-2^{9}$Correct Option: 1 Solution:...
Read More →The shortest distance between the line
Question: The shortest distance between the line $\mathrm{y}-\mathrm{x}=1$ and the curve $\mathrm{x}=\mathrm{y}^{2}$ is :- $\frac{3 \sqrt{2}}{5}$$\frac{\sqrt{3}}{4}$$\frac{3 \sqrt{2}}{8}$$\frac{2 \sqrt{3}}{8}$Correct Option: , 3 Solution:...
Read More →The value of
Question: The value of $$ \begin{aligned} \left({ }^{21} \mathrm{C}_{1}-{ }^{10} \mathrm{C}_{1}\right)+\left({ }^{21} \mathrm{C}_{2}-{ }^{10} \mathrm{C}_{2}\right)+ \\ \left({ }^{21} \mathrm{C}_{3}-{ }^{10} \mathrm{C}_{3}\right)+\left({ }^{21} \mathrm{C}_{4}-{ }^{10} \mathrm{C}_{4}\right)+\ldots .+ \\ \left({ }^{21} \mathrm{C}_{10}-{ }^{10} \mathrm{C}_{10}\right) \text { is :- } \end{aligned} $$$2^{20}-2^{10}$$2^{21}-2^{11}$$2^{21}-2^{10}$$2^{20}-2^{9}$Correct Option: 1 Solution:...
Read More →A liquid was mixed with ethanol and a drop of concentrated
Question: A liquid was mixed with ethanol and a drop of concentrated $\mathrm{H}_{2} \mathrm{SO}_{4}$ was added. A compound with a fruity smell was formed. The liquid was :-$\mathrm{CH}_{3} \mathrm{COCH}_{3}$$\mathrm{CH}_{3} \mathrm{COOH}$$\mathrm{CH}_{3} \mathrm{OH}$$\mathrm{HCHO}$Correct Option: , 2 Solution: Solution not required...
Read More →Solve this following
Question: Given $\mathrm{P}(\mathrm{x})=\mathrm{x}^{4}+\mathrm{ax}^{3}+b \mathrm{x}^{2}+\mathrm{cx}+\mathrm{d}$ such that $\mathrm{x}=0$ is the only real root of $\mathrm{P}^{\prime}(\mathrm{x})=0$. If $\mathrm{P}(-1)\mathrm{P}(1)$, then in the interval $[-1,1]$ :-$P(-1)$ is the minimum but $P(1)$ is not the maximum of $P$.Neither $\mathrm{P}(-1)$ is the minimum nor $\mathrm{P}(1)$ is the maximum of $\mathrm{P}$$\mathrm{P}(-1)$ is the minimum and $\mathrm{P}(1)$ is the maximum of $\mathrm{P}$$P(...
Read More →If the number of terms in the expansion of
Question: If the number of terms in the expansion of $\left(1-\frac{2}{x}+\frac{4}{x^{2}}\right)^{n}, x \neq 0$, is 28 , then the sum of the coefficients of all the terms in this expansion, is :-729642187243Correct Option: 1 Solution:...
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Question: If $f$ and $g$ are differentiable functions in $[0,1]$ satisfying $f(0)=2=g(1), g(0)=0$ and $f(1)=6$, then for some $c \in] 0,1[:$ $2 f^{\prime}(c)=g^{\prime}(c)$$2 f^{\prime}(c)=3 g^{\prime}(c)$$f^{\prime}(c)=g^{\prime}(c)$$f^{\prime}(c)=2 g^{\prime}(c)$Correct Option: , 4 Solution:...
Read More →The sum of coefficients of integral powers of x in the binomial expansion of
Question: The sum of coefficients of integral powers of $x$ in the binomial expansion of $(1-2 \sqrt{x})^{50}$ is :$\frac{1}{2}\left(3^{50}-1\right)$ $\frac{1}{2}\left(2^{50}+1\right)$$\frac{1}{2}\left(3^{50}+1\right)$$\frac{1}{2}\left(3^{50}\right)$Correct Option: , 3 Solution:...
Read More →Solve this following
Question: Let $f: R \rightarrow R$ be a continuous function defined by $f(x)=\frac{1}{e^{x}+2 e^{-x}}$ Statement-1 : $\mathrm{f}(\mathrm{c})=\frac{1}{3}$, for some $\mathrm{c} \in \mathrm{R}$ Statement-2 : $0\mathrm{f}(\mathrm{x}) \leq \frac{1}{2 \sqrt{2}}$, for all $\mathrm{x} \in \mathrm{R}$ Statement-1 is true, Statement- 2 is true ; Statement $-2$ is a correct explanation for Statement-1.Statement-1 is true, Statement $-2$ is true ; Statement $-2$ is not a correct explanation for statement-1...
