28278 + Interview Questions in Maths in Class 12 Page 191 InterviewSolution

9501.	If f(x) is continuous at x=a, wheref(x)=(x-a)sin((1)/(x-a)), for x!=a, then f(a)=
Answer» 1 -1 0 `OO` ANSWER :C

Discussion

9502.	int_(0)^(pi)(xdx)/(a^(2)cos^(2)x+b^(2)sin^(2)x)=
Answer» `(PI^(2))/(ab)` `(pi^(2))/(2ab)` `(pi^(2))/(4AB)` `(2pi^(2))/(3ab)` ANSWER :B

Discussion

9503.	Which of the following statements can be inferred from the data? In each of the five - year periods shown in which yearly gift shop revenue decreased, average daily full - price ticket sales also decreased. The greatest increase in total yearly gift shop revenue over any five - year period shown was $2.7 million. From 1995 to 2000, the average duration of visits to the museum increased by 12 minutes.
Answer» ANSWER :STATEMENT II only

Discussion

9504.	Sum of coefficients of terms of even powers of x in (1 - x + x^2- x^3)^7 is
Answer» `-2^17` `2^17` `2^13` `-2^13` ANSWER :C

Discussion

9505.	(i) A problem is Calculus is given to two students A and B whose chances of solving it are (1)/(3) and (1)/(4). Find the probability of the problem being solved if both of them try independently. (ii) A problem is given to three students A, B and C. The chances of their solving the same are 1//3, 1//4, 1//5 respectively. Then find the probability that the problem will be solved.
Answer» Answer :`(i) (1)/(2)` `(II) (3)/(5)`

Discussion

9506.	If 7theta=(2n+1)pi, where n=0,1,2,3,4,5,6, thenanswer the following questions. The value of sec^(2). (pi)/(7)+sec^(2). (3pi)/(7)+sec^(2). (5pi)/(7)is
Answer» -24 80 24 -80 Answer :C

Discussion

9507.	P(theta) and D(pi/2+theta) are two points on the ellipse x^2/a^2+y^2/b^2=1. Show that the locus of the point of intersection of tangents at P and Q to the ellipse is x^2/a^2+y^2/b^2=2
Answer» ANSWER :2

Discussion

9508.	If 1/2lexle1 then Cos^(-1)x+Cos^(-1)(x/2-sqrt(3-3x^(2))/2)=
Answer» `pi/2` `pi/4` `pi/3` `2COS^(-1)x-pi/3` ANSWER :A

Discussion

9509.	For (2n+1) observations x_(1), x_(2),-x_(2),..,x_(n),-x_(n) and 0, where all x's are distinct, let SD and MD denote the standard deviation and median, respectively. Then which of the following is always true ?
Answer» `SD lt MD` `SD GT MD` SD=MD Nothing can be said in general about the relationship between SD and MD Solution :On ARRANGING the given observations in ascending order, we get All NEGATIVE terms `ubrace("0")_((n+1)^(th)"term")` All positive terms Median of given observations =(n+1)th term=0 `therefore SD gt MD`

Discussion

9510.	inte^(x)((1+sinx)/(1+cosx))dx=
Answer» ANSWER :`E^(X)tanx/2+C`

Discussion

9511.	A mapping is selected at random from the set of all mappings from the set A={1,2,3} into B={1,2,3,4}. The probability that the mapping selected is many to-one, is
Answer» `(5)/(8)` `(3)/(8)` `(1)/(4)` `(24)/(64)` ANSWER :A

Discussion

9512.	Let m be a positive integer, then S=overset(m)underset(k=1)Sigmak((1)/(k)+(1)/(k+1)+(1)/(k+2)+...+(1)/(m)) is equal to:
Answer» `(1)/(4) m(m+2)` `(1)/(4)m(m+3)` `(1)/(4)m(m+4)` `(1)/(4)m(m+6)` ANSWER :B

Discussion

9513.	(i)Show that the normal to the curve 5x^(2)-10x^(3)+x+2y+6=0 at P(0,-3) meets the curve again at two points. Find the equations of the tangents to the curve at athes points. (ii) Find the length of the normal at t on the curve x = a(t+sint),y=a(1-cost)
Answer» ANSWER :(i) `2x-y-3=0` (II)`2A SIN t/2 TAN t/2`

