Saved Bookmarks
This section includes 7 InterviewSolutions, each offering curated multiple-choice questions to sharpen your Current Affairs knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
HUMAN GENOME PROJECT AND ITS GOALS |
| Answer» Main goal of human genome project is to generate detailed maps of the human genome. These maps are used in determining the location of genes within the human genome. HGP is also used for mapping and sequencing of genome. | |
| 2. |
Give the names and functions of enzymes involved in lactose metabolism in E. Coli: |
|
Answer» Enzymes involved in lactose metabolism in E.coli and their function. 1. Galactoside `rarr` transports lactose into the cell across the cell membrane 2. `beta`-galactosidase `rarr` Hydrolyzes lactoses to glucose and galactose 3. Thiogalactoside `rarr` Its role is not clear till transacetylase now. |
|
| 3. |
Which of the following is polymide ?A. TeflonB. Nylon 6,6C. TeryleneD. Bakelite |
| Answer» Nylon 6,6 is a semicrystalline polymide. It is formed by the combination of monomers hexamethylene diammine and adiopic acid. Terylene is a polyster, Teflon is a synthetic polymer while bakelite is a plastic | |
| 4. |
My father told the tenants to leave Who lived in the houses surrounding our house on the hill One by one the structures were demolished Only our own house remained and the trees Trees are sacred my grandmother used to say Felling them is a crime , but he massacred them all The sheoga , the oudumber ,the neem were all cut down But the huge banyan tree stood like a problem Whose roots lay deeper than all our lives My father ordered it to be removed. Pick out the words from the extract suggesting destruction . |
| Answer» Demolished , massacred ,cut down ,removed. | |
| 5. |
My father told the tenants to leave Who lived in the houses surrounding our house on the hill One by one the structures were demolished Only our own house remained and the trees Trees are sacred my grandmother used to say Felling them is a crime , but he massacred them all The sheoga , the oudumber ,the neem were all cut down But the huge banyan tree stood like a problem Whose roots lay deeper than all our lives My father ordered it to be removed. Name and explain the figure of speech in the following line : But the huge banyan tree stood like a problem ." |
| Answer» (iii) The figure of speech used here is a simile ,as the huge banyan tree is being compared to a big problem , making the description more vivid. | |
| 6. |
My father told the tenants to leave Who lived in the houses surrounding our house on the hill One by one the structures were demolished Only our own house remained and the trees Trees are sacred my grandmother used to say Felling them is a crime , but he massacred them all The sheoga , the oudumber ,the neem were all cut down But the huge banyan tree stood like a problem Whose roots lay deeper than all our lives My father ordered it to be removed. How are trees helpful to mankind ? |
| Answer» (ii) Trees are helpful to mankind as they provide man with food and shelter . Many trees have medicinal value . We can imagine a world without human beings but we cannot imagine a world without trees. | |
| 7. |
The Cartesian equationof a line are `3x+1=6y=2=1-z`. Find the direction ratios and write down its equation in vector form. |
|
Answer» The Cartesian equation of the line is `3x+1=6y-2=1-z` `rArr" "3(x+(1)/(3))=6(y-(1)/(3))=-(z-1)` `rArr" "(x+1//3)/(1//3)=(y-1//3)/(1//6)=(z-1)/(-1)` `therefore ` The line is passing through the point `A(-1//3. 1//3,1)` and having direction 1/3, 1/6. -1, i.e., 2, 1, -6. Let `veca` be the position through the point A w. r. t. the origin and `vecb` be the vector parallel to the line `therefore veca = -1//3 hati + 1//3 hatj +hatk and vecb = 2hati + hatj - 6 hatk` `therefore ` The vector form of the equation of the line is `vecr = vec a + lambda vecb` `vecr = (-1//3 hati + 1//3 hatj + hatk) + lambda ( 2hati + hatj- 6hatk)` |
|
| 8. |
