28278 + Interview Questions in Maths in Class 12 Page 203 InterviewSolution

10101.	Let a=2hat(i)-hat(j)+hat(k), b=hat(i)+2hat(j)-hat(k) and c=hat(i)+hat(j)-2hat(k) be three vectors, A vector in the plane of b and c whose projection on a is of magnitude sqrt(2/3), is
Answer» `2hat(i)+3hat(j)-3hat(k)` `2hat(i)+3hat(j)+3hat(k)` `2hat(i)-5hat(j)+5hat(k)` `2hat(i)+hat(j)+5hat(k)` Solution :Any vector I the PLACE of b and C is `r=mb+c(m+1)HATI+(2m+1)hati+(-m-2)hatk` PROJECTION of r on a `=(r*a)/(\|a\|)=\|sqrt(2/3)\|` `:.""(2(m+1)-(2m+1)+(-m-2))/(sqrt6)=+-sqrt(2/3)` `rArr""-m-2+-2rArrm=-3"and"1` Hence, `r=-2hati-5hatj+hatk" and "r=2hati+3hatj-3hatk`

Discussion

10102.	in the given figure y=x^(2)+bx+c is a quadratic polynomial which meets x-axis at A and B and y-axis at C Q is vertex of quadratic polynomial and foot of perpendicular from Q to x-axis and y-axis are P and R respectively. Then answer the following questions. Q. If ("area of" DeltaABC)/("Area of rectangle" OPQR)=(8)/(3) satisfies the relation b^(2)=kc then k will be
Answer» `9` `(2)/(9)` `(9)/(2)` `2` Solution :`((1)/(2)(beta-alpha)C)/(((b^(2)-4c)/(4))(-(b)/(2)))=(8)/(3)` squaring and using `(beta-alpha)^(2)=b^(2)-4c` `9C^(2)=4b^(4)-16b^(2)c` `4b^(4)-16b^(2)c-9c^(2)=0` `4b^(4)-18B^(2)c+2b^(2)c-9c^(2)=0` `(2b^(2)+c)(2b^(2)-9c)=0impliescgt0because2b^(2)+cne0` `(b^(2))/(c)=(9)/(2)implies(b^(2))/(c)=4.5`

Discussion

10103.	in the given figure y=x^(2)+bx+c is a quadratic polynomial which meets x-axis at A and B and y-axis at C Q is vertex of quadratic polynomial and foot of perpendicular from Q to x-axis and y-axis are P and R respectively. Then answer the following questions. Q. if two circles passing through A and B touches y-axis at C and R respectively then
Answer» `b^(2)=2C` `b^(2)=3C` `b^(2)=4c` `b^(2)=8C` Solution :`OA.OB=OC^(2)` `alpha.beta=c^(2)` & `((b^(2)-4c)/(4))^(2)=alphabeta` `(b^(2)-4)^(2)=16` `c=c^(2)` `b^(2)-4=4` `c=1` `b^(2)=8`

Discussion

10104.	sum _(r = 2) ^(oo) (1)/(r ^(2) - 1) is equal to :
Answer» ANSWER :`3//4`

Discussion

10105.	Find the equation of the circum circle of the triangle formed by the lines5x -3y + 4=0, 2x + 3y -5 =0 , x + y =0
Answer» ANSWER :` 49 (x^(2) +y^(2)) +280x - 259y + 245 =0 `

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10106.	Examine the following functions for continuity : f(x)=x^(3)+x^(2)-1
Answer» ANSWER :CONTINUOUS

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10107.	Evaluate the deternminant Delta=\|{:(1,2,4),(-1,3,0),(4,1,0):}\|
Answer» ANSWER :-52

