Deficiency of vitamin $mathrm{K}$ causes :
Question: Deficiency of vitamin $\mathrm{K}$ causes :Increase in blood clotting timeIncrease in fragility of $\mathrm{RBC}^{\prime}$ 'sCheilosisDecrease in blood clotting timeCorrect Option: 1 Solution: Due to deficiency of Vitmain $\mathrm{K}$ causes increases in blood clotting time. Note : Vitamin K related to blood factor...
Read More →The number of integral values of k for which
Question: The number of integral values of $k$ for which the line, $3 x+4 y=k$ intersects the circle, $x^{2}+y^{2}-2 x-4 y+4=0$ at two distinct points is_________. Solution: The given circle is $x^{2}+y^{2}-2 x-4 y+4=0$ $\therefore$ Centre of circle $(1,2), r=1$. If line cuts circle then $pr$, where $p=\left|\frac{a x_{1}+b y_{1}+c}{\sqrt{a^{2}+b^{2}}}\right|$ $\Rightarrow\left|\frac{3+8-k}{5}\right|1 \Rightarrow k \in(6,16)$ $k=7,8,9,10,11,12,13,14,15$...
Read More →Let A(1,4) and B(1,-5) be two points.
Question: Let $A(1,4)$ and $B(1,-5)$ be two points. Let $P$ be a point on the circle $(x-1)^{2}+(y-1)^{2}=1$ such that $(P A)^{2}+(P B)^{2}$ have maximum value, then the points, $\mathrm{P}, \mathrm{A}$ and $\mathrm{B}$ lie on :(1) a parabola(2) a straight line(3) a hyperbola(4) an ellipseCorrect Option: , 2 Solution: $\therefore \mathrm{PA}^{2}=\cos ^{2} \theta+(\sin \theta-3)^{2}=10-6 \sin \theta$ $\mathrm{PB}^{2}=\cos ^{2} \theta+(\sin \theta-6)^{2}=37-12 \sin \theta$ $\mathrm{PA}^{2}+\left.\...
Read More →Choose the most appropriate answer from the options given below:
Question: Choose the most appropriate answer from the options given below:$a-i i i, b-i i, c-i v, d-i$$a-i v, b-i i i, c-i i, d-i$$a-i v, b-i i i, c-i, d-i i$$a-i v, b-i i, c-i i i, d-i$Correct Option: , 2 Solution: Chlorophyll is a coordination compound of magnesium. Vitamin B-12, cyanocobalamine is a coordination compound of cobalt. Cisplatin is used as an anti-cancer drug and is a coordination compound of platinum. Grubbs catalyst is a compound of Ruthenium....
Read More →Two capacitors of capacitances
Question: Two capacitors of capacitances $\mathrm{C}$ and $2 \mathrm{C}$ are charged to potential differences $\mathrm{V}$ and $2 \mathrm{~V}$, respectively. These are then connected in parallel in such a manner that the positive terminal of one is connected to the negative terminal of the other. The final energy of this configuration is :(1) $\frac{25}{6} \mathrm{CV}^{2}$(2) $\frac{3}{2} \mathrm{CV}^{2}$(3) zero(4) $\frac{9}{2} \mathrm{CV}^{2}$Correct Option: , 2 Solution: (b) When capacitors $...
Read More →Solve the following
Question: $\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}+\mathrm{H}_{2} \mathrm{O} \stackrel{\text { Eerme } \mathrm{A}}{\longrightarrow} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}+\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}$ Sucrose Glucose Fructose $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} \stackrel{\text { Engaae } \mathrm{B}}{\longrightarrow} 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}+2 \mathrm{CO}_{2}$ Glucose In the above reactions, the enzyme $A$ and enzyme $\mathrm{B}$ respe...
Read More →In a study of diabetic patients in a village, the following observations were noted.
Question: In a study of diabetic patients in a village, the following observations were noted. Represent the above data by a frequency polygon. Solution: We take two imagined classesone at the beginning (010) and other at the end (7080)each with frequency zero.With these two classes, we have the following frequency table: Now, we plot the following points on a graph paper:A(5, 0),B(15, 2),C(25, 5),D(35, 12), E(45, 19),F(55, 9),G(65, 4) andH(75, 0)Join these points with line segmentsAB, BC, CD, D...
