How many terms of the AP 3, 7, 11, 15, ...
Question: How many terms of the AP 3, 7, 11, 15, ... will make the sum 406?(a) 10(b) 12(c) 14(d) 20 Solution: (c) 14 Here,a= 3 andd= (7-3) = 4Let the sum ofnterms be 406.Then,we have: $S n=\frac{n}{2}[2 a+(n-1) d]=406$ $\Rightarrow \quad \frac{n}{2}[2 \times 3+(n-1) \times 4]=406$ $\Rightarrow n[3+2 n-2]=406$ $\quad \Rightarrow 2 n^{2}+n-406=0$ $\Rightarrow 2 n^{2}-28 n+29 n-406=0$ $\Rightarrow 2 n(n-14)+29(n-14)=0$ $\Rightarrow(2 n+29)(n-14)=0$ $\Rightarrow n=14 \quad(\because n$ can 't be a fr...
Read More →Most suitable salt which can be used for efficient clotting of blood will be :
Question: Most suitable salt which can be used for efficient clotting of blood will be :$\mathrm{Mg}\left(\mathrm{HCO}_{3}\right)_{2}$$\mathrm{FeSO}_{4}$$\mathrm{NaHCO}_{3}$$\mathrm{FeCl}_{3}$Correct Option: , 4 Solution: Blood is a negative sol. According to hardy-Schulz's rule, the cation with high charge has high coagulation power. Hence, $\mathrm{FeCl}_{3}$ can be used for clotting blood....
Read More →Show that A (−3, 2), B (−5, −5), C (2,−3), and
Question: Show thatA(3, 2),B(5, 5),C(2,3), andD(4, 4) are the vertices of a rhombus. Solution: Let A (3, 2); B (5,5); C (2,3) and D (4, 4) be the vertices of a quadrilateral. We have to prove that the quadrilateral ABCD is a rhombus. So we should find the lengths of sides of quadrilateral ABCD. $\mathrm{AB}=\sqrt{(-5+3)^{2}+(-5-2)^{2}}$ $=\sqrt{4+49}$ $=\sqrt{53}$ $B C=\sqrt{(2+5)^{2}+(-3+5)^{2}}$ $=\sqrt{4+49}$ $=\sqrt{53}$ $\mathrm{CD}=\sqrt{(4-2)^{2}+(4+3)^{2}}$ $=\sqrt{4+49}$ $=\sqrt{53}$ $\...
Read More →The sum of first 16 terms of the AP 10, 6, 2, ..., is
Question: The sum of first 16 terms of the AP 10, 6, 2, ..., is(a) 320(b) 320(c) 352(d) 400 Solution: (b) - 320Here,a= 10,d= (6 - 10) = -4 andn = 16 Using the formula, $S_{n}=\frac{n}{2}[2 a+(n-1) d]$, we get: $S_{16}=\frac{16}{2}[2 \times 10+(16-1) \times(-4)] \quad[\because a=10, d=-4$ and $n=16]$ $=8 \times[20-60]=8 \times(-40)=-320$ Hence, the sum of the first 16 terms of the given AP is -320....
Read More →In Freundlich adsorption isotherm,
Question: In Freundlich adsorption isotherm, slope of $\mathrm{AB}$ line is $\frac{1}{n}$ with $\left(\frac{1}{n}=0\right.$ to 1$)$$\log \frac{1}{n}$ with $(n1)$$\log n$ with $(n1)$$\mathrm{n}$ with $(\mathrm{n}, 0.1$ to $0.5)$Correct Option: 1 Solution: Freundlich adsorption isotherm is : $\frac{x}{m}=k p^{1 / n}$ $x=$ mass of adsorbate $\mathrm{m}=$ mass of adsorbent $\mathrm{P}=$ eq. pressure $\mathrm{k}_{1} \mathrm{n}=\frac{1}{\mathrm{n}} \log \mathrm{p}+\log \mathrm{k}$ $y=m x+c$ compairing...