Parametric form of the equation of the plane is `bar r =(2hati + hatk ) + lambda hati + mu (hati + 2hati-3 hatk) lambda and mu` are parameters. Find normal to the plane and hence equation of the plane in normal form. Write its Cartesion form. |
|
Answer» Equation of the plane is `bar r = ( 2hati + hatk)+ lambda hati + mu ( hati + 2hatj-3hatk)" …(i)"` Comparing equation (i) With `bar r = bara + lambda barb+ mu barc` `veca=2(hati +hatk), vecb=hati, vec c= hati + 2hatj - 3hatk` `therefore ` Normal to the plane is `vecb xx vecc = |(hati, hatj, hatk),(1,0,0),(1,2,-3)|` `=hati (0-0)- hatj(-3-0)+hatk(2-0)` `3hatj+ 2hatk` Now, `bara. (barb xx barc) = (2hati + hatk). (3 hatj+ 2hatk)` `=0+0+2=2` `therefore` Equation of the plane in normal form is `vec r . (vecb xx vecc)= veca .(vecb xx vecc)` `vecr. (3hatj+2hatk)=2" ...(ii)"` If `vec r = xhati + yhatj+ zhatk`, then the equation becomes, `(x hati+y hatj+ zhatk) . (3hatj+2hatk)=2` `rArr" "x(0)+y(3)+z(2)=2` `rArr" "3y+2x=2` This is the Cartesian form of the equation of given plane. |
|
| 9. |
Find the area of the region bounded by the curve ` y = sinx `, the lines ` x = - ( pi ) /(2), x = ( pi ) /(2) ` and X- axis. |
|
Answer» Required Area `=int_(-pi//2)^(pi//2)y.dx,` where `y=sinx` `=int_(-pi//2)^(pi//2)sinx dx` `=2int_(0)^(pi//2)sinx.dx" (Using property)"` `=2[-cosx]_(0)^(pi//2)` `=2[-cos pi//2+cos0]` `=2[0+1]="2 sq. units."` |
|
| 10. |
`sinxtanx-1=tanx-sinx` |
|
Answer» `sinx. Tanx = tanx-sinx+1` `rArr sinx. Tanx-tanx+sinx-1=0` `rArr tan x(sinx-1)+1(sinx-1)=0` `rArr (sinx-1)(tanx+1)=0` `rArr sin x-1=0 or tan x+1=0` `rArr sin x= 1 " or "tanx=-1` `rArr sin x=sin.(pi)/(2)" or "tanx=-tan.(pi)/(4)` `rArr sin x=sin.(pi)/(2)" or "tanx=tan(pi-(pi)/(4))` `rArr sin x=sin.(pi)/(2)" or "tanx=tan.(3pi)/(4)` `therefore" "alpha_(1)=(pi)/(2)" or "alpha_(2)=(3pi)/(4)` `therefore" "` The general solution are `theta = npi +(-1)^(n).(pi)/(2)` |
|
| 11. |
What is the value of `DeltaS_(surr) ` for the following reaction at 298 K- ` 6CO_(2(g))+ 6 H_(2)O _(1) to C_(6)H_(12)O_(6(s))+6O_(2(g))` Given tahat : ` DeltaG^(@) = 2879 kj "mol"^(-1)` `DeltaS = -210 JK^(-1)"mol"^(-1)` |
|
Answer» Given : `6CO_(2(g))+6H_(2)O_(1) to C_(6)H_(12)O_(6(s)) + 6O_(2(g))` ` DeltaG^(@) = 2879 "KJ mol"^(-1)`, T =298 K `DeltaH^(@) = ?` ` Delta G^(@) = DeltaH - T DeltaS` ` :. DeltaH = DeltaG^(@) - TDeltaS` ` = 2879 + 298 (-0*210)` ` = 2879 - 62*58` ` = 2816*42 "KJ mol"^(-1)` Since `DeltaH gt 0` the reaction is endothermic , and system absorbs heat from surroundings . Hence , system loses heat, ` :. Delta H_("surr") = - 2816*42 "KJ mol"^(-1)` ` :. Delta S _("surr") = (DeltaH_("surr"))/T = (-2816*42)/298 = -9*45 "KJK"^(-1)` ` Delta S_("surr") = - 9*45 "KJK^(-1)` Hence , the value of `DeltaS_("surr")` for the given reaction is ` - 9.45 "KJK"^(-1)` |
|
| 12. |
The differential equation of the family of curves ` y= c_(1)e^(x) +c_(2)e^(-x)` isA. `(d^(2)y)/(dx^(2))+y=0`B. `(d^(2)y)/(dx^(2))-y=0`C. `(d^(2)y)/(dx^(2))+1=0`D. `(d^(2)y)/(dx^(2))-1=0` |
|
Answer» Correct Answer - B `y=c_(1)e^(x)+c_(2)e^(-x)" …(i)"` Differentiating w.r.t. x, we get `(dy)/(dx)=c_(1)e^(x)-c_(2)e^(-x)" …(ii)"` Again differentiating w.r.t. x, we get `(d^(2)y)/(dx^(2))=c_(1)e^(x)-c_(2)e^(-x)" ...(iii)"` `rArr" "(d^(2)y)/(dx^(2))=y" [Using (i)]"` `rArr" "(d^(2)y)/(dx^(2))-y=0` |
|
| 13. |
The primary `CO_(2)` acceptor molecule during the ` C_(3)` cycle is a |
| Answer» The first `CO_(2)` acceptor in `C_(3)` pathway is Ribulose biphosphate. | |
| 14. |
I celebrate the virtues and vices of suburban middle - class people who overwhelm the refrigerator and position colourful umbrellas near the garden that longs for a pool : for my middle class brother this principle of supreme luxury : what are you and what am I , and we go ondeciding the real truth in this world. Why ,according to you ,do the middle - class people, long for items of luxury ? |
| Answer» The middle class people long for luxury items because they believe that upreme luxury determines the value of each person . | |
| 15. |