Discussion

9514.	Let two independent eventsA and Bsuch that P(A)=0.3,P(B)=0.6 FindP(A or B)
Answer» <P> SOLUTION :GIVEN that P (A) = 0.3 and P(B) = 0.6therefore `P(A^c)`= 1-P(A) = 1-0.3=0.7 `P(B^c)` = 1-P(B) = 1-0.6=0.4 ANNB)` =P(A)+P(B)-`P(AnnB)` +0.3+0.6-0.18 +0.9-0.18=0.72

Discussion

9515.	A rectangular vessel is filled with equal volumes of water and oil, water is twice as heavy as oil. Show that the force of pressure of the mixture on the wall will reduce by one fifth if the water is replaced by oil.
Answer» <P> ANSWER :`(1)/(5)P`

Discussion

9516.	Let f :X rarr Y be an invertible function . Show that f has unique inverse . (Hint : Suppose g_(1) and g_(2) are two inverse of f. Then for all y inY,(fog_1)(y) =I_(Y) (y) = (fog_(2))(y). Use one - one ness of f).
Answer» SOLUTION :N/A

Discussion

9517.	Find the area of the region bounded by the curve y^(2)=9x,x=2,x=4 and the x-axis in the first quadrant.
Answer» ANSWER :`16-4sqrt2`

Discussion

9518.	solvetheequations 32x^3- 48 x^2+ 22 x -3=0, the roots being in A.P.
Answer» ANSWER :`1/4,1/2,3/4`

Discussion

9519.	Match the following lists and and then choose the correct code.
Answer» <P>`{:(a,b,c,d),(p,r,q,q):}` `{:(a,b,c,d),(q,p,r,s):}` `{:(a,b,c,d),(s,p,q,r):}` `{:(a,b,c,d),(r,s,q,p):}` Solution :2 a. We GET COMMON NORMAL perpendicular to y=x. So, slope `=-1rArrx+y=3a` b. Tangent to the parabola y=mx+a/m passes through the point P(h,k). `rArrm^(2)h-mk+a=0` If its roots are `m_(1)andm_(2)`, then `m_(1)m_(2)-+1` Thus, locus is x=a. c. The tangents are `y=m(x+a)+a//m`(1) `andy=(-1)/(m)(x+2a)-2am`(2) Subtracting (1) from (2), we get x+3a=0 d. If chord joining `t_(1)andt_(1)` subtends angle of `90^(@)` at vertex then `t_(1)t_(2)=-4`. Point of intersection of tangents is `(-at_(1)t_(1),-a(t_(1)+t_(1)))`. So, the locus is x=4a.

Discussion

9520.	If1/4x +2y = 11/4 and -6y -x=7, what is half
Answer» Solution :START by clearing the fractions from the first equation (by multiplying by 4) to MAKE the numbers easier to work with. Then use combination to SOLVE for y: `x + 8y=11` `(+ -x-6y=7)/(2y=18)` `y =9` TAKE half of 9 to get `9/2,` then GIRD in `9/2` or 4.5.

Discussion

9521.	Degree and order of differential equation y = x(dy)/(dx) + msqrt(1+((dy)/(dx))^(2)) are
Answer» 2,1 1,2 4,2 not defined Answer :A

Discussion

9522.	If underset(0)overset(oo)(f)(dx)/((x+sqrt(1+x^(2)))^(5))=(m)/(n)where m and relatively prime prime, then the value of (m+n) is
Answer» 31 30 29 28 Solution :Let `x+sqrt(1+x^(2))=t` `+x^(2)=t^(2)+x^(2)-2txrArr1=t^(2)-2txrArrx=(1)/(2)(t-(1)/(t))rArrdx=(1)/(2)(1+(1)/(t^(2)))dt` Now,`OVERSET(oo)underset(1)(f)(1)/(t^(5))(1)/(2)(1+(t)/(t^(2)))dt=(1)/(2)overset(oo)underset(1)(f)((1)/(t^(5))+(1)/(t^(4)))dt` `I=(-1)/(2)((1)/(4T^(4))+(1)/(6t^(6)))underset(1)overset(oo)\| ` `I=(5)/(24)=(m)/(n)` (given) So,(m+n)=29.

