28278 + Interview Questions in Maths in Class 12 Page 145 InterviewSolution

7201.	Evaluate the following integrals int sqrtx (3x^2+2x+3) dx
Answer» Solution :`int sqrtx (3X^2+2x+3)dx = int(3x^(1/2) X^2 + 2 x^(1/2)x +3 x^(1/2)) dx` =`int(3x^(5/2) +2x^(3/2) +3x^(1/2)) dx = (3x^(5/2+1))/(5/2+1) + (2x^(3/2+1))/(3/2+1) + (3x^(1/2+1))/(1/2+1) +c = 6/7 x^(7/2) +4/5 x^(5/2) +2x^(5/2) +c`

Discussion

7202.	Evaluate int_0^(pi/2) cos2xdx
Answer» Solution :`int_0^(pi/2) COS2X dx = ((sin2x)/2)_0^(pi/2)` `=1/2 (SIN pi-sin 0) = 0`

Discussion

7203.	The maximum value of 7e\|xlogx\| for 0ltxle1 is-
Answer» ANSWER :7

Discussion

7204.	Differntiate the following functions by proper substitution.tan^(-1)[(2x)/(1-x^2)]
Answer» Solution :`y=TAN^(-1)frac(2x)(1-X^2)`[Put x=`tan THETA` `=tan^(-1)frac(2tantheta)(1-tan^2theta)=tan^(-1)(tan2theta)` `2theta=2tan^(-1)x` `dy/dx=2/(1+x^2)`

Discussion

7205.	If z=costheta+isintheta, then (z^(2n)-1)/(z^(2n)+1)
Answer» `COS n theta` `SIN n theta` `-i sin" "n" "theta` `itan" "n" "theta` ANSWER :D

Discussion

7206.	int_(0)^(pi//2) " cosec "(x-(pi)/(3)) " cosec "(x-(pi)/(6)) dx=?
Answer» `-LOG 3` `-2 log 3` `2 log 3` ANSWER :C

Discussion

7207.	Figure shows x-t graph of a particle in rectilinear motion.Mark the correct statement(s) about the velocity in the respective region :
Answer» AB is negative OA is POSITIVE OA is increasing OAB is decreasing

Discussion

7208.	Equation of circle with centre (-a, -b) and radius sqrt(a^(2) - b^(2)) is
Answer» `X^(2) + y^(2) + 2ax + 2by + 2B^(2) = 0` `x^(2) + y^(2) - 2ax - 2by - 2b^(2) = 0` `x^(2) + y^(2) - 2ax - 2by + 2b^(2) = 0` `x^(2) + y^(2) - 2ax + 2by + 2a^(2) = 0` ANSWER :A

Discussion

7209.	If alpha is a root of z^(2) - z +1 = 0, then (alpha^(2014)+ (1)/(alpha^(2014)))+ (alpha^(2015+(1)/(alpha^(2015))))^(2) +(alpha^(2016)+(1)/(alpha^2016))^(3)+ (alpha^(2017)+ (1)/(alpha^(2017)))^(4)+ (alpha^(2018)+(1)/(alpha^(2018)))^(5)=
Answer» 8 5 3 -5 Answer :A

Discussion

7210.	cot[sum_(n=3)^32cot^-1(1+sum_(k=1)^n2K)]=
Answer» `10/3` `8/3` `14/3` `16/3` ANSWER :A

Discussion

7211.	Find area enclosed by \|y\|=1-x^(2).
Answer» ANSWER :`(8)/(3)`

Discussion

7212.	If the difference between the roots of x^(2) + ax + 1 = 0 is Jess than sqrt(5) then the set of possible values of a is
Answer» `(3, oo)` `(-oo, -3)` `(-3, -2) UU (2, 3)` `(-3 , oo)` Answer :C

Discussion

7213.	If (x+1)/(x^(3)+x)=A/x+(Bx+C)/(x^(2)+1), then find the principal value of sin^(-1)(A/B).
Answer» ANSWER :`- pi/2`

Discussion

7214.	The numerical value of middle terms in (1 - 1/x)^n (1 - x)^n is
Answer» `""^(2N)C_n` `""^nC_n` `-(""^(2n)C_n) ` `- (""^nC_n)` ANSWER :A