I celebrate the virtues and vices of suburban middle - class people who overwhelm the refrigerator and position colourful umbrellas near the garden that longs for a pool : for my middle class brother this principle of supreme luxury : what are you and what am I , and we go ondeciding the real truth in this world. Pick out an example of Anithesis from the extract. |
| Answer» Example of " Antithesis" : I celebrate the Virtues and Vices . | |
| 16. |
Organic farming is the form of agriculture that relies on ecological processes , biodiversity and cycles adapted to local conditions . Organic farmers ensure soil fertility with the help of crop rotation ,compost and other biologically induced soil amendments . A healthy soil structure increases its bility to hold water and the plants become beeter quipped to resist diseases and insects and there is no need to depend on synthetic fertilizers ,synthetic pesticides ,plant growth regulators ,livestock feed additives and genetically modified organisms ,all of which are extremely harmful to the plants as well as human beings who consume them. According to the International Federation of Organic Agriculture Movements , Origanic agriculture combines tradition ,innovation and science to benefit the shared enviroment and promote fair relationship and a good quality of life for all involved ..... " In India ,the Green Revolution ,which was water intensive and involved a heavy dose of chemical fertilizers , has not been a boon. Many farmers have seen the effects of chemical farming- soil erosion and loss of soil nutrients ,loss of nutrition in food ,and human diseases resulting from the chemicals that seep into the water table. But organic farming is often hard for the farmers who have to invest considerable time ,energy and resource to regenerate the soil and re - establish the delicate balance between soil ,water ,air ,animals and plants. Further ,the lack of support in maintaining such a balance makes the produts more expensive ,putting the burden on the consumers who choose to eat healthy. How is organic farming advantageous to farmers ? |
| Answer» Organic farming is advantageous to farms in many ways .It ensures soil fertility with the help of crop rotation and healthy soil structure increases the ability to hold water .Also ,plants develop resistance power to control insects and diseases. | |
| 17. |
Organic farming is the form of agriculture that relies on ecological processes , biodiversity and cycles adapted to local conditions . Organic farmers ensure soil fertility with the help of crop rotation ,compost and other biologically induced soil amendments . A healthy soil structure increases its bility to hold water and the plants become beeter quipped to resist diseases and insects and there is no need to depend on synthetic fertilizers ,synthetic pesticides ,plant growth regulators ,livestock feed additives and genetically modified organisms ,all of which are extremely harmful to the plants as well as human beings who consume them. According to the International Federation of Organic Agriculture Movements , Origanic agriculture combines tradition ,innovation and science to benefit the shared enviroment and promote fair relationship and a good quality of life for all involved ..... " In India ,the Green Revolution ,which was water intensive and involved a heavy dose of chemical fertilizers , has not been a boon. Many farmers have seen the effects of chemical farming- soil erosion and loss of soil nutrients ,loss of nutrition in food ,and human diseases resulting from the chemicals that seep into the water table. But organic farming is often hard for the farmers who have to invest considerable time ,energy and resource to regenerate the soil and re - establish the delicate balance between soil ,water ,air ,animals and plants. Further ,the lack of support in maintaining such a balance makes the produts more expensive ,putting the burden on the consumers who choose to eat healthy. What does the first paragraph focus on ? |
| Answer» The first paragraph focuses on the advantages of organic farming. | |
