28278 + Interview Questions in Maths in Class 12 Page 124 InterviewSolution

6151.	State whether the following is a probability distribution of a random variable. Give reason for your answer.
Answer» Solution :Since P(3) lt 0, the GIVEN table can't be the PROBABILITY distribution of a RANDOM variable.

Discussion

6152.	State whether the following is a probability distribution of a random variable. Give reason for your answer.
Answer» Solution :Since `0 LT P(x) lt1` for all VALUE of x and `sumP(x)=0.4+0.4+0.2=1`, the given table is the PROBABILITY DISTRIBUTION of a random variable.

Discussion

6153.	State whether the following is a probability distribution of a random variable or not. Give reason for your answer.
Answer» Solution :Since `sumP(Z) ne 1`, the given table is not the probability DISTRIBUTION of a RANDOM VARIABLE.

Discussion

6154.	State whether the following is aprobability distribution of a random variable. Give reason for your answer.
Answer» SOLUTION :Since `sumP(Z)=0.6+0.1+0.2 ne1`, the given table is not the probability distribution of a random variable.

Discussion

6155.	Evaluate :int _(-1) ^(1)(dx)/( e^(x) + 1) dx
Answer» ANSWER :`1`

Discussion

6156.	int (x)/((1 - x)^(n))dx =
Answer» `((1 - X)^(2- n))/(2 - n) + ((1 - x)^(1 -n))/(1 - n)` + C `((1 - x)^(2 + n))/(2 + n) -((1 - x)^(1+ n))/(2 + n) + c ` `((1 - x)^(2 - n))/(2 - n) -((1 - x)^(1+ n))/(1 - n) + c ` `((1- x)^(2- n))/(2 + n) + ((1 - x)^(1- n))/(1 + n) + c ` ANSWER :C

Discussion

6157.	If bar(x)xx(bar(y)xx bar(z))=(bar(x)xx bar(y))xx bar(z) then bar(y)xx(bar(z)xx bar(x)) = ………… .
Answer» `bar(Z)xx (bar(X)xx bar(y))` `bar(x)xx(bar(y)xx bar(z))` `bar(0)` `bar(x)xx(bar(z)xx bar(y))` ANSWER :C

Discussion

6158.	Let alpha, betabe the roots ofax^(2)+bx+c=0 and gamma, delta be the roots ofpx^(2)+qx+r =0and D_(1), D_(2)be the discriminants respectively. Ifalpha, beta, gamma, deltaare in A.P., thenD_(1):D_(2)is
Answer» `(a^(2))/(B^(2))` `(a^(2))/(p^(2))` `(b^(2))/(q^(2))` `(C^(2))/(R^(2))` Answer :b

Discussion

6159.	Resolve (x^(4)+13x^(2)+15)/((2x^(2)+3)(x^(2)+3)^(2)) into partial fractions
Answer» Answer :`(1)/(X^(2)+3)+(5)/((x^(2)+3)^(2))-(1)/(2X^(2)+3)`

Discussion

6160.	If alphabe the set of integral values of c for which the equations cos 2xx + c sin x =2c - 7 has solutions then find the number of distinct symmetricmatrix of order3xx3 whose treace is 18 and entries are from the set alpha
Answer» 100 125 150 180 Answer :B

Discussion

6161.	If (x_(1),y_(1)),(x_(2),y_(2)) and (x_(3),y_(3)) are the vertices of a triangle whose area is 'k' square units, then \|(x_(1),y_(1),4),(x_(2),y_(2),4),(x_(3),y_(3),4)\|^(2) is
Answer» 1)`32 k^(2)` 2)`16 k^(2)` 3)`64 k^(2)` 4)`48 k^(2)` Answer :C

Discussion

6162.	Let PSP ^(1)is a focal chord of the ellipse 4x^(2) +9y^(2) =36and SP =4, then S^(1) P^(1)=
Answer» `( 26) /(5) ` ` (36)/( 5)` ` 4` ` 5` ANSWER :A