Discussion

7215.	Find the number of +ve integers which are less than 10^8 and 3 occurs exactly once.
Answer» ANSWER :`8xx9^7`

Discussion

7216.	which of the following compound(s) give smlling product having anesthetic use in presence of Cl_(2),NaOH,Delta.
Answer» `CH_(3)-UNDERSET(I)underset(\|)CH-CH_(3)` `CH_(3)-OVERSET(O)overset(\|\|)C-OH` `Ph-overset(O)overset(\|\|)C-CH_(3)` SOLUTION :

Discussion

7217.	If ax^(2)+2hxy+by^(2)+2gx+2fy+c=0represents parallel lines then
Answer» `sqrt(G^(2)-AC)/(H^(2)+a^(2))` `sqrt(g^(2)-ac)/(h^(2)+a^(2))` `2sqrt(g^(2)-ac)/(a(a+b))` `sqrt(g^(2)+ac)/(a(a+b))` ANSWER :C

Discussion

7218.	Let A and B be two sets containing 2 elements and 4 elements respectively the number of subsets of A xx B having 3 or more elements is
Answer» 219 256 275 510 Answer :A

Discussion

7219.	Match the columns and choose the correct answer.
Answer» `{:(,,A,B,C,D),(,a,1,2,3,4):}` `{:(,,A,B,C,D),(,b,3,5,5,1):}` `{:(,,A,B,C,D),(,c,3,5,2,1):}` `{:(,,A,B,C,D),(,d,3,2,1,5):}` ANSWER :C

Discussion

7220.	(d)/(d x ) { log (sqrt(1 +x )+ sqrt( 1 -x ))/(sqrt(1 + x ) - sqrt(1-x ))}=
Answer» `(1)/(X sqrt( 1 -x^(2)))` `(-1)/(sqrt( 1 -x^(2)))` `(-1)/(xsqrt( 1 -x^(2)))` NONE Answer :D

Discussion

7221.	Determine the differentials in each of the following cases. x^2y = 2
Answer» SOLUTION :`x^2y = 2` `RARR y = 2/x^2` `DY = - 4/x^3 DX`

Discussion

7222.	Let A=[[2,4],[3,2]] , B=[[1,3],[-2,5]] , C=[[-2,5],[3,4]] Find each of the folowing 3A-C
Answer» SOLUTION :`3A-C=[[6,12],[9,6]]-[[-2,5],[3,4]]=[[6+2,12-5],[9-3,6-4]]=[[8,7],[6,2]]`

Discussion

7223.	Evaluate the following integrals : int_(pi/6)^(pi/2)(cosecx.cotx)/(1+cosec^(2)x)dx
Answer» ANSWER :`TAN^(-1)""(1)/(3)`

Discussion

7224.	Given g(x) (x+2)/(x-1) and the line 3x+y-10=0. Then the line is
Answer» tangent to G(X) normal to g(x) chord ofg(x) NONE of these ANSWER :A

Discussion

7225.	The sum of the series 1/(2!) - 1/(3!) + 1/(4!) - …….. upto infinity is
Answer» `E^((-1)/2)` `e^(1/2)` `e^(-2)` `e^(-1)` ANSWER :D

Discussion

7226.	Find the value of the integral underset(0)overset(a) int x(a^(2)-x^(2))^(7/2) dx
Answer» ANSWER :`(a^(9))/(9)`

Discussion

7227.	A plane is passing through (1,0,0) and (0,1,0) and it makes and angle (pi)/(4) with x+y = 3. The direction rations of this plane are ............
Answer» `(1, SQRT(2), 1)` `(1,1,sqrt(2))` `(1,1,2)` `(sqrt(2),1,1)` ANSWER :B

Discussion

7228.	Find the principle value of the followingtan^(-1)(-1)
Answer» SOLUTION :`TAN (-pi/4)=-tanfracpi4=-1`and`-pi/4 in(-pi/2,pi/2)` Therefore, the principal value of `tan ^(-1) (-1)=(-1)=-pi/4^cdot`

Discussion

7229.	Integrate thefunction in Exercise. (2cos x-3 sin x)/(6 cosx+4 sin x)
Answer» ANSWER :`(1)/(2) log\|2 SIN x+3 COS x\|+c`

Discussion

7230.	Given, the angles A, B and C of triangleABC. Let M be the mid-point of segment AB and let D be the foot of the bisector of angleC. Find the ratio of (Area Of triangleCDM)/(Area of triangleABC) and also cosphi=cosangleDCM.
Answer» ANSWER :`(sinA-sinB)/(2(sinA+sinB))`