| 18. |
Organic farming is the form of agriculture that relies on ecological processes , biodiversity and cycles adapted to local conditions . Organic farmers ensure soil fertility with the help of crop rotation ,compost and other biologically induced soil amendments . A healthy soil structure increases its bility to hold water and the plants become beeter quipped to resist diseases and insects and there is no need to depend on synthetic fertilizers ,synthetic pesticides ,plant growth regulators ,livestock feed additives and genetically modified organisms ,all of which are extremely harmful to the plants as well as human beings who consume them. According to the International Federation of Organic Agriculture Movements , Origanic agriculture combines tradition ,innovation and science to benefit the shared enviroment and promote fair relationship and a good quality of life for all involved ..... " In India ,the Green Revolution ,which was water intensive and involved a heavy dose of chemical fertilizers , has not been a boon. Many farmers have seen the effects of chemical farming- soil erosion and loss of soil nutrients ,loss of nutrition in food ,and human diseases resulting from the chemicals that seep into the water table. But organic farming is often hard for the farmers who have to invest considerable time ,energy and resource to regenerate the soil and re - establish the delicate balance between soil ,water ,air ,animals and plants. Further ,the lack of support in maintaining such a balance makes the produts more expensive ,putting the burden on the consumers who choose to eat healthy. Why was the Green Revolution not a boon for Indian farmers ? |
| Answer» The Green Revolution was not a boon for the Indian farmers because it was water - intensive and involved a heavy does of chemical fertilizers . Chimical farming resulted in soil erosion and loss of soil nutrients. | |
| 19. |
I celebrate the virtues and vices of suburban middle - class people who overwhelm the refrigerator and position colourful umbrellas near the garden that longs for a pool : for my middle class brother this principle of supreme luxury : what are you and what am I , and we go ondeciding the real truth in this world. How do the suburban middle -class people imitate the rich ? |
| Answer» The suburban middle class people try to imitate the rich by stocking the refrigerator fully with food and putting up colourful umbrellas near gardens . | |
| 20. |
Organic farming is the form of agriculture that relies on ecological processes , biodiversity and cycles adapted to local conditions . Organic farmers ensure soil fertility with the help of crop rotation ,compost and other biologically induced soil amendments . A healthy soil structure increases its bility to hold water and the plants become beeter quipped to resist diseases and insects and there is no need to depend on synthetic fertilizers ,synthetic pesticides ,plant growth regulators ,livestock feed additives and genetically modified organisms ,all of which are extremely harmful to the plants as well as human beings who consume them. According to the International Federation of Organic Agriculture Movements , Origanic agriculture combines tradition ,innovation and science to benefit the shared enviroment and promote fair relationship and a good quality of life for all involved ..... " In India ,the Green Revolution ,which was water intensive and involved a heavy dose of chemical fertilizers , has not been a boon. Many farmers have seen the effects of chemical farming- soil erosion and loss of soil nutrients ,loss of nutrition in food ,and human diseases resulting from the chemicals that seep into the water table. But organic farming is often hard for the farmers who have to invest considerable time ,energy and resource to regenerate the soil and re - establish the delicate balance between soil ,water ,air ,animals and plants. Further ,the lack of support in maintaining such a balance makes the produts more expensive ,putting the burden on the consumers who choose to eat healthy. What agricultural problems according to you ,do farmers face ? |