Discussion

10108.	Let f(x) is of the form alpha z _beta , where alpha, beta are constants and alpha, beta,z are complex numbers such that \|alpha\| ne \|beta\|.f(x) satisfies followingproperties : (i)If imaginary part of z is non zero, then f(x)+bar(f(z)) = f(barz)+bar(f(z)) (ii)If real part of of z is zero , then f(z)+bar(f(x)) =0 (iii)If z is real , then bar(f(x)) f(x) > (x+1)^2 AA z in R (4x^2)/((f(1)-f(-1))^2)+y^2/((f(0))^2)=1 , x , y in R, in (x,y) plane will represent :
Answer» HYPERBOLA circle ELLIPSE PAIR of LINE ANSWER :A

Discussion

10109.	Let f(x) is of the form alpha z _beta , where alpha, beta are constants and alpha, beta,z are complex numbers such that \|alpha\| ne \|beta\|.f(x) satisfies followingproperties : (i)If imaginary part of z is non zero, then f(x)+bar(f(z)) = f(barz)+bar(f(z)) (ii)If real part of of z is zero , then f(z)+bar(f(x)) =0 (iii)If z is real , then bar(f(x)) f(x) > (x+1)^2 AA z in R Consider ellipse S:x^2/((Re(alpha))^2) + y^2/(Im(beta))^2) =1 , x, y in R in (x,y) plane , then point (1,1) will lie :
Answer» OUTSIDE the ELLIPSE S INSIDE the ellipse S on the ellipse S none of these Answer :B

Discussion

10110.	sin^(2) (3^(@))+sin^(2) (6^(@))+sin^(2) (9^(@))+...+sin^(2) (84^(@))+sin^(2) (87^(@))+sin^(2) (90^(@))=
Answer» `31/2` `39/2` `59/2` 36 Answer :A

Discussion

10111.	Choose the correct answer. The degree of the differential equation 2x^2(d^2y)/(dx^2) - 3((dy)/(dx)) + y = 0 is
Answer» 2 1 0 not DEFINED ANSWER :A

Discussion

10112.	f(x) is a polynomial of degree 3 passing through the origin having local extrema atx=+- 2 Statement-I: Ratio of theareas in which f(x) cuts the circle x^(2) +y^(2) =36is 1: 1 Statement-II Both y= f(x) and the circle are symmetric about the origin
Answer» STATEMENT -I is TRUE statement -II is a CORRECT explanation for statement-I Statement -I is true ,Statement-II is not Trueexplanation for Statement-I Statement -I is True Statement-II is FALSE Statement -I is False,Statement -II is True ANSWER :A

Discussion

10113.	Figure shows three events A,B and C. Probabilities of differents events are shown in the figure. For instance,P(AnnB'nnC')=0.18, P(A'nnBnnC')=0.06 " etc". Which of the following is false?
Answer» A and B are INDEPENDENT B and C areindependent A and C are independent A and `B NN C`are independent Solution :

Discussion

10114.	If((x + 1 ))/((2x - 1 ) (3x + 1 ))= (A)/((2x - 1 ))+ (B)/((3x+ 1)) , then16 A +9 Bisequalto
Answer» 4 5 6 8 Solution : ` ((X + 1 ))/((2x - 1 )(3x+ 1 )) = (A)/((2x - 1)) + (B)/((3x+ 1 )) ` ` rArrx + 1= A (3x + 1 ) + B(2x - 1) ` ` rArrx + 1=x (3A + 2B)+(A -B) ` `3A +2B = 1` ` A -B = 1` ` rArrA =1 + B ` ` 3( 1 + B)+2B =1` `rArr3+5B = 1` ` B = (-2)/(5) ` ` A =1+B =1-( 2 ) /(5) ` ` A =(3)/(5) ` `therefore16 A +9B =16 ((3)/(5)) +9 ((-2)/(5)) =(30)/(5)= 6 `