Discussion

6163.	A box contains 4 red and 7 blue balls. Two balls are drawn at randon with replacement. Find the probability of getting (i) 2 red balls (ii) 2 balls are of blue colour (iii) one red and one blue ball is selected.
Answer» ANSWER :`(i) (16)/(121) (ii)(49)/(121)(iii)(56)/(121)`

Discussion

6164.	int_(0)^(a)(a^(2)-x^(2))^(5//2)dx=
Answer» `(PI a^(2))/(2)` `(pi a^(2))/(4)` `(2pi a^(2))/(3)` `(pi a)/(4)` Answer :B

Discussion

6165.	If alpha and beta are the eccentric angles of the ends of a focal chord of the ellipse then cos^(2)((alpha+beta)/(2))sec^(2)((alpha-beta)/(2))=
Answer» `(a^(2)+B^(2))/(a^(2))` `(a^(2)-b^(2))/(a^(2))` `(a^(2))/(a^(2)+b^(2))` `(a^(2))/(a^(2)-b^(2))` ANSWER :D

Discussion

6166.	Integrate the following function : int(dx)/(sqrt(x^(2)-6x+10))
Answer» ANSWER :`log\|(X-3)+sqrt(x^(2)-6x+10)\|+C`

Discussion

6167.	Assertion: The polynomial 5x^9+3x^5-x^4-2x^2+5 has atleast six imaginary roots. Reason: Descretes rule of sign.
Answer» (R) is ONE of the reason of prove (A) Find maximum no. of positive roots , thenfind maximum no. of negative roots. Using (R) and hence (A) can be proved . (A) is WRONG (R) cannot give CURRENT DISCUSSION to SOLVE (A) Answer :B

Discussion

6168.	Find the probability distribution of i. number of head in two tosses of a coin. ii. number of tails in the simultaneous tosses of three coins. iii.number of heads in four tosses of a coin.
Answer» ANSWER :`(##NCERT_TAM_MAT_XII_P2_C13_E04_004_A01##)` `(##NCERT_TAM_MAT_XII_P2_C13_E04_004_A02##)`

Discussion

6169.	If 2^(f(x)) = (2+x)/(2-x), x in (-2, 2) and f(x) = lambda f((8x)/(4+ x^(2))) then value 'lambda' will be
Answer» 2 `(1)/(2)` 1 `-1` ANSWER :B

Discussion

6170.	0.2 + 0.22 + 0.222 + …….. to n terms =
Answer» `(2/9) - (2/81)(1 - 10^(-N))` `n - (1/9)(1 - 10^(-n))` `(2/9)[n - (1/9)(1 - 10^(-n))]` `2/9` ANSWER :C

Discussion

6171.	IFalpha, betaare therootsofax ^2+ bx+ c=0, alpha_1 , - betathe rootsofa_1 x^2+ b _1 x + c_(1) =0thenalpha, alphaaretherootsof theequation
Answer» `(b/a+b_1/a_1)^-1x^2+x(b_1/c_1+b/c)^-1=0` `(b/a-b_1/a_1)^-1x^2-x(b_1/c_1+b/c)^-1=0` `(b/a+b_1/a_1)^-1x^2-x(b_1/c_1+b/c)^-1=0` none Answer :A

Discussion

6172.	If the value of prod_(k=1)^(50)[{:(1,2k-1),(0,1):}] is equal to [{:(1,r),(0,1):}] then r is equal to
Answer» `62500` `2500` `1250` `12500` Solution :`(B)` `[{:(1,1),(0,1):}][{:(1,3),(0,1):}]=[{:(1,4),(0,1):}]` `[{:(1,4),(0,1):}][{:(1,5),(0,1):}]=[{:(1,9),(0,1):}]` `[{:(1,9),(0,1):}][{:(1,7),(0,1):}]=[{:(1,16),(0,1):}]` If `n` is no. of matrices that are MULTIPLIED, then PRODUCT is `[{:(1,n^(2)),(0,1):}]` `:.r=2500`

