28278 + Interview Questions in Maths in Class 12 Page 49 InterviewSolution

2401.	Select the correct answer:The number of arbitrary constant in the general solution of a differential equation of third order is
Answer» `0` `1` `2` `3` ANSWER :D

Discussion

2402.	If A and B are any two events of a random experiment then show that (i) P(A^(C) nn B^(C)) = P(A^(C)) - P(B) "if A" nn B = phi (ii) P(A^(C)//B^(C)) = (1-P(A uu B))/(1-P(B)) "with P(A)" ne 0 and P(B) ne 1
Answer» Answer :(i) `P(A^(C)) - P(B)` (ii) `(1- P(A UU B))/(1-P(B))`

Discussion

2403.	Using differentials, find the approximate value of each of the following up to 3 places of decimal. (i)sqrt(25.3)""(ii)sqrt(49.5) (iii) sqrt(0.6)""(iv) (0.009)^(1/3) (v) (0.999)^(1/10)""(vi) (15)^(1/4) (vii) (26)^(1/3)""(viii) (255)^(1/4) (ix) (82)^(1/4)""(x)(401)^(1/2) (x i) (0.0037)^(1/2)""(x ii) (26.57)^(1/3) (x iii) (81.5)^(1/4)""(x iv) (3.968)^(3/2) (xv) (32.15)^(1/5
Answer» Solution :(i) `sqrt(25.3)` Let `f(x) = sqrtxrArrf'(x) = 1/(2sqrtx)` Letx= 25 andh = 0.3 Now, `f(x+H) = f(x)+hf'(x)` ` rArrf(25.3) = f (25) + 0.3 f'(25)` ` rArr sqrt(25.3)=sqrt(25) + 0.3 xx 1/(2sqrt(25)= 5+ (0.3)/10` ` = 5.03` (ii) `sqrt(49.5)` Let`f(x) = sqrtxrArrf' (x) = 1/(2sqrtx))` Let ` x = 49 and h = 0.5` Now `f(x+h) = f(x) + hf'(x)` `rArrf(49.5) = f(49) + 0.5 xx f' (49)` ` rArrsqrt(49.5) = sqrt(49)+ 0.5 xx 1/(2sqrt(49))` ` = 7 + 5/140 = 7.036` (iii) `sqrt(0.6)` Let `f(x)=sqrt xrArrf'(x) = 1/(2 sqrt x)` Let ` x = 0.64 and h = - 0.04` Now ` f(x+h) = f(x) +hf'(x)` ` rArrf(0.6) = f(0.64)-0.004 f'(0.64)` `rArrsqrt(0.6) = sqrt(0.64)-0.04xx 1/(2 sqrt(0.64)` ` = 0.8 - (0.04)/(2 xx 0.8)` ` = 0.8 - 0.025 = 0.775` (iv) `(0.009)^(1//3)` Let`f(x) = x^(1/3)rArrf'(x) = 1/3x^(2/3)` Let` x= 0.008 andh = 0.001` Now` f(x+h) = f(x) + hf'(x)` ` rArrf(0.009)=f(0.008) +0.001xx f'(0.008)` ` rArr(0.009)^(1/3) = (0.008)^(1/3) + (0.001)/(3 xx (0.008)^(2/3))` ` = 0.2 + (0.001)/(3 xx 0.04) ` ` = 0.2 + 0.008 = 0.208` (v) `(0.999)^(1/10)` Let ` f(x) = x ^(1/10) rArrf'(x) = 1/(10x^(9/10))` Let= 1 and h = - `0.001` Now` f(x+h) = f(x) + hf'(x)` `rArrf(0.999) =f(1) - 0.001 xx f'(1)` ` rArr(0.999)^(1/10) = (1)^(1/10) - 0.001 xx 1/(10(1) ^(9/10))` = 1-(0.001)/(10) = 1 - 0.0001` ` = 0.9999` (vi) ` (15)^(1/4)` Let` y = x^(1/4)rArr(dy)/(dx)=1/(4x^(3//4))` Let` x = 16 andx+ Delta x = 15rArr Delta x = - 1` arx = 16 ` y = (16)^(1//4) = 2 ` ` (dy)/(dx) = 1/ (4 (16)^(3//4)) = 1/32` and `Delta y = (dy) / (dx) Delta x = 1/32 (-1) = - 1/32` `:.y + Delta y = 2 - 1/32 = 63/32` ` rArr(15) ^(1//4) = 63/32` (vii) ` (26)^(1//3)` Let ` f(x) = x^(1/3)rArrf'(x) = 1/(3x^(2/3))` Letx = 27 and h = - 1 Nowf(x+h) = f(x) + hf'(x)` ` rArrf(26) = f(27) - 1 xx f'(27)` ` rArr(26)^(1//3) = (27)^(1//3) - 1/(3(27)^(2/3))` ` = 3- 1/27 = 3- 0.037 = 2.963 = 2.963. (viii)` (255)^(1//4)` Let `f(x) = x^(1/4)rArrf'(x) = 1/(4x^(3/4))` Letx = 256, h = - 1 Now` f(x +h) = f(x) + hf'(x)` `rArrf(255) = f(256) - 1 xx f'(256)` ` rArr (255)^(1//4) = (256)^(1//4 - 1/(4(256)^3/4))` ` = 4-1/(4 xx 64) = 4 - 0.004` (ix) Let` y = x^(1//4)rArr(dy)/(dx) = 1/(4x^(3//4))` Letx = 81andx + ` Delta x = 82rArrDelta x = 1` atx = 81, ` y = 81^(1//4) = 3` ` (dy)/(dx) = 1/ (4(81)^(3//4)) = 1/(108)` and` Delta y = (dy)/(dx) Delta x = 1/(108) xx 1 = 1/(108)` ` :.y + Delta y = 3 + 1/(108) = (325)/(108)` ` rArr(82)^(1//4) = (325)/(108)` . (x) `(401)^(1//2)` Let` f(x) = x^(1/2) rArrf'(x) = 1/(2X^(1//2))` Let` x= 400 and h = 1` Now` f(x+h) = f(x) + hf'(x)` ` rArrf(401) = f(400) + 1 xx f'(400)` ` rArr(401)^(1//2) = (400)^(1//2) + 1/(2(400)^(1//2))` ` = 20 + 1/40 = 20 + 0.025 = 20. 025` (xi)` (0.0037)^(1//2)` Let` f(x) = sqrtxrArrf'(x) = 1/(2sqrtx))` Let` x= 0.0036 and h = 0.0001` Now` f(x+h)= f(x) + h * f'(x)` ` rArrf(0.0037)= f(0.0036) + 0.0001xx f'(0.0036)` ` rArrsqrt(0.0037) = sqrt(0.0036) + 0.0001 xx 1/(2sqrt(0.0036))` ` = 0.06 + (0.0001)/(2 xx 0.06)` ` =0.06 + 0.0008 = 0.0608` (xii) ` (26.57)^(1//3)` Let`f(x)= x^(1/3)rArrf'(x) = 1/(3x^(2/3))` Let` x= 27andh = - 0.43` Now` f(x+h)= f(x) + hf'(x)` ` rArrf(26.57) = f(27) - 0.43 xx f'(27)` ` = (27)^(1/3) - (0.43 xx 1)/(3 xx (27)^(2/3))` ` = 3- (0.43)/(3 xx 9) = 3 - 0.016` ` = 2.984` (xiii) ` (81.5)^(1//4)` Let ` f(x) = x^(1/4)rArrf'(x) = 1/(4x^(3/4))` Letx = 81and h = `0.5` Now` f(x+h) = f(x) + hf'(x)` `f(81.5) = f(81) + 0.5 f'(81)` ` rArr (81.5)^(1//4) = (81)^(1//4) + (0.5)/(4(81)^(3//4))` `=3+(0.5)/(4 xx 27) = 3 + 0.0046` ` = 3.0046` (xiv) ` (3.968)^(3//2)` Let ` f(x) = x^(3/2)rArrf'(x) = 3/2 x^(1//2)` Letx = 4 andh =- 0.032 Now ` f(x+h) = f(x) + h f'(x)` ` rArrf(3.968) = f(4) - 0.032 xx f'(4)` ` rArr(3.968)^(3/2) = (4) ^(3/2) - 0.032 xx 3/2 xx (4) ^(1/2)` ` = 8- 0.048 xx 2= 8 - 0.096` ` = 7.904` . (xv) ` (32.15)^(1//5)` Let` f(x) = x^(1/5)rArrf'(x) = 1/(5x^(4/5))` Let` x = 32 andh = 0.15` Now` f(x+ h) = f(x) +hf'(x)` ` f(32.15) = f(32) + 0.15 xx f'(32)` ` rArr(32.15)^(1//5) = (32)^(1//5) + 0.15 xx 1/(5 xx (32)^(4/5))` `= 2+(0.15)/(5 xx 16) = 2 + 0.0019` ` = 2.0019`