Discussion

10115.	Find the value of sum_(1 le I,)sum_(j le n)(1).
Answer» SOLUTION :N/A

Discussion

10116.	Calculate the area enclosed in the region (i) {(x,y):x ^(2) + y ^(2) le 1 le x + y} (ii) {(x,y):x ^(2) + y ^(2) le 4x, 4x^(2) + 4y ^(2) le 9} (iii) {(x,y) : x ^(2) + y ^(2) le 16, x ^(2) le 6y} (iv){(x,y) :y ^(2) le 6 ax, x ^(2) +y ^(2) le 16a^(2)} (v) {(x,y) :x ^(2) +y ^(2) le 8, x ^(2) le 2y}.
Answer» Answer :`(i) ((pi)/(4) - (1)/(2)) (II) (( 2sqrt2)/(3) - (1)/(sqrt2) + (9pi)/(8) - (9)/(4) sin ^(-1) "" (1)/(3)) (iii) (4)/(3) (4PI + SQRT3) (iv) (4a ^(2))/(3) (4 pi + sqrt3) (v) (2pi + (4)/(3))` (sq. units).

Discussion

10117.	vec(r )=(hat(i) +2hat(j) +hat(k)) + lambda(hat(i)-hat(j) + hat(k)) vec(r )=(2hat(i) -hat(j) -hat(k)) + lambda(2hat(i) + hat(j) +2hat(k))
Answer» ANSWER :`(3sqrt(2))/(2)` UNITS

Discussion

10118.	sqrt3 cosec 20^(@) -sec 20^(@) is equal to
Answer» 2 `2 SIN 20^(@) cosec 40^(@)` 4 `4 sin 20^(@) cosec 40^(@)` ANSWER :C

Discussion

10119.	Prove the following int_-1^1 x^(17) cos^4x dx = 0
Answer» Solution :`(-X)^(17) cos^4(-x) = -x^(17)cos^4x` `GT x^(17) cos^4x` is an ODD function. THEREFORE `int_-1^1 x^(17) cos^4x dx = 0` If F(x) is an odd function, then `int_-a^a f(x) dx = 0`

Discussion

10120.	Let bar(x) and M.D be the mean and the mean deviation about bar(x)of n observations x_(p) , i=1, 2 . . . . .n . If each of the observation is increased by 5, then the new meandeviation aboutthe new mean, respectively are .
Answer» `BAR(x) , M.D` `bar(x) + 5, M.D` `bar(x), M.D. + 5` `bar(x) - 15 , m M. D. + 5` ANSWER :B

Discussion

10121.	Consider hyperbola xy = 16 to find the following: (i) Coordinates of vertices (ii) Length of transverse axis (iii) Coordinates of foci (iv) Length of latus rectum (v) Equations of two directrices (vi) Equation of tangent at point (2, 8) (vii) Equation of normal at point (2, 8) (viii) Equation of chord of contact w.r.t. point (2, 3) (ix) Equation of chord which gets bisected at point (5, 6) (x) Equation of tangent having slope - 2 (xi) Equation of noraml having slope 2
Answer» Solution :We havehyperbola xy = 16. (i) Clearly, transverse axis is `x-y=0` and conjugate axis is `x+y=0.` Vertices are points of intersection of transverse axis `x-y=0` and hyperbola. So, vertices are `A (4,4) and A'(-4,-4).` (ii) Length of transverse axis is `"AA'"=8sqrt2=(=2a).` (iii) Foci lie at distance 'ae' from centre on line `x-y=0.` Now, `ae=4sqrt2sqrt2=8` Therefore, foci are `F_(1)(4sqrt2, 4sqrt2) and F_(2)(-4sqrt2, -4sqrt2)`. (iv) Length of latus rectum `=(2b^(2))/(a)=2a=8sqrt2` (as a = b for rectangular hyperbola) (v) Each of the directrices lies at distance `(a)/(e)(=4)` from centre and is parallel to the conjugate axis `x+y=0`. So, equation of two directrices are `x+y=pm4sqrt2`. (VI) Equation of tangent at point (2, 8) is T = 0 `rArr""(2y+8x)/(2)-16=0` `rArr""4x+y-16=0` Alternatively, we can differentiate the equation of curve to get the slope of tangent. Then, we get `y+x(dy)/(dx)=0` `therefore""(dy)/(dx)=-(y)/(x)` `therefore""((dy)/(dx))_(("2,8"))=-(8)/(2)=-4` So, equation of tangent at (2, 8) is `y-8=-4(x-2)` `rArr""4x+y-16=0` (vii) Equation of normal at (2,8) is `x-4y+30=0`. (VIII) Equation of chord of contact w.r.t. point (2, 3) is T = 0 `rArr""(2y+3x)/(2)-16=0` `rArr""3x+2y-32=0` Equation of chord which GETS bisected at point (5,6) is T = `S_(1)` `rArr""(5y+6x)/(2)-16=(5)(6)-16` `rArr""6x+5y=60` (x) To find the equation of tangent having slope `-2`, we differetiate the curve and compare derivative to `-2`. `therefore""(dy)/(dx)=-(y)/(x)=-2` `therefore""y=2x` Solving this with hyperbola, we get points `P(sqrt8, 2sqrt8)`and `Q(-sqrt8,-2sqrt8)` on the hyperbola where slope of tangent is `-2.` Equation of tangent at point P is `y-2sqrt8=-2(x-sqrt8)` `rArr""2x+y=4sqrt8` Equation of tangent at point Q is `y+2sqrt8=-2(x+sqrt8)` `rArr""2x+y=-4sqrt8.` (xi) We have `(dy)/(dx)=-(y)/(x)` THUS, slope of normal at any point on the curve is `-(dx)/(dy)=(x)/(y)=2` (given) `therefore""x=2y` Solving this with hyperbola, we get points `A(2sqrt8, sqrt8)` and `B(-2sqrt8-sqrt8)` on the hyperbola where slope of normal is 2. Equation of normal at point A is `y-sqrt8=2(x-2sqrt8)` `rArr""2x-y=3sqrt8` Equation of normal at point B is `y+sqrt8=2(x+2sqrt8)` `rArr""2x-y=-3sqrt8`