Discussion

6173.	Find the value of k so that the function f(x) = {((2^(x+2) - 16)/(4^(x) - 16),"if",x ne 2),("k","if",x = 2):} is continuous at x = 2.
Answer» ANSWER :`K = (1)/(2)`

Discussion

6174.	The value of int_0^100 [ tan^(-1) x] dx is ([.] G.I. F.)
Answer» 100 `100-tan^(-1)1` `100-TAN1` `100+pi/4` Solution :We have, `int_0^100[tan^(-1)X]DX =int_(0)^(tan1)[tan^(-1)x]dx + int_(tan1)^100 [tan^(-1)x]dx` `RARR int_0^100[tan^(-1)x]dx=int_0^(tan1)0 dx + int_(tan1)^(100)1.dx=100-tan1`

Discussion

6175.	Find the approximate change in the volume V of a cube of side x meters caused by increasing the side by 2%.
Answer» ANSWER :`6%`

Discussion

6176.	Find points at which the tangent to the curve y=x^(3)-3x^(2)-9x+7 is parallel to the x-axis.
Answer» ANSWER :(3, -20) and (-1, 12)

Discussion

6177.	Evaluate the following integrals intxsin^(-1)dx
Answer» Answer :`(1)/(4)[(2X^(2)-1)SIN^(-1)x+xsqrt(1-x^(2))]+c`

Discussion

6178.	Equation of circle touching the lines.\| x- 2 \| + \| y-3\| =4is
Answer» ` (x-2 ) ^(2) + (y-3) ^(2) =1 2` ` (x-2) ^(2) + (y-3) ^(2) =4` ` (x-2) ^(2) + (y-3) ^(2) = 8` ` ( x-2) ^(2) +(y-3) ^(2) = 16` ANSWER :C

Discussion

6179.	Let f(x)={(2x+a",",x ge -1),(bx^(2)+3",",x lt -1):} and g(x)={(x+4",",0 le x le 4),(-3x-2",",-2 lt x lt 0):} If the domain of g(f(x))" is " [-1, 4],then
Answer» `a=1, b GT 5` `a=2, b gt 7` `a=2, b gt 10` `a=0, b in R` Solution :`X in [-1,2]` `or-1 le x le 2` `or -2 le 2x le 4` `or -2+a le 2x+a le 4+a` `or -2+a le -2 and 4+a le 4, i.e., a=0` b can TAKE any VALUE.

Discussion

6180.	The sum of an infinity decreasing G.P is equal to 4 and the sum of the cubes of its terms is equal to 64/. Then 5^(th) term of the progression is :
Answer» `1/4` `1/8` `1/16` `1/32` SOLUTION :Let the G.P. be, a, ar , `ar^2` `implies(a)/(1-r) =4 ""….(1)` ALSO, `a^3 + (ar)^3 + ………. = (a^3)/(1-r^3) implies(a^3)/(1-r^3)=(64)/(7)` `implies7a^3 = 64 (1-r^3) ""….(2)` USING (1) and (2) , we have `7 xx 64 (1-r)^3 = 64(1-r^3) implies2r^2 - 5R + 2 = 0impliesr=1//2,2` `therefore ` G.P. is decreasing `impliesr=1//2 ` and a=2

Discussion

6181.	Find the approximate value of root(4)(17)
Answer» ANSWER :`2.0312`

Discussion

6182.	squareABCDEF is a regular hexagone with each side a. bar(AB).bar(AF)+(1)/(2)bar(BC)^(2)= …………
Answer» a `a^(2)` `2A^(2)` 0 Answer :D