Read More →Solve this
Question: $(5+13+21+\ldots+181)=?$ (a) 2476(b) 2337(c) 2219(d) 2139 Solution: (d) 2139 Here,a= 5,d= (13-5) = 8 andl= 181Let the number of terms ben.ThenTn= 181⇒a+ (n-1)d= 181⇒ 5 + ( n-1)⨯ 8 = 181⇒8n =184⇒ n=23 $\therefore$ Required sum $=\frac{n}{2}(a+l)$ $=\frac{23}{2}(5+181)=23 \times 93=2139$ Hence, the required sum is 2139....
Read More →ABCD is a rectangle formed by joining the points A (−1, −1), B(−1 4) C (5 4) and D (5, −1).
Question: ABCDis a rectangle formed by joining the pointsA(1, 1),B(1 4)C(5 4) andD(5, 1).P,Q,RandSare the mid-points of sidesAB,BC,CDandDArespectively. Is the quadrilateralPQRSa square? a rectangle? or a rhombus? Justify your answer. Solution: We have a rectangle ABCD formed by joining the points A (1,1); B (1, 4); C (5, 4) and D (5,1). The mid-points of the sides AB, BC, CD and DA are P, Q, R, S respectively. We have to find that whether PQRS is a square, rectangle or rhombus. In general to fin...
Read More →A hard substance melts at high temperature and is an insulator in both solid and in molten state.
Question: A hard substance melts at high temperature and is an insulator in both solid and in molten state. This solid is most likely to be a / an :Ionic solidMolecular solidMetallic solidCovalent solidCorrect Option: , 4 Solution: Whalent or network solid have very high melting point and they are insulators in their solid and molten form....
Read More →Choose the correct answer in each of the following questions:
Question: Choose the correct answer in each of the following questions:What is 20th term from the end of the AP 3, 8, 13, ..., 253? (a) 163 (b) 158 (c) 153 (d) 148 Solution: The given AP is 3, 8, 13, ..., 253.Let us re-write the given AP in reverse order i.e. 253, 248, ..., 13, 8, 3.Now, the 20th term from the end of the given AP is equal to the 20th term from beginning of the AP 253, 248, ..., 13, 8, 3.Consider the AP 253, 248, ..., 13, 8, 3.Here,a= 253 andd= 248 253 = 5 20th term of this AP= 2...
Read More →The charges on the colloidal
Question: The charges on the colloidal $\mathrm{CdS}$ sol and $\mathrm{TiO}_{2}$ sol are, respectively:positive and positivepositive and negativenegative and negativenegative and positiveCorrect Option: , 4 Solution: CdS sol $\rightarrow-$ ve sol $\mathrm{TiO}_{2} \mathrm{sol} \rightarrow+$ vesol...
Read More →Which term of the AP 21, 42, 63, 84, ... is 210?
Question: Which term of the AP 21, 42, 63, 84, ... is 210?(a) 9th(b) 10th(c) 11th(d) 12th Solution: (b) 10thHere,a= 21 andd= (42 - 21) = 21Let 210be thenthterm of the given AP.Then Tn= 210⇒a+(n - 1)d= 210⇒ 21 + (n - 1)⨯ 21= 210⇒ 21n= 210⇒n= 10Hence, 210 is the 10thterm of the AP....
Read More →Choose the correct answer in each of the following questions:
Question: Choose the correct answer in each of the following questions:Which term of the AP 25, 20, 15, ... is the first negative term? (a) 10th (b) 9th (c) 8th (d) 7 th Solution: The given AP is 25, 20, 15, ... .Here,a= 25 andd= 20 25 = 5Let thenthterm of the given AP be the first negative term. Then, $a_{n}0$ $\Rightarrow 25+(n-1) \times(-5)0 \quad\left[a_{n}=a+(n-1) d\right]$ $\Rightarrow 30-5 n0$ $\Rightarrow-5 n-30$ $\Rightarrow n\frac{30}{5}=6$ $\therefore n=7$ Thus, the 7th term is the fi...
Read More →For the coagulation of a negative sol,
Question: For the coagulation of a negative sol, the species below, that has the highest flocculating power is:$\mathrm{SO}_{4}^{2-}$$\mathrm{Ba}^{2+}$$\mathrm{Na}^{+}$$\mathrm{PO}_{4}^{3-}$Correct Option: , 2 Solution: To coagulate negative sol, cation with higher charge has higher coagulation value....