Discussion

9523.	If the equation (10x-5)^(2)+(10y 4)^(2)=lambda^(2) (3x+4y-1)^(2) represents a hyperbola then
Answer» `-2 LT lambda lt 2` `lambda GT 2` `lambda gt -2, lambda gt 2` `0 lt lambda lt 2` Answer :C

Discussion

9524.	Find the second order derivatives of the function. x^(20)
Answer» ANSWER :`380 X^(18)`

Discussion

9525.	A pole on the ground lenses 60^(@) to the vertical. At a point a meters away from the base of the pole on the ground, the two halves of the pole subtend the same angle. If the pole and the point are in the same vertical plane, the length of the pole is
Answer» 3a `SQRT(3)a` `(a+sqrt(3))/3` NONE of these ANSWER :B

Discussion

9526.	The value of (sin 24^(@) +sin 48^(@) +sin 96^(@)+sin192^(@)6^(2)) is
Answer» ANSWER :`3.75`

Discussion

9527.	Let Delta =\|{:(-bc,b^(2)+bc,c^(2)+bc),(a^(2)+ac,-ac,c^(2)+ac),(a^(2)+ab,b^(2)+ab,-ab):}\| and the equationx^(3)-px^(2)+qx-r=0has roots a,b,c, where a,b,c in R^(+) The value of Dleta is
Answer» `lt=9r^(3)` `gt=27r^(2)` `lt=27r^(2)` `gt=81r^(3)` ANSWER :B

Discussion

9528.	Let f:RtoR be a differentiable function having f(2)=6,f'(2)=(1)/(48).Then Lt_(x-2)int_(6)^(f(x))(4t^(3))/(x-2)dt
Answer» 24 36 12 18 Answer :D

Discussion

9529.	Let Delta =\|{:(-bc,b^(2)+bc,c^(2)+bc),(a^(2)+ac,-ac,c^(2)+ac),(a^(2)+ab,b^(2)+ab,-ab):}\| and the equationx^(3)-px^(2)+qx-r=0has roots a,b,c, where a,b,c in R^(+) If Delta =27 and a^(2)+b^(2)+c^(2)=2 then the value of sum a^(2) b is
Answer» `3(2sqrt(2)-p)` `3(2sqrt(2)-R)` `3(2sqrt(2)-q)` `3(2sqrt(2)-p-q)` Answer :B

Discussion

9530.	Let Delta =\|{:(-bc,b^(2)+bc,c^(2)+bc),(a^(2)+ac,-ac,c^(2)+ac),(a^(2)+ab,b^(2)+ab,-ab):}\| and the equationx^(3)-px^(2)+qx-r=0has roots a,b,c, where a,b,c in R^(+) If a,b,c are in GP then
Answer» <P>`R^(3)=p^(3)Q` `p^(3)=r^(3)q` `p^(3)=q^(3)r` `q^(3=p^(3)r` ANSWER :D

Discussion

9531.	Resolve (x^(3)+x-1)/((x^(2)+1)(x^(2)+2x+3)) into partial fractions.
Answer» Answer :`:.` PARTIAL fractions are, `(X-1)/(4(x^(2)+1))+(3x-1)/(4(x^(2)+2x+3))`.

Discussion

9532.	Which of the following is/are true, (you may use f(x) = In(In x)/(Inx)
Answer» `(In 2.1)^(In2.2)gt (In 2.1)^(In2.1)` `(In 4)^(In5)lt (In 5)^(In4)` `(In 30)^(In3.1)gt (In 31)^(In30)` `(In 28)^(In30)lt (In 30)^(In28)` Answer :B::C

Discussion

9533.	Find (dy)/(dx)," if "y+ sin y= cos x.
Answer» ANSWER :`y NE (2n+1)PI`.

Discussion

9534.	Calculate the log_(10)of the ratio of the catalysed and uncatalysed rate constants at 25^(@)C. If at this temp. the energy of activation of a catalysed reaction is 162 kJ and for the uncatalysed reaction the value is 350 kJ. (Assume frequency factor is same for both reaction).
Answer» `30.94` `32.94` `35.94` `40.94` Solution :`K = Ae^(Ea//RT) implies LOG K = log A-(Ea)/(2.303RT)` `log K_("cat".) = log A - (162 xx 10^(3))/(2.303 RT)` …………(i) `log K_("uncat".) = log A - (350 xx 10^(3))/(2.303RT)` ……….(ii) `eq^(N) (i) - eq^(n) (ii)` `log K_("cat".) - log K_("uncat".) = ((350-162)xx10^(3))/(2.303 RT)` `log(K_("cat".))/(K_("uncat".)) = 32.94`.