Discussion

6183.	If the angle alpha between two forces of equal magnitude is reduced to (alpha-pi//3), then the magnitude of their resultant becomes (alpha-pi//3),times of the earlier one. The angle alpha is
Answer» `pi//2` `2pi//2` `pi//4` `4pi//5` Solution :`sqrt(F^(2)+F^(2)+2F^(2)cos(ALPHA(pi)/(3)))=sqrt3xx[sqrt(F^(2)+F^(2)+2F^(2)cosalpha)]` on solving `,alpha=(2pi)/(3)"""]"`

Discussion

6184.	A circle S having centre (alpha, beta) intersect at three points A, B and C such that normals at A,B and C are concurrent at (9,6) for parabola y^(2)=4x and O origin. Then,
Answer» Sum of modulus of SLOPES of normals at points `A, B` and `C` is 6 `alpha+beta=4` Magnitude of NORMAL having negative slope is 2 Circle `S` also passes through `O` Solution :`:'y=mx-2m-m^(3)` `implies6=9m-2m-m^(3)` `impliesm^(3)-7m+6=0impliesm=1, +2, -3` `:.` Centre is `(11/2, 3/2)`

Discussion

6185.	int_(0)^(3) sqrt((x^(3))/(3-x))dx=
Answer» `(17pi)/(8)` `(27 PI)/(8)` `(34 pi)/(17)` 1 Answer :B

Discussion

6186.	Minimize and Maximize Z = 3x + 9y subject to the constraints x+3ylt=60 x+ygt=10 xlt=y x gt= 0, y gt= 0 by the graphical method .
Answer» Answer :Maximum at point (15,5) and (0,20) with VALUE 180 , Minimum at point (5,5)with value 60

Discussion

6187.	Let S be the set of all real number and let R be relation on S , defined by a R b hArr (1+ab)gt0 then, R is
Answer» REFLEXIVE and SYMMETRIC but TRANSITIVE Reflexive and transitive but not symmetric symmetric and transitive but not reflexive None of these Answer :A

Discussion

6188.	Show that the family of curves for which the slope of the tangent at any point (x,y) on it is (x^(2)+y^(2))/(2xy), is given by x^(2)-y^(2)=Cx
Answer» ANSWER :`(y^(2) - X^(2)) = PM C_(1) x or x^(2) - y^(2) = Cx`.

Discussion

6189.	If the equation x ^(2) +ax+12 =9, x ^(2) +bx +15 =0 and x^(2) + (a+b) x +36=0 have a common positive root, then b+2a equal to.
Answer» `-6` 22 6 `-22` ANSWER :B

Discussion

6190.	Which of the following options is the only CORRECT combination
Answer» `(I) (II)(R) ` `(III) (IV) (P)` `(II), (iii) (S)` `(IV) (i) (S)` Answer :C

Discussion

6191.	Findthepolynomialwithrationalcoefficientsand whoserootsare a+b,a-b,-a+b,-a-b
Answer» ANSWER :`x^4 -2 (a^2+b^2)x^2 + (a^2 -b^2)^2 =0`

Discussion

6192.	Using {1,2,3,4,5} foure digited numbers are formed without repetation at random. The probability that the number so formed is not divisible by 5 is
Answer» `(1)/(5)` `(3)/(5)` `(2)/(5)` `(4)/(5)` ANSWER :D

Discussion

6193.	vec(a),vec(b) and vec( c ) are three vector vec(a)ne0 and \|vec(a)\|=\|vec( c )\|=1,\|vec(b)\|=4,\|vec(b)xx vec( c )\|=sqrt(15). If vec(b)-2vec( c )=lambda vec(a) then the value of lambda is ………….
Answer» `-4` `-2` 1 3 Answer :A

Discussion

6194.	For a complex number Z = a ib, let hat(Z) = b + ia. If Z_(1), Z_(2) are such complex numbers, then hat(Z_(1)Z_(2)) =
Answer» `hat(Z)_(1) hat(Z)_(2)` `hat(Z)_(1) hatbar(Z)_(2)` `BAR(Z)_(1) hat(Z)_(2)` `hat(Z)_(1)Z_(2)` ANSWER :C