Discussion

7231.	Let a,r,s,t be non-zero real numbers. Let P (at^(2), 2at),Q R(ar^(2), 2ar) and S (as^(2), 2as) be distinct point on the parabola y^(2) = 4ax. Suppose the PQ si the focal chord and line QR and PK are parallel, where K is point (2a, 0) It st = 1, then the tangent at P and the normal at S to the parabola meet at a point whose ordinate is
Answer» `((t^(2) + 1)^(2))/(2T^(3))` `(a(t^(2) + 1)^(2))/(2t^(3))` `(a(t^(2) + 1)^(2))/(t^(3))` `(a(t^(2) + 2)^(2))/(t^(3))` SOLUTION :PLAN EQUATION of tangent and NORMAL at `(at^(2), 2at)` are given by `ty = x + at^(2)` and `y + tx = 2a + at^(3)`, respectively. Tangent at `P + ty = x + at^(2)` or `y = (x)/(t) + at` Normal at `S : y (x)/(t) = (2a)/(t) + (a)/(t^(3))` Solving `2y = at + (2a)/(t) + (a)/(t^(3)) implies y = (a(t^(3) + 1)^(2))/(2t^(3))`

Discussion

7232.	Integrate the functions in exercise. (x^(2))/(1-x^(6))
Answer» ANSWER :`I=(1)/(6)log\|(1+x^(3))/(1-x^(3))\|+C`

Discussion

7233.	Find the number of words of arranging the letters of the word 'MISSING' which do not begin with 'S'.
Answer» ANSWER :900

Discussion

7234.	If A(5,-4) and B(7,6) are points in a plane, then the set of all points P(x,y) in the plane such that AP:PB=2:3 is .
Answer» a CIRCLE a HYPERBOLA an ELLIPSE a PARABOLA ANSWER :A

Discussion

7235.	If one root of the equation x^(2)+px+12=0 is 4, while the equation x^(2)+px+q=0 has equal roots, then the value of q is
Answer» `4` `12` `3` `(49)/(4)` ANSWER :D

Discussion

7236.	The sum sum_(i=0)^(m)((10)/(i))((20)/(m-i)) is maximum when m is
Answer» 5 10 15 20 Answer :C

Discussion

7237.	The integral int (dx)/(x^(2)(x^(4)+1)^(3//4)) equals
Answer» `((x^(4)+1)/(x^(4)))^(1//4)+c` `-((x^(4)+1)/(x^(4)))^(1//4)+c` `1+(1)/(x^(4))+c` `x^(4)+1+c` ANSWER :2

Discussion

7238.	We have f (x) lim_(n to oo)cos (x)/(2) cos (x)/(2^(2)) cos (x)/(2^(3)) cos (x)/(2^(4))…… ….cos (x)/(2^(n)) = ("sin" x)/(2^(n) "sin" (x)/(2^(n))) using the identity lim_(n to oo)sum_(k=1)^(n)tan ((x)/(2^(k))) equals
Answer» `(1)/(x - TAN x` `(1)/(x) - COT x` `x + cot x` `x + tan x` ANSWER :B

Discussion

7239.	We have f (x) lim_(n to oo)cos (x)/(2) cos (x)/(2^(2)) cos (x)/(2^(3)) cos (x)/(2^(4))…… ….cos (x)/(2^(n)) = ("sin" x)/(2^(n) "sin" (x)/(2^(n))) using the identity lim_(n to oo) sum_(k=1)^(n)(1)/(2^(2k)) sec^(2) ((x)/(2^(k))) equals
Answer» `COSEC^(2) X - (1)/(x^(2))` `cosec^(2) x + (1)/(x^(2))` `cosec^(2) x - x^(2)` `cosec^(2) x+ x^(2)` ANSWER :A

Discussion

7240.	The solution of the differential equation (dy)/(dx)+(y)/(x)=(1)/((1+lnx+lny)^(2)) is (where, c is an arbitrary constant)
Answer» `XY[1+(ln(xy)^(2))]=(X^(2))/(2)+c` `1+(ln(xy))^(2)=(x^(2))/(2)+y+c` `xy(1+ln(xy))=(x^(2))/(2)+c` `xy(1+ln(xy))=(x)/(2)+c` Answer :A

