The number of children in 10 families of a locality are
Question: The number of children in 10 families of a locality are2, 4, 3, 4, 2, 0, 3, 5, 1, 6.Find the mean number of children per family. Solution: Numbers of children in 10 families = 2, 4, 3, 4, 2, 0, 3, 5, 1 and 6.Thus, we have: Mean $=\frac{\text { Sum of observa tions }}{\text { Number of observations }}$ $=\frac{2+4+3+4+2+0+3+5+1+6}{10}$ $=\frac{30}{10}$ $=3$...
Read More →A circle touches the y-axis at the point
Question: A circle touches the $y$-axis at the point $(0,4)$ and passes through the point $(2,0)$. Which of the following lines is not a tangent to this circle?(1) $4 x-3 y+17=0$(2) $3 x-4 y-24=0$(3) $3 x+4 y-6=0$(4) $4 x+3 y-8=0$Correct Option: , 4 Solution: Equation of family of circle $(x-0)^{2}+(y-4)^{2}+\lambda x=0$ Passes through the point $(2,0)$ then $4+16+2 \lambda=0 \Rightarrow \lambda=-10$ Hence, the equation of circle $x^{2}+y^{2}-10 x-8 y+16=0$ $\Rightarrow(x-5)^{2}+(y-4)^{2}=25$ Ce...
Read More →Find the mean of:
Question: Find the mean of:(i) the first eight natural numbers(ii) the first ten odd numbers(iii) the first seven multiples of 5(iv) all the factors of 20(v) all prime numbers between 50 and 80. Solution: We know: Mean $=\frac{\text { Sum of observa tions }}{\text { Number of observations }}$ (i) The first eight natural numbers are 1, 2, 3, 4, 5, 6, 7 and 8.Mean of these numbers: $\frac{1+2+3+4+5+6+7+8}{8}$ $=\frac{36}{8}$ $=4.5$ (ii) The first ten odd numbers are 1, 3, 5, 7, 9, 11, 13, 15, 17 a...
Read More →The structure of Neoprene is :
Question: The structure of Neoprene is :Correct Option: Solution: neoprene...
Read More →If a line, y=m x+c is a tangent to the circle,
Question: If a line, $y=m x+c$ is a tangent to the circle, $(x-3)^{2}+y^{2}=1$ and it is perpendicular to a line $L_{1}$, where $L_{1}$ is the tangent to the circle, $x^{2}+y^{2}=1$ at the point $\left(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$; then:(1) $c^{2}-7 c+6=0$(2) $c^{2}+7 c+6=0$(3) $c^{2}+6 c+7=0$(4) $c^{2}-6 c+7=0$Correct Option: , 3 Solution: Slope of tangent of $x^{2}+y^{2}=1$ at $\left(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$ $\frac{1}{\sqrt{2}} x+\frac{1}{\sqrt{2}} y-1=0...
Read More →Let the tangents drawn from the origin to the circle,
Question: Let the tangents drawn from the origin to the circle, $x^{2}+y^{2}-8 x-4 y+16=0$ touch it at the points $A$ and $B$. The $(A B)^{2}$ is equal to:(1) $\frac{52}{5}$(2) $\frac{56}{5}$(3) $\frac{64}{5}$(4) $\frac{32}{5}$Correct Option: , 3 Solution: $L=\sqrt{S_{1}}=\sqrt{16}=4$ $R=\sqrt{16+4-16}=2$ Length of chord of contact $=\frac{2 L R}{\sqrt{L^{2}+R^{2}}}=\frac{2 \times 4 \times 2}{\sqrt{16+4}}=\frac{16}{\sqrt{20}}$ quare of length of chord of contact $=\frac{64}{5}$...
Read More →Which of the following vitamin is helpful in delaying the blood clotting ?
Question: Which of the following vitamin is helpful in delaying the blood clotting ?Vitamin BVitamin CVitamin KVitamin ECorrect Option: , 3 Solution: Vitamin $\mathrm{K}$ is used by the body to help blood clot....
Read More →Which of the following is correct structure of $lpha$-anomer of maltose :
Question: Which of the following is correct structure of $\alpha$-anomer of maltose :Correct Option: , 4 Solution:...