Discussion

6195.	A variable straight line passes through the intersection of x+2y=1,2x-y=1 and meets co-ordinate axes in A and B. The locus of mid-point of AB is :
Answer» `2x-3y=4` `(2)/(x)-(3)/(y)=6` `x+3y=10xy` `x+y=xy` Solution : Let `A(3lambda+7,2lambda+7,lambda+3)` `B(2k+1,4k-1,3k-1)` `because` DIRECTION ratios of L are 2,2,1. `implies(3lambda-2k+6)/(2)=(2lambda-4k+8)/(2)=(lambda-3k+4)/(1)` `implieslambda=2" and "k=0` `thereforeA(13,11,5),B(1,-1,-1)` `implies AB = 18`

Discussion

6196.	Let a(n) =1-(1)/(2)+(1)/(3)+…+(-1)^(n-1)(1)/(n)," then "(1)/(n+1)+(1)/(n+2)+…+(1)/(2n) is equal to
Answer» `a (2N)` `a(2n)-a(N)` `a(3N)-a(2n)` NONE of these Answer :A

Discussion

6197.	if A=[{:(-1,2,,3),(5,7,9),(-2,1,1):}]and B=[{:(-4,1,-5),(1,2,0),(1,3,1):}],thenverifythat(I) (A+B)'=A'+B',(ii) (A-b)'=A'=B'
Answer» Solution :`if A=[{:(-1,SQRT(3),2),(5,7,9),(-2,1,1):}]=[{:(-1,5,-2),(2,7,1),(3,9,1):}]` `B=[{:(-4,1,-5),(1,2,0),(1,3,1):}]=[{:(-4,1,1),(1,2,3),(-5,0,1):}]` `(i) A+B=[{:(-1,2,3),(5,7,9),(-2,1,1):}]+[{:(-4,1,-5),(1,2,0),(1,3,1):}]` `=[{:(-5,3,-2),(6,9,9),(-1,4,2):}]` `=[{:(-5 implies (A+B)'=[{:(-5,3,-2),(6,9,9),(-1,4,2):}]=[{:(-5,6,-1),(3,9,4),(-2,9,2):}]` `and A'+B'=[{:(-1,5,-2),(2,7,1),(3,9,1):}]+[{:(-4,1,1),(1,2,3),(-5,0,1):}]` `=[{:(-5,6,-1),(3,9,4),(-2,9,2):}]` `therefore(A+B)'=A'+B'` hence proved `(ii) A-B=[{:(-1,2,3),(5,7,9),(-2,1,1):}]-[{:(-4,1,-5),(1,2,0),(1,3,1):}]` `=[{:(3,1,8),(4,5,9),(-3,-2,0):}]` `implies (A-B)'=[{:(3,1,8),(4,5,9),(-3,-2,0):}]=[{:(3,4,-3),(1,5,-2),(8,9,0):}]` ` and A'-B' =[{:(-1,5,-2),(2,7,1),(3,9,1):}]-[{:(-4,1,1),(1,2,3),(-5,0,1):}]` `=[{:(3,4,-3),(1,5,-2),(8,9,0):}]` `therefore (A-B)'=A'B'` hence proved .

Discussion

6198.	A ball moving around the circle x^(2)+y^(2)-2x-4y-20=0 in anti-clockwise direction leaves it tangentially at the point P(-2,-2). After getting reflected from a straingt line, it passes through the centre of the circle. Find the equation of the straight line if its perpendicular distance from P is 5/2. You can assume that the angle of incidence is equal to the angle of reflection.
Answer» ANSWER :`=>(4sqrt3-3)X-(4+3sqrt3)y-(39-2sqrt3)=0`.