| Answer» Now - a- days ,farmers face a number of problems . Many times ,crops die from lack pf proper supply of water . Heavy labour charges make it difficult for farmers to perform agricultural activities . Farmers are unable to use organic or chemical fertilizers every time because they are too expensive to bear the cost. | |
| 21. |
Organic farming is the form of agriculture that relies on ecological processes , biodiversity and cycles adapted to local conditions . Organic farmers ensure soil fertility with the help of crop rotation ,compost and other biologically induced soil amendments . A healthy soil structure increases its bility to hold water and the plants become beeter quipped to resist diseases and insects and there is no need to depend on synthetic fertilizers ,synthetic pesticides ,plant growth regulators ,livestock feed additives and genetically modified organisms ,all of which are extremely harmful to the plants as well as human beings who consume them. According to the International Federation of Organic Agriculture Movements , Origanic agriculture combines tradition ,innovation and science to benefit the shared enviroment and promote fair relationship and a good quality of life for all involved ..... " In India ,the Green Revolution ,which was water intensive and involved a heavy dose of chemical fertilizers , has not been a boon. Many farmers have seen the effects of chemical farming- soil erosion and loss of soil nutrients ,loss of nutrition in food ,and human diseases resulting from the chemicals that seep into the water table. But organic farming is often hard for the farmers who have to invest considerable time ,energy and resource to regenerate the soil and re - establish the delicate balance between soil ,water ,air ,animals and plants. Further ,the lack of support in maintaining such a balance makes the produts more expensive ,putting the burden on the consumers who choose to eat healthy. Find out the words from the extract which mean : (i) leak slowly. (ii) substance added to inprove something. |
|
Answer» (i) to seep into . (ii) additives . |
|
| 22. |
What is bioaccumulation ? |
| Answer» The accumulation of a substance such as toxic chemical, in various tissues of a living organism. | |
| 23. |
If `y=sin^(-1)(3x)+sec^(-1)((1)/(3x)),` find `(dy)/(dx)`. |
|
Answer» `t=sin^(-1)(3x)+sec^(-1)((1)/(3x))` `y=sin^(-1)(3x)+cos^(-1)(3x)(because sin^(-1).(1)/(x)=cos^(-1)x)` `y=(pi)/(2)" "(because sin^(-1)x+cos^(-1)x=pi//2)` Differentiating w.r.t. x, we get `(dy)/(dx)=0` |
|
| 24. |
If `sec((x+y)/(x-y))=a^(2),"then "(d^(2)y)/(dx^(2))=......`A. yB. xC. `(y)/(x)`D. 0 |
|
Answer» Correct Answer - C `sec((x+y)/(x-y))=a^(2)` `rArr" "(x+y)/(x-y)=sec^(-1)(a^(2))` Differentiating w.r.t. x, we get `(x-y)(1+(dy)/(dx))-(x+y)(1-(dy)/(dx))=0` `rArr" "x=y+(x-y)(dy)/(dx)-x-y+(x+y)(dy)/(dx)=0` `rArr (dy)/(dx)(x-y+x+y)=2y` `rArr (dy)/(dx)=(2y)/(2x)` `rArr (dy)/(dx)=(y)/(x)` |
|
| 25. |
Direction cosines of the line passing through the points `A(-4, 2, 3) and B(1, 3, -2)` areA. `pm(1)/(sqrt(51)),pm(5)/(sqrt(51)),pm(1)/(sqrt(51))`B. `pm(5)/(sqrt(51)),pm(1)/(sqrt(51)),pm(-5)/(sqrt(51))`C. `pm5,pm1,pm5`D. `pmsqrt(51)msqrt(51),pmsqrt(51)` |
|
Answer» Correct Answer - B Given, points are `A-=(-4,2,3) and B-=(1,3,-2)` `1-(-4),3-2,-2-3` i.e., `5,1,-5` `therefore" "` The direction cosines of AB are `=pm(5)/(sqrt(5^(2)+1^(2)+(-5)^(2))), pm(1)/(sqrt(5^(2)+1^(2)+(-5)^(2))),pm(-5)/(sqrt(5^(2)+1^(2)+(-5)^(2)))` `=pm(5)/(sqrt(51)),pm(1)/(sqrt(51)),pm(-5)/(sqrt(51))`. |
|
| 26. |
Given X ~ B(n,p) If n= 20,, E(x)= 10 , Find p, Car(X) and S.D (X) |
|
Answer» Given, `n = 20 and E(x)=10` `E(x)=np` `therefore" "np=10" …(i)"` `" "20p=10` `p=(1)/(2)` `therefore" "q=1-p=1-(1)/(2)=(1)/(2)` `therefore" Var(x) = npq = "20(1//2)(1)/(2)=5` and `" S.D. (x)"=sqrt("Var (x)")` =`sqrt5` `= 2.23` |
|
| 27. |