Read More →If the length of the chord of the circle,
Question: If the length of the chord of the circle, $x^{2}+y^{2}=r^{2}(r0)$ along the line, $y-2 x=3$ is $r$, then $r^{2}$ is equal to:(1) $\frac{9}{5}$(2) 12(3) $\frac{24}{5}$(4) $\frac{12}{5}$Correct Option: , 2 Solution: In right $\triangle R S Q, \sin 60^{\circ}=\frac{R S}{r}$ $\Rightarrow R S=r \times \frac{\sqrt{3}}{2}=\frac{\sqrt{3} r}{2}$ Now equation of $P Q$ is $y-2 x-3=0$ $\therefore \frac{\sqrt{3} r}{2}=\frac{|0+0-3|}{\sqrt{5}}$ $\Rightarrow \frac{\sqrt{3} r}{2}=\frac{3}{\sqrt{5}} \R...
Read More →Let P Q be a diameter of the circle
Question: Let $P Q$ be a diameter of the circle $x^{2}+y^{2}=9$. If $\alpha$ and $\beta$ are the lengths of the perpendiculars from $P$ and $Q$ on the straight line, $x+y=2$ respectively, then the maximum value of $\alpha \beta$ is____________. Solution: Let $P(3 \cos \theta, 3 \sin \theta), Q(-3 \cos \theta,-3 \sin \theta)$ $\alpha=\left|\frac{3 \cos \theta+3 \sin \theta-2}{\sqrt{2}}\right|, \beta=\left|\frac{-3 \cos \theta-3 \sin \theta-2}{\sqrt{2}}\right|$ $\alpha \beta=\left|\frac{(3 \cos \t...
Read More →Which of the glycosidic linkage galactose and glucose is present in lactose?
Question: Which of the glycosidic linkage galactose and glucose is present in lactose?$C-1$ of glucose and $C-6$ of galactose$\mathrm{C}-1$ of galactose and $\mathrm{C}-4$ of glucose$C-1$ of glucose and $C-4$ of galactose$C-1$ of galactose and $C-6$ of glucoseCorrect Option: , 2 Solution:...
Read More →Draw a histogram for the following data.
Question: Draw a histogram for the following data. Using this histogram, draw the frequency polygon on the same graph. Solution: We represent the class intervals along thex-axis and the corresponding frequencies along they-axis.We construct rectangles with class intervals as bases and respective frequencies as heights.We have the scale as follows:On thex-axis:1 big division = 40 unitsOn they-axis:1 big division = 20 unitsThus, we obtain the histogram, as shown below:We join the midpoints of the ...
Read More →A parallel plate capacitor has plate of length ' l ', width ' w ' and separation of plates is ' d '.
Question: A parallel plate capacitor has plate of length ' $l$ ', width ' $w$ ' and separation of plates is ' $d$ '. It is connected to a battery of emf V. A dielectric slab of the same thickness ' $d$ ' and of dielectric constant $k=4$ is being inserved between the plates of the capacitor. At what length of the slab inside plates, will the energy stored in the capacitor be two times the initial energy stored?(1) $2 l / 3$(2) $l / 3$(3) $l / 4$(4) $l / 2$Correct Option: Solution: (2) Capacitance...
Read More →The circle passing through the intersection of the circles,
Question: The circle passing through the intersection of the circles, $x^{2}+y^{2}-6 x=0$ and $x^{2}+y^{2}-4 y=0$, having its centre on the line, $2 x-3 y+12=0$, also passes through the point:(1) $(-1,3)$(2) $(-3,6)$(3) $(-3,1)$(4) $(1,-3)$Correct Option: , 2 Solution: We know family of circle be $S_{1}+\lambda S_{2}=0$ $x^{2}+y^{2}-6 x+\lambda\left(x^{2}+y^{2}-4 y\right)=0$ $\Rightarrow(1+\lambda) x^{2}+(1+\lambda) y^{2}-6 x-4 \lambda y=0$....(1) Centre $(-g,-f)=\left(\frac{3}{1+\lambda}, \frac...
Read More →Draw a histogram and the frequency polygon from the following data.
Question: Draw a histogram and the frequency polygon from the following data. Solution: We represent the class intervals along thex-axis and the corresponding frequencies along they-axis.We construct rectangles with class intervals as bases and respective frequencies as heights.We have the scale as follows:On thex-axis, 1 big division = 5 units.On they-axis, 1 big division = 5 units.Because the scale on thex-axis starts at 15, a kink, i.e., a break, is indicated near the origin to signify that t...
Read More →Which statement is correct?
Question: Which statement is correct?Buna-S is a synthetic and linear thermosetting polymerNeoprene is addition copolymer used in plastic bucket manufacturingSynthesis of Buna-S needs nascent oxygenBuna- $N$ is a natural polymerCorrect Option: , 3 Solution: Synthesis of Buna-S needs nascent oxygen....
Read More →The ages (in years) of 360 patients treated in a hospital on a particular day are given below.