Discussion

2404.	Plot the following curves : 2^(\|x\|)\|y\|+2^(\|x\|-1)=1.
Answer» ANSWER :The complete CURVE is drawn by taking the mirror IMAGE of the above shown curve in the X-axis and the Y-axis as shown alongside.

Discussion

2405.	A fair die is rolled. Consider the events E={1,3,5}, F = {2,3} andG={2,3,4,5}. Find P((EnnF)/G) and P((EUF)/G)
Answer» <P> SOLUTION :Here, S = {1,2,3,4,5,6} `EnnF`={1,2,3,5},`EnnF`={3} `(EnnF)nnG`={2,3,5} and `(EnnF)nnG`={3} `P((EnnF)nnG)`=1/6 `P((EnnF)nnG)=P((EnnF)nnG)/P(G)` 3/6/4/6=3/4 and `P((EnnF)nnG)=P((EnnF)nnG)/P(G)` =1/6/4/6=1/4

Discussion

2406.	Let N denotes the set of all natural numbers. On N xx N define R as follows: (a,b), (c,d) in N xx N (a,b)R (c,d) if ad(b+c) = bc(a+d), then
Answer» R is REFLEXIVE and symmetric only R is reflexive and TRANSITIVE only R is an equivalence relation R is anti-symmetric ANSWER :C

Discussion

2407.	Two cricket teams honored their players for three values, excellent batting, to the point bowling and unparalleled fielding by giving Rs x, Rs y and Rs z per player respectively. The first team paid respectively 2, 2 and 1 players for the above values with a total money of 11 lakhs, while the second team paid respectively 1,2 and 2 players for these values with a total prize money of Rs. 9 lakhs. If the total award money for one person each for these values amount to Rs.6 lakhs, then express the above situation as a matrix equation and find award money per person for each value.
Answer» ANSWER :Excellent batting: 3 lakhs point BOWLING: 2 lakhs FIELDING: 1 lakh

Discussion

2408.	Column–I (A) Four different movies are running in a town. Ten students go to watch these four movies. The number of ways in which every movie is watched by atleast one student, is (Assume each way differs only by number of students watching a movie) (B) Consider 8 vertices of a regular octagon and its centre. If T denotesthe number of triangles and S denotes the number of straight lines that can be formed with these 9 points then the value of (T – S) equals (C) In an examination, 5 children were found to have their mobiles in their pocket. The Invigilator fired them and took their mobiles in his possession. Towards the end of the test, Invigilator randomly returned their mobiles. The number of ways in which at most two children did not get their own mobiles is (D) The product of the digits of 3214 is 24. The number of 4 digit natural numbers such that the product of their digits is 12, is (E) The number of ways in which a mixed double tennis game can be arranged from amongst 5 married couple if no husband & wife plays in the same game, is Column -II (P) 11 (Q) 36 (R) 52 (S) 60 (T) 84
Answer» ANSWER : (A)–T ;(B)–R ;(C)–P ;(D)–Q ;(E)–S