Discussion

10122.	If y= sqrt(sin x + y), then (dy)/(dx) is equal to
Answer» `(COS X)/(2y-1)` `(cos x)/(1-2y)` `(SIN x)/(1-2y)` `(sin x)/(2y-1)` ANSWER :A

Discussion

10123.	If X represents difference between the number of heads and number of tails obtained when a fair coin is tossed 3 times. Then find mean and variance of X.
Answer» ANSWER :MEAN = 0, VARIANCE =3

Discussion

10124.	f(x)= \|(sin x,cos x),(tan x,cot x)\| then f'((pi)/(4))= …….
Answer» 0 `-SQRT2` `-2 sqrt2` `sqrt2` ANSWER :D

Discussion

10125.	If f(x) is a polynomial such that (alpha+1)f(alpha)-alpha=0AA alpha epsilon Nuu{0}, alpha le n, then
Answer» `f(76)` is 1 `f(21)` is `10/11` `f(37)` is `1/7` `f(148)` is `9/13` Solution :`G(X)=(x+1)f(x)-xs` `g(x)=0` for `x=0,1,2,……..n` `g(x)=ax(x-1)…….(x-n)` `:. (f(x)=((-1)^(n+1)x.(x-1)…..(x-n))/(\|___(n+1))+x)/(x+1`

Discussion

10126.	Find (dy)/( dx), if x=a [ cos t + log ( tan ""t//2)]& y= a sin t
Answer» ANSWER :`(DY)/( dx) = (dy//dt)/( dx//dt) = ( a COS t)/( ( a cos^(2) t)/( sin t) )= ( SINT )/( cos t) = TAN t`

Discussion

10127.	underset(r=0)overset(10)sum (40-r)C_(5)=
Answer» `""^(41)C_(5)-""^(30)C_(5)` `""^(41)C_(6)-""^(30)C_(6)` `""^(41)C_(5)+""^(30)C_(5)` `""^(41)C_(6)` Answer :B

Discussion

10128.	a is perpendicular to both b and c . The angle between b and c is (2 pi)/(3). If \|a\| = 2, \|b\| = 3, \|c\| = 4, then c. (a xx b) is equal to
Answer» `18 sqrt(3)` `12 sqrt(3)` `8 sqrt(3)` `6 sqrt(3)` ANSWER :B