Discussion

9535.	int_(-2)^(2)\|xcos pix\|dx is equal to
Answer» `8/(PI)` `4/(pi)` `2/(pi)` `1/(pi)` ANSWER :A

Discussion

9536.	If Ais a squarematrixsuchthatA^2 =Athen(I+A)^2 -7A =……
Answer» I `I-A` `A` `3A` ANSWER :A

Discussion

9537.	If theta is tbe acute angle between the diagonals of a cube, then which one of the following is correct?
Answer» `thetalt30^@` `theta=60^@` `30^@ltthetalt60^@` `thetagt60^@` Solution : LET there be cube of side 'a'. Co-ordinates of its vertices O,A,B,C,D,E,F have be marked in the figure. Diagonals are OE, FC, GB and AD. Direction ratios `(dr_3)` of these diagonals are : `OE((a-0),(a-0),(a-0))=(a,a,a)FC((-a,a,-a),GB((-a,a,a))and AD((a,a,-a))` Their dcs are: `OE,{a/sqrt(a^2+a^2+a^2),a/sqrt(a^2+a^2+a^2),a/sqrt(a^2+a^2+a^2)}` `=(1/sqrt3,1/sqrt3,1/sqrt3)` `AD,(:a/sqrt(Sigmaa^2),a/sqrt(Sigmaa^2),(-a)/sqrt(Sigmaa^2),:)=(:1/sqrt3,1/sqrt3,(-1)/sqrt3:)` Angle ,`theta`, between AD and OE is given by `costheta=pm(1/sqrt3xx1/sqrt3+1/sqrt3xx1/sqrt3-1/sqrt3xx1/sqrt3)/sqrt({(1/sqrt3)^2+(1/sqrt3)^2+(1/sqrt3)^2}{(1/sqrt3)^2+(1/sqrt3)^2+(-1/sqrt3)^2})` `=(1/3)/(1xx1)=pm1/3` Since the cube is in positive OCTANT, we take `+1/3` So, `costheta=1/3rArrthetagt60` [Since value of `costheta` DECREASES as `theta` increases in 0 to `90^@.costheta=1" when "theta=0^@ and costheta=0" when "theta=90^@]`

Discussion

9538.	Let a, b, c be distinct non negative numbers. The vectors ahati+a hatj+chatk, hati+hatk and c hati+c hatj+b hatk lie in a plane then c is :
Answer» AM of a and B GM of a and b HM of a and b NONE of these SOLUTION :N/A

Discussion

9539.	Find the shortes and largest distance from the point (2,-7) to the circle
Answer» ANSWER :LARGEST DISTANCE = PB=r+CP=15+13=328

Discussion

9540.	Statement-1 Let three are 2010 vectors in a plane such that sum of every 2009 vectors is a multiple of remaining vector and not all vectors are multiple of each other then sum of all the vectors is equal to 0 and Statement-2 Four or more vectors are always linearly dependent vectors.
Answer» STATEMENT -1 is true, Statement -2 is true, Statement-2 is a CORRECT explanation for Statement -1 Statement-1 is true,Statement-2 is true,Statement-2is NOT a correct explanation for Statement-1 Statement-1 is True,Statement-2 is false Statement-1 is false, Statement-2 is true Answer :B

Discussion

9541.	For what value of lambda, the vectors (lambda-2)veca+vecb and (4lambda-2)veca+3vecb are collinear
Answer» 2 2, -4 4 -4 Answer :D

Discussion

9542.	A probability distribution of random variable X is as follows. b= ….., E(X) =…..
Answer» 0.1, 3.66 0.1, 16.8 0.01, 3.66 0.01, 3.4 ANSWER :A

Discussion

9543.	Evaluate int((tantheta)^(-7//6)-(tan theta)^(17//6))/(tan theta)^(1//3)(sec^(2)+tantheta)^(1/2)+(tan theta)^(1//2)(sec^(2)theta+tan theta)^(1//3)d theta.
Answer» ANSWER :`(TAN THETA+(1)/(tan theta)+1)^(1//6)`

Discussion

9544.	Maximum value of the objective function Z = ax + by in a LPP always occurs at only one corner point of the feasible region.
Answer» ANSWER :FALSE STATEMENT