`int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx.` Hence evaluate : `int_(a)^(b)(f(x))/(f(x)+f(a+b-x))dx.` |
|
Answer» `intf(x)dx=int_(a)^(b)f(a+b-x)Dx` Since we know that the following properties, `int_(a)^(b)f(x)dx=-int_(b)^(a)f(x)dx" …(i)"` and `" "int_(a)^(b)f(x)=int_(a)^(b)f(t)dt" …(ii)"` Consider, `int_(a)^(b)f(x)dx` Putting `x=a+b - t." "(because t = a+b-x)` `rArr" "dx=-dt` When `x=a,` then `t=a+b-a=b` When `x=b`, then `t=a+b-b=a` `therefore int_(a)^(b)f(x)dx=int_(b)^(a)f(a+b-t)(-dt)` `=-int_(b)^(a)f(a+h-t)dt` `=int_(a)^(b)f(a+b-t)dt" [By equation (i)]"` `=int_(a)^(b)f(a+b-t)dx" [By equation (ii)]"` And now, `int_(a)^(b)(f(x))/(f(x)+f(a+b-x))dx` `"Let I"=int_(a)^(b)(f(x))/(f(x)+f(a+b-x))dx" ...(iii)"` And`" I"=int_(a)^(b)(f(a+b-x))/(f(a+b-x)+f(x))" ...(iv)"` Adding equations (i) and (ii), we get `2I=int_(a)^(b)(f(x)+f(a+b-x))/(f(x)+f(a+b-x))dx` `=int_(a)^(b)1.dx` `=[x]_(a)^(b)` `therefore" "2I=b-a` `therefore" "I=(b-a)/(2)` `therefore" "=int_(a)^(b)(f(x))/(f(x)+f(A+b-x))dx` `=(b-a)/(2)` |
|
| 28. |
Select and write the most appropriate answer from the given alternatives in each of the following : The inverse of the matrix `{:((2,0,0),(0,1,0),(0,0,-1)):}` isA. `[((1)/(2),0,0),(0,1,0),(0,0,-1)]`B. `[(-(1)/(2),0,0),(0,-1,0),(0,0,1)]`C. `[(-1,0,0),(0,-(1)/(2),0),(0,0,(1)/(2))]`D. `-(1)/(2)[(-(1)/(2),0,0),(0,-1,0),(0,0,-1)]` |
|
Answer» Correct Answer - A Let `A=[(2,2,0),(0,1,0),(0,0,-1)]` `therefore" "|A|=2(-1-0)-0+0=-2 ne 0` `therefore" "A^(-1)` exists. Consider`" "A A^(-1)=1` `therefore" "[(2,0,0),(0,1,0),(0,0,-1)]A^(-1)=[(1,0,0),(0,1,0),(0,0,1)]` Applying `R_(1) rarr (1)/(2)R_(1) and R_(3) rarr -R_(3)`, we get `[(1,0,0),(0,1,0),(0,0,1)]A^(-1)=[(1//2,0,0),(0,1,0),(0,0,-1)]` `A^(-1)[(1//2,0,0),(0,1,0),(0,0,-1)]` |
|
| 29. |
If `[vec a vecb vec c] ne 0 ` and `vecP=(vec b xx vec c)/([veca vecb vec c]), vecq=(vec c xx veca)/([veca vec b vec c]), vec r =(vec a xx vec b)/([veca vecb vec c ])`, then `veca. vecp+ vecb. vecq+ vec c.vecr` is equal to ………… |
|
Answer» Correct Answer - D Given `vecP=(vecbxxvecc)/([vecavecbvecc]),vecq=(veccxxveca)/([vecavecbvecc])and c=(vecaxxvecb)/([vecavecbvecc])` `therefore" "veca.vecp+vecb.vecq+vecc.vecr=veca.(vecbxxvecc)/([veca vecb vecc])+vecb.(vecc xx veca)/([veca vecb vecc])+vecc.(vecaxxvecb)/([veca vecb vecc])` `=([vecavecbvecc])/([vecavecbvecc])+([vecavecbvecc])/([vecavecbvecc])+([vecavecbvecc])/([vecavecbvecc])` `because veca.(vecbxxvecc)+vecb.(veccxxveca)+vecc.(vecaxxvecb)` `=[vecavecbvecc]` `=1+1+1=3` |
|
| 30. |
Evaluate : `intx log x dx` |
|
Answer» Let `I=int x log x dx` Integrating by parts, we get `=log x int x dx-int[(d)/(dx)(logx).intxdx]dx` `=logx.(x^(2))/(2)-int(1)/(x).(x^(2))/(2)dx` `=(1)/(2)x^(2).logx-(1)/(2)intx dx` `=(x^(2))/(2)log x-(x^(2))/(4)+c` |
|
| 31. |
Show that the function defined by `f(x) = | cos x |`is a continuous function. |
|
Answer» Let `g(x)=cos x` and `h(x)=|x|` be two functions defined on R. Then `" (hog) (x) = h (g (x))"` `" "=h(cosx)=|cosx|` `" "=f(x)," for all " x in R` g(x) = cos x, being a cosine function, is continuous on R. h(x) = cos x, being a modulus function, is continuous on R. `therefore" "f(x)=(hog)(x)`, being a composition of two continuous functions, is continuous on R. Hence, f(x) = |cos x | is continuous function. |
|
| 32. |
Examine the continuity of the following function at given point : `f(x)=(log x-log 8)/(x-8)", for "x ne 8` `"8 ,for "x=8` `"at , "x=8` |
|
Answer» Given `f(8)=8" …(i)"` `underset(xrarr8)(lim)f(x)=underset(xrarr8)(lim)(logx-log8)/(x-8)` Putting `x=8+h,` then `x-8=h` and as `xrarr8, hrarr0.` `therefore" "underset(xrarr8)(lim)f(x)=underset(hrarr0)(lim)(log(8+h)-log8)/(h)` `=underset(hrarr0)(lim)(log((8+h)/(8)))/(h)` `=underset(hrarr0)(lim)(log(1+(h)/(8)))/((h)/(8))xx(1)/(8)` `=(1)/(8)xx1(because underset(xrarr0)(lim)(log(1+x))/(x)=1)" ...(ii)"` From equation (i) and (ii), `underset(xrarr8)(lim)f(x) ne f(8)` `therefore" f is discontinuous at x = 8."` |
|
| 33. |
The probability that a certain kind of component will survive a check test is 0.5. Find the probability that exactly two of the next four components tested will survive. |