Discussion

10129.	If the normal at P ony^(2)= 4ax cuts the axis of the parabola in G and S is the focus then SG=
Answer» <P>SP 2 SP `(1)/(2)` SP `sqrt(P)` Answer :A

Discussion

10130.	Evaluate the following integrals (v) int_(0)^(1)x tan^(-1) x dx
Answer» ANSWER :`(pi-2)/(4)`

Discussion

10131.	b=2.35+0.25x c=1.75+0.40x In the equations above, b and c represent the price per pound, in dollars, of beef and chicken, respectively, x weeks after July 1 during last summer. What was the price per pound of beef when it was equal to the price per pound of chicken?
Answer» `$2.60` `$2.85` `$2.95` `$3.35` ANSWER :D

Discussion

10132.	You are given that A and B are two events such that P(B)= (3)/(5), P(A//B)= (1)/(2)and P(A cup B)= (4)/(5)then P(A) equal …….
Answer» `(3)/(10)` `(1)/(5)` `(1)/(2)` `(3)/(5)` ANSWER :C

Discussion

10133.	If the point P(4, –2) is the one end of the focal chord PQ of the parabola y^(2) = x, then the slope of the tangent at Q is
Answer» `-1//4` `1/4` `4` `-4` Solution :The equation of the tangent at (4, -2) to `y^(2) = X` is `-2y = 1/2(x+4) or x + 4y + 4 = 0` Its slope is `-1/4` Therefore the slope of the perpendicular line is 4. Since the tangents at the end of FOCAL chord of a PARABOLA are at RIGHT angle, the slope of the tangent at Q is 4. Hence, (C) is the correct answer.

Discussion

10134.	P is a point satisfying arfz = pi//4 ,such that sum of its distance form two given point (0,1) and (0,2) is minimum, then P must bek/2 (1+i) then numerical value of k should be ________.
Answer» ANSWER :3

Discussion

10135.	D=\|{:(a^2+2a,2a+1,1),(2a+1,a+2,1),(3,3,1):}\| then,
Answer» `DGT0 if AGT1` `Dlt0if alt1` `D=0 if a=1` All the GIVEN ALTERNATES ANSWER :D

Discussion

10136.	Expressisqrt3 =rcos theta +ir sin theta complex numbers in the polar form.
Answer» SOLUTION :where`r=sqrt(a^2+b^2)=SQRT3` `"and theta=TAN^(-1)(sqrt3/0)=tan^(-1)prop=pi/2` `:.isqrt3=sqrt3(COS pi/2+isin pi/2)

Discussion

10137.	thevalue cos 480^@ . Sin150^@ + sin600^@ . Cos390^@ =
Answer» 0 1 `1/2` `-1` ANSWER :D

Discussion

10138.	The value of {x in R[log(1.6)^(1-x^(2))-(0.625)^(6(1+8))]in R}
Answer» `(-OO,-1)UU (7,oo)` `(-1,5)` `(1,7)` `(-1,7)` ANSWER :D

Discussion

10139.	For positive real numbers x and y, define their special mean to be average of their arithmetic and geometric means. Find the total numbe of pairs of integers (x,y) with x le y, from the set of numbers (1,2,……,2016), such that the special mean of x and y is a perfect square.
Answer» ANSWER :506