Discussion

7241.	If a, b and c are in geometric progression and the roots of the equation ax^(2) + 2bx + c = 0 are alpha and beta and those of cx^(2) + 2bx + a = 0 are gamma and delta
Answer» `ALPHA != BETA != GAMMA != delta` `alpha != beta and gamma != delta` `a alpha = a beta and c gamma = c delta` `alpha = beta and gamma = delta` ANSWER :C

Discussion

7242.	If (sinalpha+icosalpha)^4(cos2alpha-isin2alpha)^(-2)=costheta+isintheta," then "theta=
Answer» 0 `4alpha` `6alpha` `5alpha` ANSWER :A

Discussion

7243.	Find the approximate value of f(5.001), where f(x)=x^(3)-7x^(2)+15.
Answer» ANSWER :`=-34.995`

Discussion

7244.	Evaluate int tan^(6) x dx
Answer» ANSWER :`(TAN^(5))/(5)-(tan^3)/(3)+tanx+c`

Discussion

7245.	Differentiate the functions given in Exercises 1 to 11 w.r.t. x. ( x)^(cos x)
Answer»

Discussion

7246.	Find the area bounded by the curves (x -1)^(2) + y^(2) = 1 and x^(2) + y^(2) = 1.
Answer» ANSWER :`((2PI)/(3) -sqrt3/2)`

Discussion

7247.	Let S = {a_1, a_2,…... a_n} where a_1, a_2………, a_n are nonzero real numbers. If the number of ordered pairs(a_(i),a_(j)),with i < j such that a_(i)a_(j) gt 0is 99 and the number of ordered pairs (a_(i),a_(j)) with i lt jsuch that a_(i)a_(j) lt 0is 91, then n is equal to
Answer» 11 13 20 18 Answer :C

Discussion

7248.	Integrate the following int(x)/(sqrt(x^2-a^2)dx
Answer» Solution :`INT(X)/sqrt(x^2-a^2)dx [ put `x^2-a^2=t^2` then 2xdx=2tdt or xdx=tdt] `int(tdt)/t=intdt=t+C `sqrt(x^2-a^2)+C`

Discussion

7249.	If O is origin and affixes of P, Q, R are respectively z, iz, z + iz. Locate the points on complex plane. If DeltaPQR = 200then find sides of quadrilateral OPRQ
Answer» ANSWER :`OP=OQ=PR=QR=20`

Discussion

7250.	int sqrt(tan x)dx
Answer» ANSWER :`(1)/(sqrt(2))log\|(sinx+cos X)+ sqrt(2 sinx+cosx)\|+C`

Discussion

Explore topic-wise InterviewSolutions in .

Evaluate the following integrals int sqrtx (3x^2+2x+3) dx

Evaluate int_0^(pi/2) cos2xdx

The maximum value of 7e|xlogx| for 0ltxle1 is-

Differntiate the following functions by proper substitution.tan^(-1)[(2x)/(1-x^2)]

If z=costheta+isintheta, then (z^(2n)-1)/(z^(2n)+1)

int_(0)^(pi//2) " cosec "(x-(pi)/(3)) " cosec "(x-(pi)/(6)) dx=?

Figure shows x-t graph of a particle in rectilinear motion.Mark the correct statement(s) about the velocity in the respective region :

Equation of circle with centre (-a, -b) and radius sqrt(a^(2) - b^(2)) is

If alpha is a root of z^(2) - z +1 = 0, then (alpha^(2014)+ (1)/(alpha^(2014)))+ (alpha^(2015+(1)/(alpha^(2015))))^(2) +(alpha^(2016)+(1)/(alpha^2016))^(3)+ (alpha^(2017)+ (1)/(alpha^(2017)))^(4)+ (alpha^(2018)+(1)/(alpha^(2018)))^(5)=

cot[sum_(n=3)^32cot^-1(1+sum_(k=1)^n2K)]=

Find area enclosed by |y|=1-x^(2).

If the difference between the roots of x^(2) + ax + 1 = 0 is Jess than sqrt(5) then the set of possible values of a is

If (x+1)/(x^(3)+x)=A/x+(Bx+C)/(x^(2)+1), then find the principal value of sin^(-1)(A/B).

The numerical value of middle terms in (1 - 1/x)^n (1 - x)^n is

Find the number of +ve integers which are less than 10^8 and 3 occurs exactly once.

which of the following compound(s) give smlling product having anesthetic use in presence of Cl_(2),NaOH,Delta.