Question: The ages (in years) of 360 patients treated in a hospital on a particular day are given below. Draw a histogram and a frequency polygon on the same graph to represent the above data. Solution: We represent the class intervals along thex-axis and the corresponding frequencies along they-axis.We construct rectangles with class intervals as bases and respective frequencies as heights.We have the scale as follows:On thex-axis:1 big division = 10 yearsOn they-axis:1 big division = 2 patient...
Read More →In polymer Buna-S; 'S' stands for :
Question: In polymer Buna-S; 'S' stands for :StyreneSulphurStrengthSulphonationCorrect Option: 1 Solution: Buna-S is the co-polymer of buta- 1,3 diene \ styrene....
Read More →Let the latus ractum of the parabola
Question: Let the latus ractum of the parabola $y=4 x$ be the common chord to the circles $C_{1}$ and $C_{2}$ each of them having radius $2 \sqrt{5}$. Then, the distance between the centres of the circles $C_{1}$ and $C_{2}$ is :(1) $8 \sqrt{5}$(2) 8(3) 12(4) $4 \sqrt{5}$Correct Option: , 2 Solution: Distance between the centres $=C_{1} C_{2}=2 C_{1} S=2 \sqrt{20-4}=8$...
Read More →Match List I with List II.
Question: Match List I with List II. Choose the correct answer from the options given below : $(\mathrm{a}) \rightarrow(i i i),(\mathrm{b}) \rightarrow(i v),(\mathrm{c}) \rightarrow(i),(\mathrm{d}) \rightarrow(i i)$(a) $\rightarrow$ (i), (b) $\rightarrow$ (ii), (c) $\rightarrow$ (iii), (d) $\rightarrow$ (iv)(a) $\rightarrow$ (ii), (b) $\rightarrow$ (i), (c) $\rightarrow$ (iv), (d) $\rightarrow$ (iii)$(\mathrm{a}) \rightarrow(\mathrm{iv}),(\mathrm{b}) \rightarrow(\mathrm{iii}),(\mathrm{c}) \right...
Read More →Draw a frequency polygon for the following frequency distribution.
Question: Draw a frequency polygon for the following frequency distribution. Solution: Though the given frequency table is in inclusive form, class marks in case of inclusive and exclusive forms are the same.We take the imagined classes (-9)0 at the beginning and 6170 at the end, each with frequency zero.Thus, we have: Along thex-axis, we mark 4.5, 5.5, 15.5, 25.5, 35.5, 45.5, 55.5 and 65.5.Along they-axis, we mark 0, 8, 3, 6, 12, 2, 7 and 0.We have chosen the scale as follows :On thex-axis, 1 b...
Read More →In the circuit shown, charge on the $5 mu mathrm{F}$ capacitor is :
Question: In the circuit shown, charge on the $5 \mu \mathrm{F}$ capacitor is : (1) $18.00 \mu \mathrm{C}$(2) $10.90 \mu \mathrm{C}$(3) $16.36 \mu \mathrm{C}$(4) $5.45 \mu \mathrm{C}$Correct Option: 1 Solution: Let $q_{1}$ and $q_{2}$ be the charge on the capacitors of $2 \mu \mathrm{F}$ and $4 \mu \mathrm{F}$. Then charge on capacitor of $5 \mu \mathrm{F}$ $Q=q_{1}+q_{2}$ $\Rightarrow 5 V_{0}=2\left(6-V_{0}\right)+4\left(6-V_{0}\right)$ $\Rightarrow 5 V_{0}=12-2 V_{0}+24-4 V_{0}$ $\Rightarrow 1...
Read More →The diameter of the circle,
Question: The diameter of the circle, whose centre lies on the line $x+y=2$ in the first quadrant and which touches both the lines $x=3$ and $y=2$, is_______. Solution: $\Rightarrow$ Radius $\left(r_{1}\right)=3-k$ $\because$ Centre lies on $x+y=2$ Let $x=k$ $\therefore y=2-k$ $\Rightarrow$ Centre $=(k, 2-k)$ Also, radius $\left(r_{2}\right)=2-(2-k)$ $\therefore 3-k=2-(2-k)$ $\Rightarrow k=\frac{3}{2}$ $r=3-\frac{3}{2}=\frac{3}{2}$ Hence, diameter $=3$....
Read More →Out of the following, which type of interaction is responsible for the stabilisation
Question: Out of the following, which type of interaction is responsible for the stabilisation $\alpha$-helix structure of proteins?Ionic bondingHydrogen bondingvander Waals forcesCovalent bondingCorrect Option: , 2 Solution: The $\alpha$-helix is stabilized by hydrogen bond between the NH and CO group of the main chain....
Read More →Deficiency of vitamin 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...
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