Discussion

10140.	Find the approximate value of each of the following :(65)^((1)/(3))
Answer» ANSWER :`4.021`

Discussion

10141.	Forany twovectors overset(to)(u) " and" overset(to)(v) prove that (i) \|overset(to)(u).overset(to)(v)\|^(2) +\|overset(to)(u) xx overset(to)(v)\|^(2) =\|overset(to)(u)\|^(2)\| overset(to)(v)\|^(2) (ii) (1+\|overset(to)(u)\|^(2))(1+\|overset(to)(v)\|^(2))=\|1-overset(to)(u).overset(to)(v)\|^(2)+\|overset(to)(u)+overset(to)(v)+(overset(to)(u)xxoverset(to)(v))\|^(2)
Answer» SOLUTION :(i) Since`vec(u) ". " vec(v) = \|vec(u) \|\|vec(v)\| COS0` and `vec(u) xx vec(v) = \|vec(u)\|\|vec(v)\|` sin 0 `HAT(n)` where0 is theanglebetween`vec(u)" and" vec(v)" and" vec(n)` isunitvector perpendicular to theplaneof `vec(u) " and" vec(v)` Again `\|ve(u) ". " vec(v)\|^(2) =\|vec(u)\|^(2) \|vec(v)\|^(2) \| cos^(2) 0` and ` \|vec(u) xx vec(v)\|^(2)= \|vec(u)\|^(2)\|vec(v)\|^(2) sin^(2) 0= \|vec(u)\|^(2) \|vec(v)\|^(2) sin^(2) 0` `:. \|vec(u)"." vec(v)\|^(2) +\|vec(u)xx vec(v)\|^(2)=\|vec(u)\|^(2) \|vec(v)\|^(2) (cos^(2) 0+sin^(2)0)` `=\|vec(u)\|^(2) \|vec(v)\|^(2)` (ii) `\|vec(u)+vec(v)+(vec(u)xxvec(v)\|^(2)` `\|vec(u)+vec(v)\|^(2) +\|vec(u)xxvec(v)\|^(2)+2(vec(u)+vec(v)).(vec(u)xxvec(v))` `=\|vec(u)\|^(2)+\|vec(v)\|^(2)+2vec(u)"."vec(v)+\|vec(u)xx vec(v)\|^(2) +0` [`:' vec(u) xx vec(v)` isperpendicularto theplaneof `vec(u)" and " vec(v)`] `:. \|vec(u) \|^(2) +\|vec(v)\|^(2)+2vec(u)". " vec(v) +\|vec(u)xx vec(v)\|^(2) +1 -2 vec(u)". " vec(v) + \|vec(u) ". " vec(v)\|^(2)` `=\|vec(u)\|^(2) + \|vec(v)\|^(2) +1+ \|vec(u)\|^(2) \|vec(v)\|^(2)` ` =\|vec(u)\|^(2) (1+\|vec(v)\|^(2)) +(1+\|vec(v)\|^(2)) =(1+\|vec(v)\|^(2)) (1+\|vec(u)\|^(2))`

Discussion

10142.	If the tangents to the ellipse at M and N meet at R and the normal to the parabola at M meets the x-axis at Q, then the ratio of area of the triangle MQR to area of the quadrilateral MF_1NF_2 is
Answer» 3:4 4:5 5:8 0.085416666666667 Answer :C

Discussion

10143.	[PtCl(NH_(3))_(3)][Cu(NH_(3))Cl_(3)] correct name of complex.
Answer» Triammine CHLORIDE platinum (II) ammine trichlorido cuprate (II) Triammine chloride platinate (+2) ammine trichlorido copper (-2) Triammine chloride platinate (II) ammine trichlorido copper (II) Triammine chloride platinum (+1) ammine trichlorido cuprate (-1) Solution :`{:(+2,,+2),([PTCL(NH_(3))_(3)],,[CU(NH_(3)Cl_(3))]):}` Triammine chlorido platinum (II) ammine trichloride cuprate (II) or `[PtCl(NH_(3))_(3)]^(+)[Cu(NH_(3)Cl_(3))]^(-)` Triammine chlorido platinum (+1) ammine trichloride cuprate (-1)

Discussion

10144.	(dy)/(dx) +2x tan(x-y) = 1 rArr sin(x-y) =
Answer» `A E^(-X^(2))` `A e^(2x)` `Ae^(x^(2))` `Ae^(-2x)` ANSWER :C

Discussion

10145.	If (x^(2)+13x+15)/((x-1)(x^(2)+2))=(A)/(x-1)+(Bx+C)/(x^(2)+2), then the descending order of A, B, C is
Answer» A, B, C B, C, A C, A, B A, C, B Answer :D