Read More →With respect to drug-enzyme interaction,
Question: With respect to drug-enzyme interaction, identify the wrong statement:Non-Competitive inhibitor binds to the allosteric siteAllosteric inhibitor changes the enzyme's active siteAllosteric inhibitor competes with the enzyme's active siteCompetitive inhibitor binds to the enzyme's active siteCorrect Option: , 3 Solution: Some durg do not bind to the Enzyme's active site. These bind to a different site of enzyme which called allosteric site. This binding of inhibitor at allosteric site ch...
Read More →Find the ratio in which the point P(−1, y) lying on the line segment
Question: Find the ratio in which the point P(1,y) lying on the line segment joining A(3, 10) and B(6 8) divides it. Also find the value ofy. [CBSE 2013] Solution: Suppose P(1,y) divides theline segment joining A(3, 10) and B(6 8) in the ratiok: 1.Using section formula, we get Coordinates of $\mathrm{P}=\left(\frac{6 k-3}{k+1}, \frac{-8 k+10}{k+1}\right)$ $\therefore\left(\frac{6 k-3}{k+1}, \frac{-8 k+10}{k+1}\right)=(-1, y)$ $\Rightarrow \frac{6 k-3}{k+1}=-1$ and $y=\frac{-8 k+10}{k+1}$ Now, $\...
Read More →Choose the correct answer in each of the following questions:
Question: Choose the correct answer in each of the following questions:Which term of the AP 72, 63, 54, ... is 0? (a) 8th (b) 9 th (c) 10 th (d) 11 th Solution: The given AP is 72, 63, 54, ... .Here,a= 72 andd= 63 72 =9Supposenthterm of the given AP is 0. Then, $a_{n}=0$ $\Rightarrow 72+(n-1) \times(-9)=0 \quad\left[a_{n}=a+(n-1) d\right]$ $\Rightarrow-9 n+81=0$ $\Rightarrow n=\frac{81}{9}=9$ Thus, the 9th term of the given AP is 0.Hence, the correct answer is option B....
Read More →Choose the correct answer in each of the following questions:
Question: Choose the correct answer in each of the following questions: If $a_{n}$ denotes the $n$th term of the AP $3,8,13,18, \ldots$ then what is the value of $\left(a_{30}-a_{20}\right) ?$ (a) 40 (b) 36 (c) 50 (d) 56 Solution: The given AP is 3, 8, 13, 18, ... .Here,a= 3 andd= 8 3 = 5 $\therefore a_{30}-a_{20}$ $=[3+(30-1) \times 5]-[3+(20-1) \times 5] \quad\left[a_{n}=a+(n-1) d\right]$ $=148-98$ $=50$ Thus, the required value is 50.Hence, the correct answer is option C....
Read More →A point P divides the line segment joining the points
Question: A point $P$ divides the line segment joining the points $A(3,-5)$ and $B(-4,8)$ such that $\frac{A P}{P B}=\frac{k}{1}$. If $P$ lies on the line $x+y=0$, then find the value of k Solution: It is given that $\frac{\mathrm{AP}}{\mathrm{PB}}=\frac{k}{1}$. So, P divides the line segment joining the points A(3, 5) and B(4, 8) in the ratiok: 1.Using the section formula, we get Coordinates of $\mathrm{P}=\left(\frac{-4 k+3}{k+1}, \frac{8 k-5}{k+1}\right)$ Since P lies on the linex+y= 0, so $\...
Read More →Choose the correct answer in each of the following questions:
Question: Choose the correct answer in each of the following questions: What is the common difference of an AP in which $a_{18}-a_{14}=32 ?$ (a) 8 (b) $-8$ (c) 4 (d) $-4$ Solution: Letabe the first term anddbe the common difference of the AP. Then, $a_{18}-a_{14}=32$ $\Rightarrow(a+17 d)-(a+13 d)=32 \quad\left[a_{n}=a+(n-1) d\right]$ $\Rightarrow 4 d=32$ $\Rightarrow d=8$ Thus, the common difference of the AP is 8.Hence, the correct answer is option is A....