Read More →In the circle given below,
Question: In the circle given below, let $O A=1$ unit, $O B=13$ unit and $P Q \perp O B$. Then, the area of the triangle PQB (in square units) is: (1) $26 \sqrt{3}$(2) $24 \sqrt{2}$(3) $24 \sqrt{3}$(4) $26 \sqrt{2}$Correct Option: , 3 Solution: $\mathrm{OC}=\frac{13}{2}=6.5$ $\mathrm{AC}=\mathrm{CO}-\mathrm{AO}$ $=6.5-1$ $=5.5$ In $\Delta \mathrm{PAC}$ $\mathrm{PA}=\sqrt{6.5^{2}-5.5^{2}}$ $P A=\sqrt{12}$ $\Rightarrow P_{Q}=2 P A=2 \sqrt{12}$ Now, area of $\Delta \mathrm{PQB}=\frac{1}{2} \times \...
Read More →Draw a histogram to represent the following information:
Question: Draw a histogram to represent the following information: Solution: Here the class intervals are of unequal size. So, we calculate the adjusted frequency using the formula, Adjusted freq $=\frac{\min \text { class size }}{\text { class size of this class }} \times$ freq Minimum class size = 5...
Read More →Fructose is an example of :-
Question: Fructose is an example of :-PyranoseKetohexoseAldohexoseHeptoseCorrect Option: , 2 Solution: Fructose is a ketohexose....
Read More →If the area of the triangle formed by the positive
Question: If the area of the triangle formed by the positive $x$-axis, the normal and the tangent to the circle $(x-2)^{2}+(y-3)^{2}=25$ at the point $(5,7)$ is $\mathrm{A}$, then $24 \mathrm{~A}$ is equal to Note: NTA has dropped this question in the final official answer key. Solution: Equation of normal at $\mathrm{P}$ $(y-7)=\left(\frac{7-3}{5-2}\right)(x-5)$ $3 y-21=4 x-20$ $\Rightarrow 4 x-3 y+1=0 \ldots(1)$ $\Rightarrow M\left(-\frac{1}{4}, 0\right)$ Equation of tangent at $\mathrm{P}$ $(...
Read More →Which of the following polymer is used in the manufacture of wood laminates?
Question: Which of the following polymer is used in the manufacture of wood laminates? cis -poly isopreneMelamine formaldehyde resinUrea formaldehyde resinPhenol and formaldehyde resinCorrect Option: , 3 Solution: Urea $-\mathrm{HCHO}$ resin is used in manufacture of wood laminates....
Read More →A capacitor C is fully charged with voltage
Question: A capacitor $C$ is fully charged with voltage $V_{0}$. After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance $\frac{C}{2}$. The energy loss in the process after the charge is distributed between the two capacitors is :(1) $\frac{1}{2} C V_{0}^{2}$(2) $\frac{1}{3} C V_{0}^{2}$(3) $\frac{1}{4} C V_{0}^{2}$(4) $\frac{1}{6} C V_{0}^{2}$Correct Option: , 4 Solution: (4) When two capacitors with capacitance $C_{1}$ and $C_{2}$ at ...
Read More →Draw a histogram to represent the following information:
Question: Draw a histogram to represent the following information: Solution: Here the class intervals are of unequal size. So, we calculate the adjusted frequency using the formula, Adjusted freq $=\frac{\min \text { class size }}{\text { class size of this class }} \times$ freq Class sizes are $10-5=5$ $15-10=5$ $25-15=10$ $45-25=20$ $75-45=30$ Minimum class size = 5...
Read More →If one of the diameters o of the circle
Question: If one of the diameters o of the circle $x^{2}+y^{2}-2 x-6 y+6=0$ is a chord of another circle ${ }^{\prime} C^{\prime}$ whose center is at $(2,1)$, then its radius is Solution: distance between $(1,3)$ and $(2,1)$ is $\sqrt{5}$ $\therefore(\sqrt{5})^{2}+(2)^{2}=r^{2}$ $\Rightarrow r=3$...
Read More →100 surnames were randomly picked up from a local telephone directory
Question: 100 surnames were randomly picked up from a local telephone directory and frequency distribution of the number of letters in the English alphabet in the surnames was found as follows: (i) Draw a histogram to depict the given information.(ii) Write the class interval in which the maximum number of surnames lie. Solution: (i) Here the class intervals are of unequal size. So, we calculate the adjusted frequency using the formula, Adjusted freq $=\frac{\min \text { class size }}{\text { cl...
Read More →The secondary structure of protein is stabilised by:
Question: The secondary structure of protein is stabilised by:Peptide bondglycosidic bondHydrogen bondingvan der Waals forcesCorrect Option: , 3 Solution: The secondary structure of protein includes two type : (a) $\alpha$-Helix (b) $\beta$-pleated sheet In $\alpha$-Helix structure, the poly peptide chain is coil around due to presence of Intramolecular H-Bonding....