|
Answer» Let X = number of tested components survive. p = probability that the component survive the check test. `therefore" "p=0.5 =(5)/(10)=(1)/(2)` `therefore" "q=1-p=1-(1)/(2)=(1)/(2)` Given n = 4 `therefore X ~ B(4, 1//4)` The probability mass function as : `P(X=x)=.^(n)C_(x)p^(x).q^(n-x)` i.e., `p(x)=.^(4)C_(x)((1)/(2))^(2x)((1)/(2))^(4-x)` P(exactly 2 components survive) `=P(X=2)=p(2)` `=.^(4)C_(2)((1)/(2))^(2)((1)/(2))^(4-2)` `=(4!)/(2!.2!).((1)/(2))^(2).((1)/(2))^(2)` `=(4.3.2!)/(2.1.2!)xx((1)/(2))^(4)` `=(6)/(16)=0.375` Hence, the probabillity that exactly 2 of the 4 tested components survive is 0.375. |
|
| 34. |
`3e^(x) tan y dx + (1+e^(x)) sec^(2) dy =0 , " when" x = 0 and y = pi` |
|
Answer» `3e^(x) tan y dx+(1_e^(x))sec^(2)y dy=0` On separating the variables, we get `3e^(x)tany dx = -(1+e^(x))sec^(2)ydy` `(3e^(x))/(1+e^(x))dx=-(sec^(2)y)/(tany)dy` On integrating, we get `3int(e^(x))/(1+e^(x))dx=-int(sec^(2)y)/(tany)dy` Let `1+e^(x)=t rArr e^(x)dx=dt` and `tan y = v rArr sec^(2)y dy = dv` `rArr" "3int(1)/(t)dt=-int(1)/(v)dv` `rArr" "3log|t|=-log|v|+log|c|` `rArr" "log|t|^(3)+log|v|=log|c|` `rArr" "logt^(3).v=logc` `rArr" "(1+e^(x))^(3).tany=c` Which is the required general equation Now, when x = 0 and `y=pi`, we get `(1+e^(0))^(3).tanpi =c` `(2)^(3).0=c rArr c=0` Hence proved. |
|
| 35. |
Find the joint equation of the pair of the lines through the origin each of which is making an angle of `30^(@)` with the line `3x+2y-11=0`. |
|
Answer» The slope of the line `3x+2y-11=0` is `m_(1)=-(3)/(2)` Let m be the slope of the lines making an angle of `30^(@)` `tan 30^(@)=|(m-(-(3)/(2)))/(1+m(-(3)/(2)))|` `rArr" "(1)/(sqrt3)=|(2m+3)/(2-3m)|` On squaring both sides, we get `(1)/(3)=((2m+3)^(2))/((2-3m)^(2))` `rArr" "4+9m^(2)-12m=3(4m^(2)+9+12m)` `rArr" "4+9m^(2)-12m=12m^(@)+27+36m` `rArr" "3m^(2)+48m+23=0" ...(i)"` For the joint equation of the pair of the lines is obtained by putting `m=y//x.` `therefore " The joint equaiton of the two lines is : "` `3((y)/(x))^(2)+48((y)/(x))+23=0` `rArr" "3y^(2)+48xy+23x^(2)` `rArr" "23x^(2)+48xy+3y^(2)=0` |
|
| 36. |
Write the truth values of the following statements : (b) `EE n in N` such that `n+5 gt 10` |
|
Answer» Take the value of `n ge 6, EE n in N` So, the given statement is true, hence its truth value is T. |
|
| 37. |
Find the vector equation of the plane which is at a distance of 5 units from the origin and which is normal to the vector `2hati + hatj + 2hatk`. |
|
Answer» Let `vecn = 2hati+ hatj+2 hatk` be a normal vector to the plane. `therefore` Unit vector along the normal to the plane `hatn =(veca)/(|veca|)` `=(2hati + hatj + 2hatk)/(sqrt(2^(2)+1^(2)+2^(2)))` `=(2hati+hatj+2hatk)/(3)` `therefore `Equation of the required plane is `vecr . hatn = p` `rArr" "vecr.((2hati + hatj + 2hatk)/(3))=5` `rArr" "vecr. (2hati+hatj+2hatk)=15` |
|
| 38. |
If `barc=3bara-2barb`, then prove that `[bara barb barc]0` |
|
Answer» Given `" "vecc=3veca-2vecb` `therefore" "[vec a vec b vec c]=veca . (vecb xx vec)` `=veca . [vecb xx (3 veca xx2vecb)]` `=veca. (3 vecb xx veca - 2 vecb xx vecb)` `=veca.(3vecb xx vec a -0)` `(because vecb xx vec b=0)` `=3xx0=0" Hence proved"` |
|
| 39. |
Write the truth values of the following statements : (a) `sqrt5` is an irrational number but `3+sqrt5` is a complex number |
|
Answer» (a) Let `p:sqrt5` is an irrational number `q:3 + sqrt5` is a complex number Then the truth value of the given statement is `T ^^ T-=T` |
|
| 40. |
What is the IUPAC name of A. a- Amino butyric acidB. 2- Amino butric acidC. a-Amino butyric acidD. 2- Amino butanoic acid |
|
Answer» Correct Answer - A::B::C::D The IUPAC name of given compound is 2 aminobutanoic acid. |
|
| 41. |
Which among the following molecular formulae represents urotropine ?A. `C_(6)H_(12)N_(4)`B. `C_(6)H_(24)N`C. `C_(6)H_(12)N_(4)O_(2)`D. `C_(6)H_(24)N_(4)O_(2)` |
|
Answer» Correct Answer - A::B::C::D The molecular formulae of urotrophine is `C_(6)H_(12)N_(4)` It is also called as hexamethylene tetramine . |
