number of values of k, for which the system
Question: The number of values of $k$, for which the system of equations : $(k+1) x+8 y=4 k$ $\mathrm{kx}+(\mathrm{k}+3) \mathrm{y}=3 \mathrm{k}-1$ has no solution, is -infinite123Correct Option: 2, Solution:...
Read More →Which of the following is the wrong statement?
Question: Which of the following is the wrong statement?$\mathrm{ONCl}$ and $\mathrm{ONO}^{-}$are not isoelectronic$\mathrm{O}_{3}$ molecule is bentOzone is violet-black in solid stateOzone is diamagnetic gasCorrect Option: 1 Solution:...
Read More →Solve this following
Question: Let $\overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{b}}$ and $\overrightarrow{\mathrm{c}}$ be three unit vectors such that $\overrightarrow{\mathrm{a}} \times(\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{c}})=\frac{\sqrt{3}}{2}(\overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{c}})$. If $\overrightarrow{\mathrm{b}}$ is not parallel to $\overrightarrow{\mathrm{c}}$, then the angle between $\vec{a}$ and $\vec{b}$ is :-$\frac{5 \pi}{6}$$\frac{3 \pi}{4}$$\frac{\pi}{2}...
Read More →The expression
Question: The expression $\frac{\tan \mathrm{A}}{1-\cot \mathrm{A}}+\frac{\cot \mathrm{A}}{1-\tan \mathrm{A}}$ can be written assinA cosA + 1secA cosecA + 1tanA + cotAsecA + cosecACorrect Option: , 2 Solution:...
Read More →If the trivial solution is the only solution of the
Question: If the trivial solution is the only solution of the system of equations $x-k y+z=0$ $k x+3 y-k z=0$ $3 x+y-z=0$ Then the set of all values of $k$ is:$\{2,-3\}$$\mathrm{R}-\{2,-3\}$$\mathrm{R}-\{2\}$$R-\{-3\}$Correct Option: , 2 Solution:...
Read More →A straight line through a fixed point (2, 3) intersects the coordinate axes at distinct points P and Q.
Question: A straight line through a fixed point (2, 3) intersects the coordinate axes at distinct points P and Q. If O is the origin and the rectangle OPRQ is completed, then the locus of R is :2x + 3y = xy3x + 2y = xy3x + 2y = 6xy3x + 2y = 6Correct Option: , 2 Solution:...
Read More →Which one of the following
Question: Which one of the following molecules is expected to exhibit diamagnetic behaviour ?$\mathrm{C}_{2}$$\mathrm{N}_{2}$$\mathrm{O}_{2}$$S_{2}$Correct Option: , 2 Solution:...
Read More →Which of the following compounds will
Question: Which of the following compounds will be suitable for Kjeldahl's method for nitrogen estimation ?Correct Option: 1 Solution: Kjeldahl's is suitable for Aniline. This method is used for quantitative analysis of N compound in organic substance $\left(\mathrm{NH}_{3} / \mathrm{NH}_{4}^{+}\right)$....
Read More →Solve the following
Question: In a $\triangle P Q R$, if $3 \sin P+4 \cos Q=6$ and $4 \sin Q+3 \cos P=1$, then the angle $R$ is equal to :$\frac{3 \pi}{4}$$\frac{5 \pi}{6}$$\frac{\pi}{6}$$\frac{\pi}{4}$Correct Option: , 3 Solution:...
Read More →Two sides of a rhombus are along the lines,
Question: Two sides of a rhombus are along the lines, x y + 1 = 0 and 7x y 5 = 0. If its diagonals intersect at (1, 2), then which one of the following is a vertex of this rhombus ?$\left(-\frac{10}{3},-\frac{7}{3}\right)$$(-3,-9)$$(-3,-8)$$\left(\frac{1}{3},-\frac{8}{3}\right)$Correct Option: , 4 Solution:...
Read More →The number of values of k for which
Question: The number of values of $k$ for which the linear equations $4 x+k y+2 z=0$ $k x+4 y+z=0$ $2 x+2 y+z=0$ possess a non-zero solution is :-1zero32Correct Option: , 4 Solution:...
Read More →In the presence of a small amount of phosphorous,
Question: In the presence of a small amount of phosphorous, aliphatic carboxylic acids react with chlorine or bromine to yield a compound in which- hydrogen has been replaced by halogen. This reaction is known as :Etard reactionHell - Volhard - Zelinsky reactionWolff - Kischner reactionRosenmund reactionCorrect Option: , 2 Solution: Solution not required...
Read More →Among the following
Question: Among the following chloro-compound having the lowest dipole moment is :-$\mathrm{CH}_{2} \mathrm{Cl}_{2}$$\mathrm{CH}_{3} \mathrm{Cl}$Correct Option: 1 Solution:...
