Prove that in any triangle ABC,
Question: Prove that in any triangle ABC, , wherea,b,care the magnitudes of the sides opposite to the vertices A, B, C, respectively. Solution: In triangle ABC, the components of c are c cos A and c sin A....
Read More →Using vectors, prove that the parallelogram on the same
Question: Using vectors, prove that the parallelogram on the same base and between the same parallels are equal in area. Solution: Lets consider ABCD and ABFE be two parallelograms on the same base AB and between same parallel lines AB and DF....
Read More →Using vectors,
Question: Using vectors, find the area of the triangle ABC with vertices A(1, 2, 3), B(2, 1, 4) and C(4, 5, 1). Solution: Given vertices A(1, 2, 3), B(2, 1, 4) and C(4, 5, 1)....
Read More →Solve the following systems of equations:
Question: If $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$ are the points with position vectors $\hat{i}+\hat{j}-\hat{k}, 2 \hat{i}-\hat{j}+3 \hat{k}$, $2 \hat{i}-3 \hat{k}, 3 \hat{i}-2 \hat{j}+\hat{k}$, respectively, find the projection of $\overrightarrow{\mathrm{AB}}$ along $\overrightarrow{\mathrm{CD}}$. Solution: We have,...
Read More →Find the sine of the angle between the vectors
Question: Find the sine of the angle between the vectors $\vec{a}=3 \hat{i}+\hat{j}+2 \hat{k}$ and $\vec{b}=2 \hat{i}-2 \hat{j}+4 \hat{k}$ Solution:...
Read More →Prove the following
Question: If $\vec{a}+\vec{b}+\vec{c}=0$, show that $\vec{a} \times \vec{b}=\vec{b} \times \vec{c}=\vec{c} \times \vec{a}$. Interpret the result geometrically? Solution:...
Read More →Find the angle between the vectors
Question: Find the angle between the vectors $2 \hat{i}-\hat{j}+\hat{k}$ and $3 \hat{i}+4 \hat{j}-\hat{k}$ Solution:...
Read More →Which of the following compounds will behave as a reducing sugar in an aqueous
Question: Which of the following compounds will behave as a reducing sugar in an aqueous $\mathrm{KOH}$ solution $?$Correct Option: 1 Solution:...
Read More →Find the angle between the vectors
Question: Find the angle between the vectors $2 \hat{i}-\hat{j}+\hat{k}$ and $3 \hat{i}+4 \hat{j}-\hat{k}$ Solution:...
Read More →Observation of "Rhumann's purple" is a confirmatory test for the presence of:
Question: Observation of "Rhumann's purple" is a confirmatory test for the presence of:StarchReducing sugarCupric ionProteinCorrect Option: 1 Solution: Solution not required...
Read More →Find a vector of magnitude 6 ,
Question: Find a vector of magnitude 6 , which is perpendicular to both the vectors $2 \hat{i}-\hat{j}+2 \hat{k}$ and $4 \hat{i}-\hat{j}+3 \hat{k}$ Solution:...
Read More →Prove the following
Question: A vectorhas magnitude 14 and direction ratios 2, 3, 6. Find the direction cosines and components of, given thatmakes an acute angle withx-axis. Solution:...
Read More →Consider the following sequence for aspartic acid:
Question: Consider the following sequence for aspartic acid: The pI (isoelectric point) of aspartic acid is :$1.88$$2.77$$3.65$$5.74$Correct Option: , 4 Solution: Solution not required...
Read More →Accumulation of which of the following molecules in the muscles occurs as a result of vigorous exercise :-
Question: Accumulation of which of the following molecules in the muscles occurs as a result of vigorous exercise :-Pyruvic acidL-lactic acidGlycogenGlucoseCorrect Option: , 2 Solution: Solution not required...
Read More →Complete hydrolysis of starch gives :
Question: Complete hydrolysis of starch gives : glucose and fructose in equimolar amountsglucose onlygalactose and fructose in equimolar amountsglucose and galactose in equimolar amountsCorrect Option: , 2 Solution: Starch is polymer of Glucose...
Read More →Which of the vitamins given below is water soluble?
Question: Which of the vitamins given below is water soluble?Vitamin EVitamin $\mathrm{K}$Vitamin $\mathrm{C}$Vitamin DCorrect Option: , 3 Solution:...
Read More →The most suitable reagent for the conversion of
Question: The most suitable reagent for the conversion of $\mathrm{R}-\mathrm{CH}_{2}-\mathrm{OH} \rightarrow \mathrm{R}-\mathrm{CHO}$ is :-$\mathrm{CrO}_{3}$PCC (Pyridinium chlorochromate)$\mathrm{KMNO}_{4}$$\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}$Correct Option: , 2 Solution: Solution not required...
Read More →Which one of the following bases is not present in DNA?
Question: Which one of the following bases is not present in DNA?CytosineThymineQuinolineAdenineCorrect Option: , 4 Solution: All cytosine, thymine and adenine are present in DNA. Only quinoline is not present in DNA....
Read More →Synthesis of each molecule of glucose in photosynthesis involves :-
Question: Synthesis of each molecule of glucose in photosynthesis involves :- 18 molecules of ATP10 molecules of ATP8 molecules of ATP6 molecules of ATPCorrect Option: 1, Solution:...
Read More →Which one of the following statements is correct?
Question: Which one of the following statements is correct?All amino acids except glutamic acid are optically activeAll amino acids except lysine are optically activeAll amino acids are optically activeAll amino acids except glycine are optically activeCorrect Option: , 4 Solution: Solution not required...
Read More →Which of the following will change the colour of acidic dichromate solution.
Question: Which of the following will change the colour of acidic dichromate solution.Correct Option: 1 Solution:...
Read More →The change in the optical rotation of freshly prepared solution of glucose is known as :-
Question: The change in the optical rotation of freshly prepared solution of glucose is known as :- tautomerismracemisationspecific rotationmutarotationCorrect Option: , 4 Solution: Solution not required...
Read More →The formation of which of the following polymers
Question: The formation of which of the following polymers involves hydrolysis reaction ?Nylon 6BakeliteNylon 6,6TeryleneCorrect Option: 1 Solution:...
Read More →