If ax^(2)+2hxy+by^(2)+2gx+2fy+c=0represents parallel lines then

Let A and B be two sets containing 2 elements and 4 elements respectively the number of subsets of A xx B having 3 or more elements is

Match the columns and choose the correct answer.

(d)/(d x ) { log (sqrt(1 +x )+ sqrt( 1 -x ))/(sqrt(1 + x ) - sqrt(1-x ))}=

Determine the differentials in each of the following cases. x^2y = 2

Let A=[[2,4],[3,2]] , B=[[1,3],[-2,5]] , C=[[-2,5],[3,4]] Find each of the folowing 3A-C

Evaluate the following integrals : int_(pi/6)^(pi/2)(cosecx.cotx)/(1+cosec^(2)x)dx

Given g(x) (x+2)/(x-1) and the line 3x+y-10=0. Then the line is

The sum of the series 1/(2!) - 1/(3!) + 1/(4!) - …….. upto infinity is

Find the value of the integral underset(0)overset(a) int x(a^(2)-x^(2))^(7/2) dx

A plane is passing through (1,0,0) and (0,1,0) and it makes and angle (pi)/(4) with x+y = 3. The direction rations of this plane are ............

Find the principle value of the followingtan^(-1)(-1)

Integrate thefunction in Exercise. (2cos x-3 sin x)/(6 cosx+4 sin x)

Given, the angles A, B and C of triangleABC. Let M be the mid-point of segment AB and let D be the foot of the bisector of angleC. Find the ratio of (Area Of triangleCDM)/(Area of triangleABC) and also cosphi=cosangleDCM.

Integrate the functions in exercise. (x^(2))/(1-x^(6))

Find the number of words of arranging the letters of the word 'MISSING' which do not begin with 'S'.

If A(5,-4) and B(7,6) are points in a plane, then the set of all points P(x,y) in the plane such that AP:PB=2:3 is .

If one root of the equation x^(2)+px+12=0 is 4, while the equation x^(2)+px+q=0 has equal roots, then the value of q is

The sum sum_(i=0)^(m)((10)/(i))((20)/(m-i)) is maximum when m is

The integral int (dx)/(x^(2)(x^(4)+1)^(3//4)) equals

We have f (x) lim_(n to oo)cos (x)/(2) cos (x)/(2^(2)) cos (x)/(2^(3)) cos (x)/(2^(4))…… ….cos (x)/(2^(n)) = ("sin" x)/(2^(n) "sin" (x)/(2^(n))) using the identity lim_(n to oo)sum_(k=1)^(n)tan ((x)/(2^(k))) equals

We have f (x) lim_(n to oo)cos (x)/(2) cos (x)/(2^(2)) cos (x)/(2^(3)) cos (x)/(2^(4))…… ….cos (x)/(2^(n)) = ("sin" x)/(2^(n) "sin" (x)/(2^(n))) using the identity lim_(n to oo) sum_(k=1)^(n)(1)/(2^(2k)) sec^(2) ((x)/(2^(k))) equals

The solution of the differential equation (dy)/(dx)+(y)/(x)=(1)/((1+lnx+lny)^(2)) is (where, c is an arbitrary constant)

If a, b and c are in geometric progression and the roots of the equation ax^(2) + 2bx + c = 0 are alpha and beta and those of cx^(2) + 2bx + a = 0 are gamma and delta

If (sinalpha+icosalpha)^4(cos2alpha-isin2alpha)^(-2)=costheta+isintheta," then "theta=

Find the approximate value of f(5.001), where f(x)=x^(3)-7x^(2)+15.

Evaluate int tan^(6) x dx

Differentiate the functions given in Exercises 1 to 11 w.r.t. x. ( x)^(cos x)

Find the area bounded by the curves (x -1)^(2) + y^(2) = 1 and x^(2) + y^(2) = 1.

Let S = {a_1, a_2,…... a_n} where a_1, a_2………, a_n are nonzero real numbers. If the number of ordered pairs(a_(i),a_(j)),with i < j such that a_(i)a_(j) gt 0is 99 and the number of ordered pairs (a_(i),a_(j)) with i lt jsuch that a_(i)a_(j) lt 0is 91, then n is equal to

Integrate the following int(x)/(sqrt(x^2-a^2)dx

If O is origin and affixes of P, Q, R are respectively z, iz, z + iz. Locate the points on complex plane. If DeltaPQR = 200then find sides of quadrilateral OPRQ

int sqrt(tan x)dx