Read More →Solve this following
Question: Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three non-zero vectors such that no two of them are collinear and $(\overrightarrow{\mathrm{a}}, \times \overrightarrow{\mathrm{b}}) \times \overrightarrow{\mathrm{c}}=\frac{1}{3}|\overrightarrow{\mathrm{b}}||\overrightarrow{\mathrm{c}}| \overrightarrow{\mathrm{a}}$. If $\theta$ is the angle between vectors $\overrightarrow{\mathrm{b}}$ and $\overrightarrow{\mathrm{c}}$, then a value of $\sin \theta$ is :$\frac{2}{3}$$\frac{-2 \sqrt{3}}{3}$$\frac...
Read More →Solve the following
Question: If $\mathrm{A}=\sin ^{2} \mathrm{x}+\cos ^{4} \mathrm{x}$, then for all real $\mathrm{x}:-$$1 \leq A \leq 2$$\frac{3}{4} \leq \mathrm{A} \leq \frac{13}{16}$$\frac{3}{4} \leq A \leq 1$$\frac{13}{16} \leq \mathrm{A} \leq 1$Correct Option: , 3 Solution:...
Read More →Locus of the image of the point (2, 3) in the line
Question: Locus of the image of the point (2, 3) in the line (2x 3y + 4) + k (x 2y + 3) = 0, k R, is acircle of radius $\sqrt{2}$circle of radius $\sqrt{3}$straight line parallel to $\mathrm{x}$-axisstraight line parallel to y-axisCorrect Option: 1 Solution: Slope of PS...
Read More →In the reaction
Question: In the reaction $\mathrm{CH}_{3} \mathrm{COOH} \underset{\mathrm{LiAlH}_{4}}{\longrightarrow} \mathrm{A} \stackrel{\mathrm{PCl}_{5}}{\longrightarrow} \mathrm{B} \stackrel{\text { aleKOH }}{\longrightarrow} \mathrm{C} \quad$ 'C' isEthyleneAcetyl chlorideAcetaldehydeAcetyleneCorrect Option: 1 Solution: Solution not required...
Read More →The formation of molecular
Question: The formation of molecular complex $\mathrm{BF}_{3}-\mathrm{NH}_{3}$ results in a change in hybridisation of boronfrom $s p^{3}$ to $s p^{3} d$from $s p^{2}$ to $d s p^{2}$from $s p^{3}$ to $s p^{2}$from $s p^{2}$ to $s p^{3}$Correct Option: , 4 Solution: $\mathrm{CH}_{2} \mathrm{Cl}_{2}$ has lowest dipole moment...
Read More →Consider the system of linear equations :
Question: Consider the system of linear equations : $x_{1}+2 x_{2}+x_{3}=3$ $2 x_{1}+3 x_{2}+x_{3}=3$ $3 x_{1}+5 x_{2}+2 x_{3}=1$ The system hasInfinite number of solutionsExactly 3 solutionsA unique solutionNo solutionCorrect Option: 4, Solution:...
Read More →Let PS be the median of the triangle with vertices P (2, 2), Q (6, –1) and R (7, 3).
Question: Let PS be the median of the triangle with vertices P (2, 2), Q (6, 1) and R (7, 3). The equation of the line passing through (1, 1) and parallel to PS is :4x 7y 11 = 02x + 9y + 7 = 04x + 7y + 3 = 02x 9y 11 = 0Correct Option: , 2 Solution:...
Read More →Among the following the molecule with the lowest dipole moment is :-
Question: Among the following the molecule with the lowest dipole moment is :-$\mathrm{CHCl}_{3}$$\mathrm{CH}_{2} \mathrm{Cl}_{2}$$\mathrm{CCl}_{4}$$\mathrm{CH}_{3} \mathrm{Cl}$Correct Option: , 3 Solution:...
Read More →Solve the following
Question: Let $\cos (\alpha+\beta)=\frac{4}{5}$ and let $\sin (\alpha-\beta)=\frac{5}{13}$, where $0 \leq \alpha, \beta \leq \frac{\pi}{4}$. Then $\tan 2 \alpha=$$\frac{25}{16}$$\frac{56}{33}$$\frac{19}{12}$$\frac{20}{7}$Correct Option: , 2 Solution:...
Read More →On heating an aliphatic primary amine with
Question: On heating an aliphatic primary amine with chloroform ethenolic potassium hydroside the organic compound formed isAn alkyl cyanideAn alkyl isocyanidean alkanolan alkanediolCorrect Option: , 2 Solution: Solution not required...
Read More →If the image of point P(2, 3) in a line L is Q (4, 5) then,
Question: If the image of point P(2, 3) in a line L is Q (4, 5) then, the image of point R (0, 0) in the same line is :(4, 5)(2, 2)(3, 4)(7, 7)Correct Option: , 3 Solution:...
Read More →Let a, b, c be such that
Question: Let $a, b, c$ be such that $b(a+c) \neq 0$. If $\left|\begin{array}{ccc}a a+1 a-1 \\ -b b+1 b-1 \\ c c-1 c+1\end{array}\right|+\left|\begin{array}{ccc}a+1 b+1 c-1 \\ a-1 b-1 c+1 \\ (-1)^{n+2} a (-1)^{n+1} b (-1)^{n} c\end{array}\right|=0$ then the value of $n$ is :-Any odd integerAny integerZeroAny even integerCorrect Option: 1 Solution:...
Read More →