Discussion

6199.	Find graphically the minimum value of Z=5x+7y, subject to the constraints given below: 2x+y ge 8, x +2y ge 0 and x, y ge 0
Answer» SOLUTION :N/A

Discussion

6200.	Let f_(1) (x)= int_(0)^(x) f(t) dt, f_(2) (x) = int_(0)^(x) f_(1) (t) dt and f_(3) (x) = int_(0)^(x) f_(2) (t) dt if f_(3) (x) =A int_(0)^(x) f(t) (x-t)^(2) dt then the value of A is
Answer» `1` `1//2` `2` NONE of these Answer :B

Discussion

Explore topic-wise InterviewSolutions in .

State whether the following is a probability distribution of a random variable. Give reason for your answer.

State whether the following is a probability distribution of a random variable. Give reason for your answer.

State whether the following is a probability distribution of a random variable or not. Give reason for your answer.

State whether the following is aprobability distribution of a random variable. Give reason for your answer.

Evaluate :int _(-1) ^(1)(dx)/( e^(x) + 1) dx

int (x)/((1 - x)^(n))dx =

If bar(x)xx(bar(y)xx bar(z))=(bar(x)xx bar(y))xx bar(z) then bar(y)xx(bar(z)xx bar(x)) = ………… .

Let alpha, betabe the roots ofax^(2)+bx+c=0 and gamma, delta be the roots ofpx^(2)+qx+r =0and D_(1), D_(2)be the discriminants respectively. Ifalpha, beta, gamma, deltaare in A.P., thenD_(1):D_(2)is

Resolve (x^(4)+13x^(2)+15)/((2x^(2)+3)(x^(2)+3)^(2)) into partial fractions

If alphabe the set of integral values of c for which the equations cos 2xx + c sin x =2c - 7 has solutions then find the number of distinct symmetricmatrix of order3xx3 whose treace is 18 and entries are from the set alpha

If (x_(1),y_(1)),(x_(2),y_(2)) and (x_(3),y_(3)) are the vertices of a triangle whose area is 'k' square units, then |(x_(1),y_(1),4),(x_(2),y_(2),4),(x_(3),y_(3),4)|^(2) is

Let PSP ^(1)is a focal chord of the ellipse 4x^(2) +9y^(2) =36and SP =4, then S^(1) P^(1)=

A box contains 4 red and 7 blue balls. Two balls are drawn at randon with replacement. Find the probability of getting (i) 2 red balls (ii) 2 balls are of blue colour (iii) one red and one blue ball is selected.

int_(0)^(a)(a^(2)-x^(2))^(5//2)dx=

If alpha and beta are the eccentric angles of the ends of a focal chord of the ellipse then cos^(2)((alpha+beta)/(2))sec^(2)((alpha-beta)/(2))=

Integrate the following function : int(dx)/(sqrt(x^(2)-6x+10))

Assertion: The polynomial 5x^9+3x^5-x^4-2x^2+5 has atleast six imaginary roots. Reason: Descretes rule of sign.

Find the probability distribution of i. number of head in two tosses of a coin. ii. number of tails in the simultaneous tosses of three coins. iii.number of heads in four tosses of a coin.

If 2^(f(x)) = (2+x)/(2-x), x in (-2, 2) and f(x) = lambda f((8x)/(4+ x^(2))) then value 'lambda' will be

0.2 + 0.22 + 0.222 + …….. to n terms =

IFalpha, betaare therootsofax ^2+ bx+ c=0, alpha_1 , - betathe rootsofa_1 x^2+ b _1 x + c_(1) =0thenalpha, alphaaretherootsof theequation

If the value of prod_(k=1)^(50)[{:(1,2k-1),(0,1):}] is equal to [{:(1,r),(0,1):}] then r is equal to

Find the value of k so that the function f(x) = {((2^(x+2) - 16)/(4^(x) - 16),"if",x ne 2),("k","if",x = 2):} is continuous at x = 2.