Discussion

2409.	Whenredox reaction occurswithin the reactant , in which one component acts as oxidising agent andother component acts as reducing agent, then it is named as intra-molecular redox reaction, which usually occur in thermaldecomposition of ionic compounds. Which of the following compounds does not give nitrogen gas on heating ?
Answer» `NH_(4)NO_(2)` `(NH_(4))_(2)SO_(4)` `NH_(4)ClO_(4)` `(NH_(4))_(2)Cr_(2)O_(7)` Solution :(A)`NH_(4)NO_(2)overset(DELTA)rarrN_(2)+2H_(2)O` (B)`(NH_(4))_(2)SO_(4)overset(Delta)rarrNH_(3)+H_(2)SO_(4)` (C)`2NH_(4)ClO_(4)overset(Delta)rarrN_(2)+Cl_(2)+2O_(2)+4H_(2)O` (D) `(NH_(4))_(2)Cr_(2)O_(7)overset(Delta)rarrN_(2)+Cr_(2)O_(3)+4H_(2)O`

Discussion

2410.	Whenredox reaction occurswithin the reactant , in which one component acts as oxidising agent andother component acts as reducing agent, then it is named as intra-molecular redox reaction, which usually occur in thermaldecomposition of ionic compounds. Which of hte following salt does not give NO_(2) gas on heating ?
Answer» `Pb(NO_(3))_(2)` `HG(NO_(3))_(2)` `KNO_(2)` `AgNO_(3)` SOLUTION :(A) `2Pb(NO_(3))_(2)overset(Delta)rarr2PbO+4NO_(2)+O_(2)` (B) `Hg(NO_(3))_(2)overset(Delta)rarrHg+2NO_(2)+O_(2)` (C)`KNO_(2)overset(Delta)rarrKNO_(2)+(1)/(2)O_(2)` (D) `2AgNO_(3)overset(Delta)rarr2Ag+2NO_(2)+O_(2)`

Discussion

2411.	If PN is the perpendicular from a point on a rectangular hyperbola to its asymptotes, the locus of the midpoints of PN is
Answer» CIRCLE PARABOLA ELLIPSE HYPERBOLA ANSWER :D

Discussion

2412.	Cards are numbered 1 to 25 . Two cards are drawn at random. Find the probability that number on one card is a multiple of 7 and on the other is a multiple of 11
Answer» ANSWER :`(1)/(50)~~0.02`

Discussion

2413.	int" sec (tan"^(_1)" x ) dx "
Answer» ANSWER :`(1)/(2)[xsqrt(1+x^(2))+log\|x+sqrt(1+x^(2))\|]+C`

Discussion

2414.	Angle subtended by AB at centre the hyperbola is
Answer» `SIN^(-1) . 4/5` `sin^(-1) . 2/5` `sin^(-1) . 3/5` NONE of these SOLUTION :N/A

Discussion

2415.	If the expansion of (3sqrt(x)/7 - 5/(2xsqrt(x)))^(13n) contains a term independent of x, then n should be a multiple of
Answer» 10 5 6 4 Answer :D

Discussion

2416.	Fill in the gaps with correct answers.If alpha and beta lie in 1st and 2nd quadrants respectively, and if sin alpha = (1)/2, sin beta = (1)/3, then sin (alpha + beta) = _____.
Answer» SOLUTION :`((1)/(2SQRT3) + (SQRT2)/3`

Discussion

2417.	Column–I (A) In a plane a set of 8 parallel lines intersect a set of n parallel lines, that goes in another direction, forming a total of 1260 parallelograms. The value of n is equal to (B) If (""^(n-1)P_(3))/(""^(n)P_(4)) = (1)/(9) then n is equal to (C) Number of ways in which 5 persons A, B, C, D and E can be seated on round table if A and D do not sit next to each other (D) Number of cyphers at the end of the number""^(50)P_(25) Column -II (P) 6 (Q) 9 (R) 10 (S) 12
Answer» ANSWER :(A)–R ; (B)–Q ;(C)–S ;(D)–P

Discussion

2418.	Find the number of proper divisors of 2520 How many of them are odd ? Find their sum
Answer» ANSWER :623

Discussion

2419.	Integrate the following : int(x^(4/7)+1/(x^(1/3)))dx
Answer» Solution :`INT(X^(4/7)+1/x^(1/3))dx`=`intx^4dx`+`intx^(-1/3)dx` =`x^(11/7)/(11/7)`+`x^(2/3)/(2/3)`+C=`7/11x^(11/7)+3/2x^(2/3)+C`