Discussion

10146.	Evaluate the following definite integrals : int_(0)^(pi/2)sqrt(1-cos2x)dx
Answer» ANSWER :`SQRT2`

Discussion

10147.	Evaluate the following : [[sin^2theta,cos^2theta,1],[cos^2theta,sin^2theta,1],[-10,12,2]]
Answer» SOLUTION :`[[sin^2theta,cos^2theta,1],[cos^2theta,sin^2theta,1],[-10,12,2]]` =`[[0,cos^2theta,1],[0,sin^2theta,1],[0,12,2]]` `(C_1=C_1+C_2-C_3)` =0`(THEREFORE C_1=0)`

Discussion

10148.	Select the CORRECT order according to given property ?
Answer» Li lt Na : Reducing NATURE in water `Na^+` lt `Li^+` : Ionic MOBILITY in water `Na_((g)) lt Li_((g))` : Size `Na_((AQ))^+ lt Li_((aq))^+` : RADIUS

Discussion

10149.	int sin^(2)8xdx =
Answer» `(1)/(2)(x + (SIN 16x)/(16)) +C ` `(1)/(2)(x - (sin 16x)/(16)) +C ` `(1)/(8)(x + (sin 16x)/(2)) +C ` `(1)/(16)(x - (sin 16x)/(16)) +C ` Answer :B

Discussion

10150.	Which of the following statement(s) is / are correct
Answer» The internal energy of an ideal gas may be increased by adding more molecules to it, at constant temperature. The molar enthalpy of any substance decrease on COOLING , at constant pressure. A diabatic FREE EXPANSION & isothermal free expansion are similar PROCESSS for an ideal gas . It is possible to have a process in which the entropy of an isolated system is DECREASED. . Solution :(A),(B),(C ),(D)

Discussion

Explore topic-wise InterviewSolutions in .

Let a=2hat(i)-hat(j)+hat(k), b=hat(i)+2hat(j)-hat(k) and c=hat(i)+hat(j)-2hat(k) be three vectors, A vector in the plane of b and c whose projection on a is of magnitude sqrt(2/3), is

sum _(r = 2) ^(oo) (1)/(r ^(2) - 1) is equal to :

Find the equation of the circum circle of the triangle formed by the lines5x -3y + 4=0, 2x + 3y -5 =0 , x + y =0

Examine the following functions for continuity : f(x)=x^(3)+x^(2)-1

Evaluate the deternminant Delta=|{:(1,2,4),(-1,3,0),(4,1,0):}|

sin^(2) (3^(@))+sin^(2) (6^(@))+sin^(2) (9^(@))+...+sin^(2) (84^(@))+sin^(2) (87^(@))+sin^(2) (90^(@))=

Choose the correct answer. The degree of the differential equation 2x^2(d^2y)/(dx^2) - 3((dy)/(dx)) + y = 0 is

f(x) is a polynomial of degree 3 passing through the origin having local extrema atx=+- 2 Statement-I: Ratio of theareas in which f(x) cuts the circle x^(2) +y^(2) =36is 1: 1 Statement-II Both y= f(x) and the circle are symmetric about the origin

Figure shows three events A,B and C. Probabilities of differents events are shown in the figure. For instance,P(AnnB'nnC')=0.18, P(A'nnBnnC')=0.06 " etc". Which of the following is false?

If((x + 1 ))/((2x - 1 ) (3x + 1 ))= (A)/((2x - 1 ))+ (B)/((3x+ 1)) , then16 A +9 Bisequalto

Find the value of sum_(1 le I,)sum_(j le n)(1).