Read More →The INCORRECT statements below regarding colloidal solutions is:
Question: The INCORRECT statements below regarding colloidal solutions is:A colloidal solution shows colligative properties.An ordinary filter paper can stop the flow of colloidal particles.The flocculating power of $\mathrm{Al}^{3+}$ is more than that of $\mathrm{Na}^{+}$A colloidal solution shows Brownian motion of colloidal particles.Correct Option: , 2 Solution: * Colloidel solution exhibits colligative properties * An ordinary filter can not stop the flow of colloidal particles. * Flocculat...
Read More →A (4, 2), B(6, 5) and C (1, 4) are the vertices of ΔABC.
Question: A(4, 2),B(6, 5) andC(1, 4) are the vertices of ΔABC.(i) The median fromAmeetsBCinD.Find the coordinates of the pointD.(ii) Find the coordinates of pointPandADsuch thatAP:PD= 2 : 1.(iii) Find the coordinates of the pointsQandRon mediansBEandCFrespectively such thatBQ:QE= 2 : 1 andCR:RF= 2 : 1(iv) What do you observe? Solution: We have triangle $\triangle \mathrm{ABC}$ in which the co-ordinates of the vertices are $\mathrm{A}(4,2) ; \mathrm{B}(6,5)$ and $\mathrm{C}(1,4)$ (i)It is given t...
Read More →Choose the correct answer in each of the following questions:
Question: Choose the correct answer in each of the following questions:How many three-digit numbers are divisible by 9? (a) 86 (b) 90 (c) 96 (d) 100 Solution: The three-digit numbers divisible by 9 are 108, 117, 126, ..., 999.Clearly, these numbers are in AP.Here,a= 108 andd= 117 108 = 9Let this AP containsnterms. Then, $a_{n}=999$ $\Rightarrow 108+(n-1) \times 9=999 \quad\left[a_{n}=a+(n-1) d\right]$ $\Rightarrow 9 n+99=999$ $\Rightarrow 9 n=999-99=900$ $\Rightarrow n=100$ Thus, there are 100 t...
Read More →Choose the correct answer in each of the following questions:
Question: Choose the correct answer in each of the following questions:How many two-digit numbers are divisible by 3? (a) 25 (b) 30 (c) 32 (d) 36 Solution: The two-digit numbers divisible by 3 are 12, 15, 18, ..., 99.Clearly, these number are in AP.Here,a= 12 andd= 15 12 = 3Let this AP containsnterms. Then, $a_{n}=99$ $\Rightarrow 12+(n-1) \times 3=99 \quad\left[a_{n}=a+(n-1) d\right]$ $\Rightarrow 3 n+9=99$ $\Rightarrow 3 n=99-9=90$ $\Rightarrow n=30$ Thus, there are 30 two-digit numbers divisi...
Read More →A mixture of gases
Question: A mixture of gases $\mathrm{O}_{2}, \mathrm{H}_{2}$ and $\mathrm{CO}$ are taken in a closed vessel containing charcoal. The graph that represents the correct behaviour of pressure with time is:Correct Option: , 2 Solution: Initially, adsorption of gases at the surface of charcoal occurs rapidly which results in a sudden decrease in pressure. As the number of vacant sites at the surface of adsorbent decreases with the passage of time, rate of adsorption decreases. Therefore, pressure te...
Read More →Find the coordinates of the points which divide the line
Question: Find the coordinates of the points which divide the line segment joining A(2, 2) and B (2, 8) into four equal parts. Solution: The co-ordinates of the midpoint $\left(x_{n}, y_{n}\right)$ between two points $\left(x_{1}, y_{1}\right)$ and $\left(x_{2}, y_{2}\right)$ is given by, $\left(x_{m}, y_{m}\right)=\left(\left(\frac{x_{1}+x_{2}}{2}\right),\left(\frac{y_{1}+y_{2}}{2}\right)\right)$ Here we are supposed to find the points which divide the line joiningA(2,2) andB(2,8) into 4 equal ...
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