Discussion

2420.	vec(a)=hati+2hatj+3hatk and vec(b)=2hati+4hatj-5hatk are adjacent side of a parallelogram then find the unit vector in the direction of the diagonal of the parallelogram.
Answer» ANSWER :`(1)/(7)(3hati+6hatj-2hatk)`

Discussion

2421.	solvetheequations x^3-3x^2 - 6x+8=0 therootsbeingin A.P
Answer» ANSWER :`-2,1,4`

Discussion

2422.	vec(r) =(3-t) hat(i)+(4+2t) hat(j) +(t-2) hat(k) vec(r ) =(1+s) hat(i) +(3s -7) hat(j) + (2s-2) hat(k)
Answer» ANSWER :`SQRT(35)` UNITS

Discussion

2423.	Express the vector 2hati+3hatj+hatk as the sum of two vectors, one vector is perpendicualr to 2hati-4hatj+hatk and the other vector is parallel to 2hati-4hatj+hatk.
Answer» Answer :`B_(1)=(-(2)/(3),(4)/(3),(1)/(3)),B_(2)=((8)/(3),(5)/(3),(4)/(3))`

Discussion

2424.	If roots of equation 2x^(4) - 3x^(3) + 2x^2 - 7x -1 = 0 are alpha, beta, gammaand 5 then value of sum(alpha+1)/alpha is equal to:
Answer» ANSWER :`-3`

Discussion

2425.	Ifsec(theta-alpha),sec(theta+alpha) are in AP , where cos alphane1, then what is the value of sin^(2)theta+cosalpha?
Answer» 0 1 `-1` `1//2` Solution :`(2)/(costheta)=(cos(theta+ALPHA)+cos(theta-alpha))/(cos(theta+alpha)cos(theta-alpha))=(2costheta.cosalpha)/(cos^(2)theta-sin^(2)alpha)` `rArrcos^(2)thetacosalpha=cos^(2)theta-sin^(2)alpha` `rArrsin^(2)alpha=cos^(2)theta(1-cosalpha)` `rArrcos^(2)theta=(sin^(2)alpha)/(1-cosalpha)=1+cosalpha` `rArr1-sin^(2)theta=1+cosalpha` `rArrsin^(2)theta+cosalpha=0`

Discussion

2426.	If there is a possible error of 0.02 cm in the measurement of the diameter of a sphere then the possible percentage error in tits volume when the radius 10 cm is
Answer» 0.1 0.2 0.3 0.4 Answer :C

Discussion

2427.	(i) Prove that (adj adj A) = \|A\|^(n – 2) A (ii) Find the value of \|adj adj adj A\| in terms of \|A\|
Answer» ANSWER :(II) `\|A\|^((n-1)^(3))`

Discussion

2428.	int(e^((x^(2)+4lnx)-x^(3)e^(x^(2))))/(x-1) dx equal to
Answer» `((e^(3lnx)-e^(lnx))/(2x))e^(X^(2))+C` `((x-1)XE^(x^(2)))/(2)+C` `((x^(2)-1))/(2x)e^(x^(2))+C` `((x^(2)-1)xe^(x^(2)))/(2)+C` Solution :LET `I=int(e^((x^(2)+4lnx))-x^(3)e^(x^(2)))/(x-1)dx=int(e^(x^(2)).x^(4)-x^(3)e^(x^(2)))/(x-1)dx` `rArr I=intx^(3)e^(x^(2))dx=(1)/(2)intte^(t)dt,` where `t=x^(2)` `rArr I=(1)/(2)(t-1)e^(t)+C=(1)/(2)(x^(2)-1)e^(x^(2))+C`

Discussion

2429.	The value of int_(-1)^(1) (x)/( sqrt(1-x^(2) ) ) log ((1+x)/( 1-x)) dx is (pi=3.14)
Answer» ANSWER :`6.28`

Discussion

2430.	Find the area of the region bounded by the hyperbola xy=1 and x=0 between y= 1 and y=2
Answer» ANSWER :(L N 2)

Discussion

2431.	if a+b=5 and ab=3, then the value of a^2(a+1)+b^2(b+1) is :
Answer» 99 79 49 80