Discussion

9545.	bar( r )xx bar(a)=bar(b)xx bar(a),bar( r )xx bar(b)=bar(a)xx bar(b),bar(a) ne bar(0),bar(b) ne bar(0)bar(a)ne lambda bar(b). If bar(a).bar(b)=0 then bar( r ) = ………….
Answer» `BAR(a)-bar(B)` `bar(a)+bar(b)` `bar(a)XX bar(b)+bar(a)` `bar(a)xx bar(b)+bar(b)` ANSWER :B

Discussion

9546.	Which of the following is equivalent to 8^(2) cdot 4^(0.5)?
Answer» `2^(7)` `4^(4.5)` `8^(2.5)` `16^(2)` Answer :A

Discussion

9547.	Equation of line passing through the point (1, 2) and perpendicular to the line y=3x-1 is
Answer» 1.`x+3y-7=0` 2.`x+3y+7=0` 3.`x+3y=0` 4.`x-3y=0` ANSWER :A

Discussion

9548.	The maximum value of \|x log x\| for 0 lt x le 1 is (e= 2.71)
Answer» ANSWER :0.37

Discussion

9549.	If(a, b) is midpoint of a chord passing through the vertex of the parabola y^(2)=4x then
Answer» a=2B 2A=B `a^(2)=2b` `b^(2)=2a` ANSWER :D

Discussion

9550.	Differentiate the following w.r.t.xe^(sin^-1x)
Answer» SOLUTION :`d/dx(E^(sin-1)X)=e^(sin-1)xd/dx(sin^-1x)=e^(sin-1)x1/SQRT(1-x^2)=(e^(sin-1)x)/sqrt(1-x^2)`

Discussion

Explore topic-wise InterviewSolutions in .

If f(x) is continuous at x=a, wheref(x)=(x-a)sin((1)/(x-a)), for x!=a, then f(a)=

int_(0)^(pi)(xdx)/(a^(2)cos^(2)x+b^(2)sin^(2)x)=

Sum of coefficients of terms of even powers of x in (1 - x + x^2- x^3)^7 is

If 7theta=(2n+1)pi, where n=0,1,2,3,4,5,6, thenanswer the following questions. The value of sec^(2). (pi)/(7)+sec^(2). (3pi)/(7)+sec^(2). (5pi)/(7)is

P(theta) and D(pi/2+theta) are two points on the ellipse x^2/a^2+y^2/b^2=1. Show that the locus of the point of intersection of tangents at P and Q to the ellipse is x^2/a^2+y^2/b^2=2

If 1/2lexle1 then Cos^(-1)x+Cos^(-1)(x/2-sqrt(3-3x^(2))/2)=

For (2n+1) observations x_(1), x_(2),-x_(2),..,x_(n),-x_(n) and 0, where all x's are distinct, let SD and MD denote the standard deviation and median, respectively. Then which of the following is always true ?

inte^(x)((1+sinx)/(1+cosx))dx=

A mapping is selected at random from the set of all mappings from the set A={1,2,3} into B={1,2,3,4}. The probability that the mapping selected is many to-one, is

Let m be a positive integer, then S=overset(m)underset(k=1)Sigmak((1)/(k)+(1)/(k+1)+(1)/(k+2)+...+(1)/(m)) is equal to:

(i)Show that the normal to the curve 5x^(2)-10x^(3)+x+2y+6=0 at P(0,-3) meets the curve again at two points. Find the equations of the tangents to the curve at athes points. (ii) Find the length of the normal at t on the curve x = a(t+sint),y=a(1-cost)

Let two independent eventsA and Bsuch that P(A)=0.3,P(B)=0.6 FindP(A or B)

A rectangular vessel is filled with equal volumes of water and oil, water is twice as heavy as oil. Show that the force of pressure of the mixture on the wall will reduce by one fifth if the water is replaced by oil.

Let f :X rarr Y be an invertible function . Show that f has unique inverse . (Hint : Suppose g_(1) and g_(2) are two inverse of f. Then for all y inY,(fog_1)(y) =I_(Y) (y) = (fog_(2))(y). Use one - one ness of f).

Find the area of the region bounded by the curve y^(2)=9x,x=2,x=4 and the x-axis in the first quadrant.

solvetheequations 32x^3- 48 x^2+ 22 x -3=0, the roots being in A.P.

Match the following lists and and then choose the correct code.