Calculate the area enclosed in the region (i) {(x,y):x ^(2) + y ^(2) le 1 le x + y} (ii) {(x,y):x ^(2) + y ^(2) le 4x, 4x^(2) + 4y ^(2) le 9} (iii) {(x,y) : x ^(2) + y ^(2) le 16, x ^(2) le 6y} (iv){(x,y) :y ^(2) le 6 ax, x ^(2) +y ^(2) le 16a^(2)} (v) {(x,y) :x ^(2) +y ^(2) le 8, x ^(2) le 2y}.

vec(r )=(hat(i) +2hat(j) +hat(k)) + lambda(hat(i)-hat(j) + hat(k)) vec(r )=(2hat(i) -hat(j) -hat(k)) + lambda(2hat(i) + hat(j) +2hat(k))

sqrt3 cosec 20^(@) -sec 20^(@) is equal to

Prove the following int_-1^1 x^(17) cos^4x dx = 0

Let bar(x) and M.D be the mean and the mean deviation about bar(x)of n observations x_(p) , i=1, 2 . . . . .n . If each of the observation is increased by 5, then the new meandeviation aboutthe new mean, respectively are .

If y= sqrt(sin x + y), then (dy)/(dx) is equal to

If X represents difference between the number of heads and number of tails obtained when a fair coin is tossed 3 times. Then find mean and variance of X.

f(x)= |(sin x,cos x),(tan x,cot x)| then f'((pi)/(4))= …….

If f(x) is a polynomial such that (alpha+1)f(alpha)-alpha=0AA alpha epsilon Nuu{0}, alpha le n, then

Find (dy)/( dx), if x=a [ cos t + log ( tan ""t//2)]& y= a sin t

underset(r=0)overset(10)sum (40-r)C_(5)=

a is perpendicular to both b and c . The angle between b and c is (2 pi)/(3). If |a| = 2, |b| = 3, |c| = 4, then c. (a xx b) is equal to

If the normal at P ony^(2)= 4ax cuts the axis of the parabola in G and S is the focus then SG=

Evaluate the following integrals (v) int_(0)^(1)x tan^(-1) x dx

b=2.35+0.25x c=1.75+0.40x In the equations above, b and c represent the price per pound, in dollars, of beef and chicken, respectively, x weeks after July 1 during last summer. What was the price per pound of beef when it was equal to the price per pound of chicken?

You are given that A and B are two events such that P(B)= (3)/(5), P(A//B)= (1)/(2)and P(A cup B)= (4)/(5)then P(A) equal …….

If the point P(4, –2) is the one end of the focal chord PQ of the parabola y^(2) = x, then the slope of the tangent at Q is

P is a point satisfying arfz = pi//4 ,such that sum of its distance form two given point (0,1) and (0,2) is minimum, then P must bek/2 (1+i) then numerical value of k should be ________.

D=|{:(a^2+2a,2a+1,1),(2a+1,a+2,1),(3,3,1):}| then,

Expressisqrt3 =rcos theta +ir sin theta complex numbers in the polar form.

thevalue cos 480^@ . Sin150^@ + sin600^@ . Cos390^@ =

The value of {x in R[log(1.6)^(1-x^(2))-(0.625)^(6(1+8))]in R}

For positive real numbers x and y, define their special mean to be average of their arithmetic and geometric means. Find the total numbe of pairs of integers (x,y) with x le y, from the set of numbers (1,2,……,2016), such that the special mean of x and y is a perfect square.

Find the approximate value of each of the following :(65)^((1)/(3))

If the tangents to the ellipse at M and N meet at R and the normal to the parabola at M meets the x-axis at Q, then the ratio of area of the triangle MQR to area of the quadrilateral MF_1NF_2 is

[PtCl(NH_(3))_(3)][Cu(NH_(3))Cl_(3)] correct name of complex.

(dy)/(dx) +2x tan(x-y) = 1 rArr sin(x-y) =

If (x^(2)+13x+15)/((x-1)(x^(2)+2))=(A)/(x-1)+(Bx+C)/(x^(2)+2), then the descending order of A, B, C is

Evaluate the following definite integrals : int_(0)^(pi/2)sqrt(1-cos2x)dx

Evaluate the following : [[sin^2theta,cos^2theta,1],[cos^2theta,sin^2theta,1],[-10,12,2]]

Select the CORRECT order according to given property ?

int sin^(2)8xdx =

Which of the following statement(s) is / are correct