Discussion

2432.	LetA ={ 1,2,3,4,5}and Rbe therelationon AdefinedbyR= {(a,b}: b=a^2} findthe rangeof R.
Answer» ANSWER :`R={1,4}`

Discussion

2433.	Cards are numbered 1 to 25 . Two cards are drawnat random . Findthe probabilitythat number on one card is a multiple of 7 and on the other is a multiple of 11.
Answer» ANSWER :`(1)/(50) = 0.02`

Discussion

2434.	Integration by partial fraction : int(dx)/(x^(2)(x+1))=x...+c
Answer» `log\|(x)/(x+1)\|-(1)/(x)` `log\|x(x+1)\|-(1)/(x)` `log\|(x+1)/(x)\|-(1)/(x)` `log\|(x+1)/(x^(2))\|+(1)/(x^(2))` ANSWER :C

Discussion

2435.	A : The gradiant of the curve y=x^3-3x^2-2x+7 at (1,3)is -5. R : The gradiant of the curve y=f(x) "at" P "is" ((dy)/(dx))_p
Answer» A and R are TRUE and R is the CORRECT EXPLANATION of A A and R are true and R is not correct explanation of A A is true but R is FALSE A is false but R is true Answer :A

Discussion

2436.	Let f(n)=[(1)/(5)+(3n)/(100)]n, where [x] denotes the greatest integer less thena or equal to x. Then overset(61)underset(n=1)Sigmaf(n)
Answer» 2013 1869 1947 1661 Answer :D

Discussion

2437.	Solve the following differential equations. (dy)/(dx)=(2x+9y-20)/(6x+2y-10)
Answer» ANSWER :`(2x-y)^(2) = C(x+2y-5)`

Discussion

2438.	Evaluate the following determinants. [[1,0,0],[2,3,5],[4,1,3]]
Answer» SOLUTION :`[[1,0,0],[2,3,5],[4,1,3]]` `1[[3,5],[1,3]]`=9-5=4

Discussion

2439.	If the roots of the equation (p-3) x^(2) + 2(p -3) x + 2p-5 =0 are real number distinct for alpha lt p lt beta and (beta - alpha) is maximum, then the extreme value of the quadratic expression -(alpha + beta) x^(2) + alpha beta x+ (alpha -beta) is
Answer» OPTIONA`-(4)/(5)` OptionB5 OptionC`-1` OptionD`(4)/(5)` ANSWER :D

Discussion

2440.	Let a, b, c be three non-zero vectors such that no two of these are collinear. If the vector a + 2b is collinear with c, then a + 2b + 6 c equals
Answer» `LAMBDAA(lambda ne 0,"a SCALAR")` `lambdab(lambda ne 0,"a scalar")` `lambdac(lambda ne 0,"a scalar")` 0 Solution :SINCE, a + 2b = KC `therefore a+2b+6c=kc+6c` `=(k+6)c=lambdac""[because lambda=k+rne0]`

Discussion

2441.	Let x+y=k be a normal to the parabola y^(2)=12x. If p is length of the perpendicular from the focus of the parabola onto this normal, then 4k-2p^(2) is equal to
Answer» 1 0 `-1` 2 Answer :B

Discussion

2442.	Evaluat int(1)/(sinx+sqrt3cosx)dx
Answer» Answer :`(1)/(2)LOG\|(SQRT(3)TAN""(X)/(2)+1)/(sqrt(3)(sqrt(3)-tan""(x)/(2)))\|+C`

Discussion

2443.	For the circle x^(2)+y^(2)-2x-4y-4=0, then lines 2x+3y-1=0, 2x+y+5=0 are
Answer» PERPENDICULAR tangents conjugate parallel tangents perpendicular chords Answer :B

Discussion

2444.	The tangent to the curve y^(2)-xy+9=0 is vertical when …............. .
Answer» `y=0` `y=pm SQRT3` `y=(1)/(2)` `y = pm sqrt3` Answer :B

Discussion

2445.	Solve : sqrt(tan alphax+ sin x)+sqrt(tan x-sinx)=2 cos sqrt(tanx)
Answer» ANSWER :`N PI, (8n-1) (pi)/(2),(8n+1)(pi)/(6)`