If1/4x +2y = 11/4 and -6y -x=7, what is half

Degree and order of differential equation y = x(dy)/(dx) + msqrt(1+((dy)/(dx))^(2)) are

If underset(0)overset(oo)(f)(dx)/((x+sqrt(1+x^(2)))^(5))=(m)/(n)where m and relatively prime prime, then the value of (m+n) is

If the equation (10x-5)^(2)+(10y 4)^(2)=lambda^(2) (3x+4y-1)^(2) represents a hyperbola then

Find the second order derivatives of the function. x^(20)

A pole on the ground lenses 60^(@) to the vertical. At a point a meters away from the base of the pole on the ground, the two halves of the pole subtend the same angle. If the pole and the point are in the same vertical plane, the length of the pole is

The value of (sin 24^(@) +sin 48^(@) +sin 96^(@)+sin192^(@)6^(2)) is

Let Delta =|{:(-bc,b^(2)+bc,c^(2)+bc),(a^(2)+ac,-ac,c^(2)+ac),(a^(2)+ab,b^(2)+ab,-ab):}| and the equationx^(3)-px^(2)+qx-r=0has roots a,b,c, where a,b,c in R^(+) The value of Dleta is

Let f:RtoR be a differentiable function having f(2)=6,f'(2)=(1)/(48).Then Lt_(x-2)int_(6)^(f(x))(4t^(3))/(x-2)dt

Let Delta =|{:(-bc,b^(2)+bc,c^(2)+bc),(a^(2)+ac,-ac,c^(2)+ac),(a^(2)+ab,b^(2)+ab,-ab):}| and the equationx^(3)-px^(2)+qx-r=0has roots a,b,c, where a,b,c in R^(+) If Delta =27 and a^(2)+b^(2)+c^(2)=2 then the value of sum a^(2) b is

Let Delta =|{:(-bc,b^(2)+bc,c^(2)+bc),(a^(2)+ac,-ac,c^(2)+ac),(a^(2)+ab,b^(2)+ab,-ab):}| and the equationx^(3)-px^(2)+qx-r=0has roots a,b,c, where a,b,c in R^(+) If a,b,c are in GP then

Resolve (x^(3)+x-1)/((x^(2)+1)(x^(2)+2x+3)) into partial fractions.

Which of the following is/are true, (you may use f(x) = In(In x)/(Inx)

Find (dy)/(dx)," if "y+ sin y= cos x.

Calculate the log_(10)of the ratio of the catalysed and uncatalysed rate constants at 25^(@)C. If at this temp. the energy of activation of a catalysed reaction is 162 kJ and for the uncatalysed reaction the value is 350 kJ. (Assume frequency factor is same for both reaction).

int_(-2)^(2)|xcos pix|dx is equal to

If Ais a squarematrixsuchthatA^2 =Athen(I+A)^2 -7A =……

If theta is tbe acute angle between the diagonals of a cube, then which one of the following is correct?

Let a, b, c be distinct non negative numbers. The vectors ahati+a hatj+chatk, hati+hatk and c hati+c hatj+b hatk lie in a plane then c is :

Find the shortes and largest distance from the point (2,-7) to the circle

Statement-1 Let three are 2010 vectors in a plane such that sum of every 2009 vectors is a multiple of remaining vector and not all vectors are multiple of each other then sum of all the vectors is equal to 0 and Statement-2 Four or more vectors are always linearly dependent vectors.

For what value of lambda, the vectors (lambda-2)veca+vecb and (4lambda-2)veca+3vecb are collinear

A probability distribution of random variable X is as follows. b= ….., E(X) =…..

Evaluate int((tantheta)^(-7//6)-(tan theta)^(17//6))/(tan theta)^(1//3)(sec^(2)+tantheta)^(1/2)+(tan theta)^(1//2)(sec^(2)theta+tan theta)^(1//3)d theta.

Maximum value of the objective function Z = ax + by in a LPP always occurs at only one corner point of the feasible region.

bar( r )xx bar(a)=bar(b)xx bar(a),bar( r )xx bar(b)=bar(a)xx bar(b),bar(a) ne bar(0),bar(b) ne bar(0)bar(a)ne lambda bar(b). If bar(a).bar(b)=0 then bar( r ) = ………….

Which of the following is equivalent to 8^(2) cdot 4^(0.5)?

Equation of line passing through the point (1, 2) and perpendicular to the line y=3x-1 is

The maximum value of |x log x| for 0 lt x le 1 is (e= 2.71)

If(a, b) is midpoint of a chord passing through the vertex of the parabola y^(2)=4x then

Differentiate the following w.r.t.xe^(sin^-1x)