The value of int_0^100 [ tan^(-1) x] dx is ([.] G.I. F.)

Find the approximate change in the volume V of a cube of side x meters caused by increasing the side by 2%.

Find points at which the tangent to the curve y=x^(3)-3x^(2)-9x+7 is parallel to the x-axis.

Evaluate the following integrals intxsin^(-1)dx

Equation of circle touching the lines.| x- 2 | + | y-3| =4is

Let f(x)={(2x+a",",x ge -1),(bx^(2)+3",",x lt -1):} and g(x)={(x+4",",0 le x le 4),(-3x-2",",-2 lt x lt 0):} If the domain of g(f(x))" is " [-1, 4],then

The sum of an infinity decreasing G.P is equal to 4 and the sum of the cubes of its terms is equal to 64/. Then 5^(th) term of the progression is :

Find the approximate value of root(4)(17)

squareABCDEF is a regular hexagone with each side a. bar(AB).bar(AF)+(1)/(2)bar(BC)^(2)= …………

If the angle alpha between two forces of equal magnitude is reduced to (alpha-pi//3), then the magnitude of their resultant becomes (alpha-pi//3),times of the earlier one. The angle alpha is

A circle S having centre (alpha, beta) intersect at three points A, B and C such that normals at A,B and C are concurrent at (9,6) for parabola y^(2)=4x and O origin. Then,

int_(0)^(3) sqrt((x^(3))/(3-x))dx=

Minimize and Maximize Z = 3x + 9y subject to the constraints x+3ylt=60 x+ygt=10 xlt=y x gt= 0, y gt= 0 by the graphical method .

Let S be the set of all real number and let R be relation on S , defined by a R b hArr (1+ab)gt0 then, R is

Show that the family of curves for which the slope of the tangent at any point (x,y) on it is (x^(2)+y^(2))/(2xy), is given by x^(2)-y^(2)=Cx

If the equation x ^(2) +ax+12 =9, x ^(2) +bx +15 =0 and x^(2) + (a+b) x +36=0 have a common positive root, then b+2a equal to.

Which of the following options is the only CORRECT combination

Findthepolynomialwithrationalcoefficientsand whoserootsare a+b,a-b,-a+b,-a-b

Using {1,2,3,4,5} foure digited numbers are formed without repetation at random. The probability that the number so formed is not divisible by 5 is

vec(a),vec(b) and vec( c ) are three vector vec(a)ne0 and |vec(a)|=|vec( c )|=1,|vec(b)|=4,|vec(b)xx vec( c )|=sqrt(15). If vec(b)-2vec( c )=lambda vec(a) then the value of lambda is ………….

For a complex number Z = a ib, let hat(Z) = b + ia. If Z_(1), Z_(2) are such complex numbers, then hat(Z_(1)Z_(2)) =

A variable straight line passes through the intersection of x+2y=1,2x-y=1 and meets co-ordinate axes in A and B. The locus of mid-point of AB is :

Let a(n) =1-(1)/(2)+(1)/(3)+…+(-1)^(n-1)(1)/(n)," then "(1)/(n+1)+(1)/(n+2)+…+(1)/(2n) is equal to

if A=[{:(-1,2,,3),(5,7,9),(-2,1,1):}]and B=[{:(-4,1,-5),(1,2,0),(1,3,1):}],thenverifythat(I) (A+B)'=A'+B',(ii) (A-b)'=A'=B'

Find graphically the minimum value of Z=5x+7y, subject to the constraints given below: 2x+y ge 8, x +2y ge 0 and x, y ge 0

Let f_(1) (x)= int_(0)^(x) f(t) dt, f_(2) (x) = int_(0)^(x) f_(1) (t) dt and f_(3) (x) = int_(0)^(x) f_(2) (t) dt if f_(3) (x) =A int_(0)^(x) f(t) (x-t)^(2) dt then the value of A is