Discussion

2446.	Let 'A' denotes the real part of the complex number z=(19+7i)/(9-i)+(20+5i)/(7+6i)and 'B' denotes the sum of theimaginary parts of the roots of the equation z^2 – 8(1 – i)z + 63 – 16i = 0and 'C' denotes the sum of the series, 1 + i + i^2 + i^3 + ..... + i^(2008) where i =sqrt(-1) and D' denotes the value of the product (1+omega)(1+omega^2)(1+omega^4)(1-omega^8) where omega is the imaginary cube root of unity . Find the value of (A-B)/(C+D)
Answer» ANSWER :6

Discussion

2447.	Obtain equation of tangent and normal at point (1, 1) to the curve x^((2)/(3))+y^((2)/(3))=2.
Answer» ANSWER :TANGENT : `x+y-2=0`, NORMAL : `x-y=0`

Discussion

2448.	Nate walks 25 meters in 13.7 seconds. If he walks at this same rate, which of the following is closest to the distance he will walk in 4 minutes?
Answer» 150 METERS 450 meters 700 meters 1,400 meters ANSWER :B

Discussion

2449.	Consider the followingset of reactions : CHCl_(2)COOH+NaOHrarrCHCl_(2)COONa+H_(2)O "" Delta H_(1) = - 12830 Cal. HCl + NaOH rarr NaCl + H_(2)O "" DeltaH_(2) = - 13680 Cal. NH_(4)OH + HCl rarr NH_(4)Cl + H_(2)O"" Delta H_(3) = - 12270 cal. Select the correct option (s) :
Answer» ENTHALPHY of neutralization of `CHCl_(2)COOH`by`NH_(4)OH`is `11420` Cal. Enthalphy of dissociation of `CHCl_(2)COOH = - 850` Cal. Enthalphy of dissociation of `NH_(4)OH = 1410`Cal. Enthalphy change for the reaction`H_(2)O rarr H^(+) + OH^(-)` is `-13680`Cal. Answer :C

Discussion

2450.	underset(xto0)lim(1)/(x)cos^(1)((1-x^(2))/(1+x^2)) is equal to
Answer» `tan^(-1)X` `0` 1 `-1` Answer :B

Discussion

Explore topic-wise InterviewSolutions in .

Select the correct answer:The number of arbitrary constant in the general solution of a differential equation of third order is

If A and B are any two events of a random experiment then show that (i) P(A^(C) nn B^(C)) = P(A^(C)) - P(B) "if A" nn B = phi (ii) P(A^(C)//B^(C)) = (1-P(A uu B))/(1-P(B)) "with P(A)" ne 0 and P(B) ne 1

Plot the following curves : 2^(|x|)|y|+2^(|x|-1)=1.

A fair die is rolled. Consider the events E={1,3,5}, F = {2,3} andG={2,3,4,5}. Find P((EnnF)/G) and P((EUF)/G)

Let N denotes the set of all natural numbers. On N xx N define R as follows: (a,b), (c,d) in N xx N (a,b)R (c,d) if ad(b+c) = bc(a+d), then

If PN is the perpendicular from a point on a rectangular hyperbola to its asymptotes, the locus of the midpoints of PN is

Cards are numbered 1 to 25 . Two cards are drawn at random. Find the probability that number on one card is a multiple of 7 and on the other is a multiple of 11

int" sec (tan"^(_1)" x ) dx "

Angle subtended by AB at centre the hyperbola is

If the expansion of (3sqrt(x)/7 - 5/(2xsqrt(x)))^(13n) contains a term independent of x, then n should be a multiple of

Fill in the gaps with correct answers.If alpha and beta lie in 1st and 2nd quadrants respectively, and if sin alpha = (1)/2, sin beta = (1)/3, then sin (alpha + beta) = _____.

Find the number of proper divisors of 2520 How many of them are odd ? Find their sum

Integrate the following : int(x^(4/7)+1/(x^(1/3)))dx

vec(a)=hati+2hatj+3hatk and vec(b)=2hati+4hatj-5hatk are adjacent side of a parallelogram then find the unit vector in the direction of the diagonal of the parallelogram.

solvetheequations x^3-3x^2 - 6x+8=0 therootsbeingin A.P

vec(r) =(3-t) hat(i)+(4+2t) hat(j) +(t-2) hat(k) vec(r ) =(1+s) hat(i) +(3s -7) hat(j) + (2s-2) hat(k)

Express the vector 2hati+3hatj+hatk as the sum of two vectors, one vector is perpendicualr to 2hati-4hatj+hatk and the other vector is parallel to 2hati-4hatj+hatk.