Read More →In the circuit shown in the figure,
Question: In the circuit shown in the figure, the total charge is $750 \mu \mathrm{C}$ and the voltage across capacitor $C_{2}$ is $20 \mathrm{~V}$. Then the charge on capacitor $C_{2}$ is : (1) $450 \mu \mathrm{C}$(2) $590 \mu \mathrm{C}$(3) $160 \mu \mathrm{C}$(4) $650 \mu \mathrm{C}$Correct Option: 2, Solution: (2) According to question, $Q=750 \mu C=q_{2}+q_{3}$ Capacitors $C_{2}$ and $C_{3}$ are in parallel hence, Voltage across $C_{2}=$ voltage across $C_{3}=20 \mathrm{~V}$ Change on capac...
Read More →Which among the following pairs of Vitamins is stored in our body
Question: Which among the following pairs of Vitamins is stored in our body relatively for longer duration?Thiamine and Vitamin AVitamin A and Vitamin DThiamine and Ascorbic acidAscorbic acid and Vitamin DCorrect Option: , 2 Solution: Vitamin-A \ Vitamin-D...
Read More →Let S1
Question: Let $S_{1}: x^{2}+y^{2}=9$ and $S_{2}:(x-2)^{2}+y^{2}=1$ Then the locus of center of a variable circle $S$ which touches $S_{1}$ internally and $S_{2}$ externally always passes through the points: (1) $(0, \pm \sqrt{3})$(2) $\left(\frac{1}{2}, \pm \frac{\sqrt{5}}{2}\right)$(3) $\left(2, \pm \frac{3}{2}\right)$(4) $(1, \mathrm{a} 2)$Correct Option: 3, Solution: $\because \mathrm{c}_{1} \mathrm{c}_{2}=\mathrm{r}_{1}-\mathrm{r}_{2}$ $\therefore$ given circle are touching internally Let a ...
Read More →Draw a histogram to represent the following data.
Question: Draw a histogram to represent the following data. Solution: In the given frequency distribution, class sizes are different.So, we calculate the adjusted frequency for each class.The minimum class size is 4. Adjusted frequency of a class $=\frac{\text { Minimum class size }}{\text { Class size of the class }} \times$ Its frequency We have the following table: We mark the class intervals along thex-axis and the corresponding adjusted frequencies along they-axis.We have chosen the scale a...
Read More →The following table shows the number of illiterate persons in the age group (10−58 years) in. a town:
Question: The following table shows the number of illiterate persons in the age group (1058 years) in. a town: Draw a histogram to represent the above data. Solution: The given frequency distribution is inclusive form.So, we will convert it into exclusive form, as shown below: We will mark the age groups (in years) along thex-axis frequencies (number of illiterate persons) along they-axis.The scale is as follows:Onx-axis: 1 big division = 7 yearsOny-axis: 1 big division = 50 personsBecause the s...
Read More →Solve this
Question: A $10 \mu \mathrm{F}$ capacitor is fully charged to a potential difference of $50 \mathrm{~V}$. After removing the source voltage it is connected to an uncharged capacitor in parallel. Now the potential difference across them becomes $20 \mathrm{~V}$. The capacitance of the second capacitor is :(1) $15 \mu \mathrm{F}$(2) $30 \mu \mathrm{F}$(3) $20 \mu \mathrm{F}$(4) $10 \mu \mathrm{F}$Correct Option: 1 Solution: (1) Given, Capacitance of capacitor, $C_{1}=10 \mu \mathrm{F}$ Potential d...
Read More →For the four circles
Question: For the four circles $\mathrm{M}, \mathrm{N}, \mathrm{O}$ and $\mathrm{P}$, following four equations are given : Circle $M: x^{2}+y^{2}=1$ Circle $\mathrm{N}: \mathrm{x}^{2}+\mathrm{y}^{2}-2 \mathrm{x}=0$ Circle $\mathrm{O}: \mathrm{x}^{2}+\mathrm{y}^{2}-2 \mathrm{x}-2 \mathrm{y}+1=0$ Circle $P: x^{2}+y^{2}-2 y=0$ If the centre of circle $M$ is joined with centre of the circle $N$, further centre of circle $\mathrm{N}$ is joined with centre of the circle $\mathrm{O}$, centre of circle ...
Read More →Construct a histogram for the following frequency distribution.
Question: Construct a histogram for the following frequency distribution. Solution: The given frequency distribution is in inclusive form.So, we will convert it into exclusive form, as shown below: We will mark class intervals along thex-axis and frequencies along they-axis.The scale is as follows:Onx-axis: 1 big division = 8 unitsOny-axis: 1 big division = 2 unitsBecause the scale on thex-axis starts at 4.5, a kink, i.e., a break, is indicated near the origin to signify that the graph is drawn ...
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