Read More →If the coefficients of
Question: If the coefficients of $x^{3}$ and $x^{4}$ in the expansion of $\left(1+a x+b x^{2}\right)(1-2 x)^{18}$ in powers of $x$ are both zero, then $(\mathrm{a}, \mathrm{b})$ is equal to :-$\left(16, \frac{251}{3}\right)$$\left(14, \frac{251}{3}\right)$$\left(14, \frac{272}{3}\right)$$\left(16, \frac{272}{3}\right)$Correct Option: , 4 Solution:...
Read More →Solve this following
Question: If the curves $\mathrm{y}^{2}=6 \mathrm{x}, 9 \mathrm{x}^{2}+\mathrm{by}^{2}=16$ intersect each other at right angles, then the value of $b$ is :$\frac{7}{2}$4$\frac{9}{2}$6Correct Option: , 3 Solution:...
Read More →The term independent of x in expansion of
Question: The term independent of $x$ in expansion of $\left(\frac{x+1}{x^{2 / 3}-x^{1 / 3}+1}-\frac{x-1}{x-x^{1 / 2}}\right)^{10}$ is :4120210310Correct Option: , 3 Solution:...
Read More →If n is a positive integer, then
Question: If $\mathrm{n}$ is a positive integer, then $(\sqrt{3}+1)^{2 \mathrm{n}}-(\sqrt{3}-1)^{2 \mathrm{n}}$ is :a rational number other than positive integersan irrational numberan odd positive integeran even positive integerCorrect Option: , 2 Solution:...
Read More →The coefficient of
Question: The coefficient of $x^{7}$ in the expansion of $\left(1-x-x^{2}+x^{3}\right)^{6}$ is :- 144132144 132Correct Option: 1 Solution:...
Read More →The number of stereoisomers possible for a compound
Question: The number of stereoisomers possible for a compound of the molecular formula $\mathrm{CH}_{3}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}(\mathrm{OH})-\mathrm{Me}$ is :-4632Correct Option: 1 Solution: Solution not required...
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Question: Consider $f(x)=\tan ^{-1}\left(\sqrt{\frac{1+\sin x}{1-\sin x}}\right), x \in\left(0, \frac{\pi}{2}\right)$. A normal to $y=f(x)$ at $x=\frac{\pi}{6}$ also passes through the point :$\left(\frac{\pi}{4}, 0\right)$$(0,0)$$\left(0, \frac{2 \pi}{3}\right)$$\left(\frac{\pi}{6}, 0\right)$Correct Option: 3, Solution:...
Read More →Solve the following
Question: Let $S_{1}=\sum_{j=1}^{10} j(j-1)^{10} C_{j}, S_{2}=\sum_{j=1}^{10} j^{10} C_{j}$ and $S_{3}=\sum_{j=1}^{10} j^{210} C_{j}$ Statement-1: $\mathrm{S}_{3}=55 \times 2^{9}$. Statement-2 : $S_{1}=90 \times 2^{8}$ and $S_{2}=10 \times 2^{8}$.(1) Statement1 is true, Statement2 is true ; Statement2 is a correct explanation for Statement1.Statement1 is true, Statement2 is true ; Statement2 is not a correct explanation for Statement1.Statement1 is true, Statement2 is false.Statement1 is false, ...
Read More →The normal to the curve
Question: The normal to the curve, $x^{2}+2 x y-3 y^{2}=0$, at $(1,1)$ :meets the curve again in the third quadrantmeets the curve again in the fourth quadrantdoes not meet the curve againmeets the curve again in the second quadrantCorrect Option: , 2 Solution:...
Read More →The remainder left out when
Question: The remainder left out when $8^{2 \mathrm{n}}-(62)^{2 \mathrm{n}+1}$ is divided by 9 is :-7802Correct Option: Solution:...
Read More →Solve this following
Question: The intercepts on $x$-axis made by tangents to the curve, $y=\int_{0}^{x}|t| d t, x \in R$, which are parallel to the line $\mathrm{y}=2 \mathrm{x}$, are equal to $\pm 1$$\pm 2$$\pm 3$$\pm 4$Correct Option: 1 Solution:...
Read More →The equation of the tangent to the curve
Question: The equation of the tangent to the curve $y=x+\frac{4}{x^{2}}$, that is parallel to the $x$-axis, is :- $y=0$$y=1$$y=2$$y=3$Correct Option: , 4 Solution:...
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