If roots of equation 2x^(4) - 3x^(3) + 2x^2 - 7x -1 = 0 are alpha, beta, gammaand 5 then value of sum(alpha+1)/alpha is equal to:

Ifsec(theta-alpha),sec(theta+alpha) are in AP , where cos alphane1, then what is the value of sin^(2)theta+cosalpha?

If there is a possible error of 0.02 cm in the measurement of the diameter of a sphere then the possible percentage error in tits volume when the radius 10 cm is

(i) Prove that (adj adj A) = |A|^(n – 2) A (ii) Find the value of |adj adj adj A| in terms of |A|

int(e^((x^(2)+4lnx)-x^(3)e^(x^(2))))/(x-1) dx equal to

The value of int_(-1)^(1) (x)/( sqrt(1-x^(2) ) ) log ((1+x)/( 1-x)) dx is (pi=3.14)

Find the area of the region bounded by the hyperbola xy=1 and x=0 between y= 1 and y=2

if a+b=5 and ab=3, then the value of a^2(a+1)+b^2(b+1) is :

LetA ={ 1,2,3,4,5}and Rbe therelationon AdefinedbyR= {(a,b}: b=a^2} findthe rangeof R.

Cards are numbered 1 to 25 . Two cards are drawnat random . Findthe probabilitythat number on one card is a multiple of 7 and on the other is a multiple of 11.

Integration by partial fraction : int(dx)/(x^(2)(x+1))=x...+c

A : The gradiant of the curve y=x^3-3x^2-2x+7 at (1,3)is -5. R : The gradiant of the curve y=f(x) "at" P "is" ((dy)/(dx))_p

Let f(n)=[(1)/(5)+(3n)/(100)]n, where [x] denotes the greatest integer less thena or equal to x. Then overset(61)underset(n=1)Sigmaf(n)

Solve the following differential equations. (dy)/(dx)=(2x+9y-20)/(6x+2y-10)

Evaluate the following determinants. [[1,0,0],[2,3,5],[4,1,3]]

If the roots of the equation (p-3) x^(2) + 2(p -3) x + 2p-5 =0 are real number distinct for alpha lt p lt beta and (beta - alpha) is maximum, then the extreme value of the quadratic expression -(alpha + beta) x^(2) + alpha beta x+ (alpha -beta) is

Let a, b, c be three non-zero vectors such that no two of these are collinear. If the vector a + 2b is collinear with c, then a + 2b + 6 c equals

Let x+y=k be a normal to the parabola y^(2)=12x. If p is length of the perpendicular from the focus of the parabola onto this normal, then 4k-2p^(2) is equal to

Evaluat int(1)/(sinx+sqrt3cosx)dx

For the circle x^(2)+y^(2)-2x-4y-4=0, then lines 2x+3y-1=0, 2x+y+5=0 are

The tangent to the curve y^(2)-xy+9=0 is vertical when …............. .

Solve : sqrt(tan alphax+ sin x)+sqrt(tan x-sinx)=2 cos sqrt(tanx)

Obtain equation of tangent and normal at point (1, 1) to the curve x^((2)/(3))+y^((2)/(3))=2.

Nate walks 25 meters in 13.7 seconds. If he walks at this same rate, which of the following is closest to the distance he will walk in 4 minutes?

Consider the followingset of reactions : CHCl_(2)COOH+NaOHrarrCHCl_(2)COONa+H_(2)O "" Delta H_(1) = - 12830 Cal. HCl + NaOH rarr NaCl + H_(2)O "" DeltaH_(2) = - 13680 Cal. NH_(4)OH + HCl rarr NH_(4)Cl + H_(2)O"" Delta H_(3) = - 12270 cal. Select the correct option (s) :

underset(xto0)lim(1)/(x)cos^(1)((1-x^(2))/(1+x^2)) is equal to