|
| 42. |
Assuming p and q as given, write the verbal statement for the following symoblic statements : p : It is a day time. " " q : It is warm. (i) `p^^~q` (ii) `~ptoq` (iii) `qto""p` |
|
Answer» (a) P : It is a day time, q : It is warm `p ^^ ~ q` : It is a day time but it is not warm. (b) `~p rarr q` : It is not a day time the it is warm. (c) `q harr p ` : It is warm if and only if it is a day time. |
|
| 43. |
Write chemical formulae of the following ores: (a ) Calamine (b ) Haematite (c ) Magnetite (d) Corundum |
|
Answer» (a) Calamine - `ZnCO_(3)` (b) Haematite - `Fe_(2)O_(3)` (c ) Magnetite - `Fe_(3)O_(4)` (d ) Corundum - `Al_(2)O_(3)` |
|
| 44. |
What is the process in which concentrated ore is reduced to the corresponding metal by heating at high temperature with reducing agent ?A. PollingB. PyrometallurgyC. HydrometallurgyD. Calcination |
|
Answer» Correct Answer - Pyrometallurgy Pyrometallurgy is extraction and purification of metals by process involving tha application of heat . In the process of pyrometallurgy , the concentrated ore is reduced to the corresponding metal by heating at high temperature with reducing agent . |
|
| 45. |
If the enthalpy of vaporisation of water is `186.5 J mol^(-1)`, then entropy of its vaporisation will beA. `4.0 JK^(-1)mol^(-1)`B. `3.0JK^(-1) mol^(-1)`C. `1.5JK^(-1) mol^(-1)`D. `0.5 JK^(-1)mol^(-1)` |
|
Answer» Correct Answer - A ` Delta _("vap") H = 186.5 J//mol = 0.1865 KJ//mol.` Temperature T = ` 273 + 100 = 373 K ` ` Delta _("vap") H^(@) = 0.1865 KJ//mol` Entropy changes `Delta S = (Delta_("vap").H^(@))/T` ` T = 273 + 100 = 373 K` ` = (0.1865)/373 = 0.5J//K mol` |
|
| 46. |
Atomicity of sulphur in rhombic sulphur isA. 8B. 6C. 4D. 2 |
| Answer» Atomicity of sulphur = 8, in one molecule of sulphur (`S_(8))` thus , eight atoms are present in orthorhombic sulphur , so , it is found as `S_(8)`. | |
| 47. |
The major binding force of diamond, silicon and quartz isA. Covalent bondB. Ionic bondC. Metallic bondD. Co- ordinate covalent bond |
|
Answer» Correct Answer - Covalent bond Diamond is a covalent crystalline solid . It has a big giant network structure consisting of large number of carbon atoms bonded to each other by covalent bonds . Thus, the major binding force in diamond is covalent bond . |
|
| 48. |
Water boils at a lower tempature at high altitudes, becauseA. The temperature is lowB. The atmospheric pressure is lowC. The temperature is highD. The atmospheric pressure is high |
|
Answer» Correct Answer - The atmospheric pressure is low The boiling point becomes progressively lower altitudes due to lower air (barometric) pressure , It decreses by `1^(@)F` for every 540 of altitude . Thus , boiling point of water at high altitude is low because atmospheric pressure is low . |
|
| 49. |
Describe anomalous behaviour of oxygen as compared with other elements of group 16 with reference to : (a) Magnetic property (b) Oxidation state (c ) Hydrides |
|
Answer» (a) Magnetic property : Oxygen `(O_(2))` is paramagnetic while others are diamagnetic . Oxygen is paramagnetic due to two unpaired electrons in its outermost shell . (b) Oxiddation state : Oxygen shows oxidtion state of - 2 in most of its compunds . It also shows an oxidation state of `+` 2 in `Fe_(2)O " and" -1 "in " H_(2)O_(2)` and it connot show oxidation state beyond 2, while , other elements shows oxidation state of `+ 2 , + 4 "and" + 6 ` because these elements have vacant d - orbitals , so that their shell can expand . (c ) Hydrides : Hydrides of oxygen such as `H_(2)O` axists as liquid while all other hydrides are gases. |
|
| 50. |
if `int_0^k (dx)/(2+8x^2)=pi/16` then find the value of `k` |
|
Answer» `int_(0)^(h)(1)/(2+8x^(2))dx=(pi)/(16)` `rArr" "(1)/(8)int_(0)^(h)(1)/(x^(2)+(1//2)^(2))dx=(pi)/(16)` `rArr" "(1)/(8)xx(1)/(1//2)[tan^(-1)((x)/(1//2))]_(0)^(h)=(pi)/(16)` `rArr" "(1)/(4)[tan^(-1)2x]_(0)^(h)=(pi)/(16)` `rArr" "[tan^(-1)2h- tan^(-1)0]=(pi)/(4)` `rArr" "tan^(-1)2h=(pi)/(4)` `rArr" "tan^(-1)2h=tan^(-1)1` `rArr" "2h=1` `rArr" "h=(1)/(2)`. |
|