28278 + Interview Questions in Maths in Class 12 Page 538 InterviewSolution

26851.	Match the following. {:(I." If "(5x^(2)+2)/(x^(3)+x)=A/x+(Bx)/(x^(2)+1) " then "B=, "a) "2), (II." If "(4x)/(x^(2)-1)=A/(x-1)+B/(x+1) " then "A=, "b) "3), (III. " If "(3x+2)/(2-x-x^(2))=A/(2+x)+B/(1-x)" then "A=, "c) "-3//2), (IV." If "(2x+1)/((x-1)(x^(2)+1))=A/(x-1)+(Bx+C)/(x^(2)+1) " then "B=, "d) "-4//3):}
Answer» c, d, a, b b, a, d, c c, a, b, d c, b, a, d Answer :B

Discussion

26852.	Evaluate the following integrals int_1^2e^(4x+1)dx
Answer» SOLUTION :`int_1^2e^(4x+1)DX=[E^(4x+1)/4]_1^2=(1/4){e^9-e^5}`

Discussion

26853.	What is the maximum slope of the curve y=-x^(3)+3x^(2)+2x-27 ? Also find the point.
Answer» ANSWER :`(1,-23), 5`

Discussion

26854.	int (1)/(sqrt(sin^(2) x cos^(2) x - sin^(4) x))dx=
Answer» `- cos^(-1)` (cot x ) + C `- " COSH"^(-1)`(cot x ) + C `"cosh"^(-1)` (cot x ) + C `cos^(-1)`(cot x ) + C Answer :B

Discussion

26855.	What is the maximum value of the function sin x + cos x?
Answer» ANSWER :. MAXIMUM VALUE = `SQRT(2)`

Discussion

26856.	Let x_(1), x_(2) be the roots of x^(2)-3x +a=0 and x_(3), x_(4) be the roots of x^(2)-12x+b=0. If x_(1) lt x_(2) lt x_(3) lt x_(4) and x_(1), x_(2), x_(3) , x_(4) are in G.P., then ab equals
Answer» `(24)/(5)` 64 16 8 Answer :B

Discussion

26857.	Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is 4r/3. Also, find maximum volume in terms of volume of the sphere.
Answer» ANSWER :MAXIMUM volume of CONE `= (8)/(27)` times the volume of SPHERE

Discussion

26858.	Evaluate(i) int(xe^(x))/((x+1)^(2))dx(ii) int x^3e^(-x) dx
Answer»

Discussion

26859.	Show that * on R-{-1} defined by (a*b) =(a)/(b+1) is neither commutative nor associative
Answer» Solution :(i)` 23=(2)/(3+1)=2/4=1/2and 32=(3)/(2+1)=3/3=1` `therefore 23 NE 332` so * is not ocmmutative (II) `(23)1=1/21=(1//2)/(1+1)=1/4` `(33)=(3)/(1+1)=3/2 ` `therefore 2(31)=23/2=(2)/(3/2+1)=(2xx2/5)=4/5` Thus (23)1 ne 2(3*1)

Discussion

26860.	Expand :3sqrt(3) in ascending powers of (1)/(3)
Answer» SOLUTION :N/A

Discussion

26861.	Which of the followingstatement(s) is/are incorrect ?
Answer» The lines`(x-4)/(-3)=(y+6)/(-1)=(z+6)/(-1) and (x-1)/(-1)=(y-2)/(-2)=(z-3)/(2)` are ORTHOGONAL The planes`3x-2y-4z=3` and the PLANE `x-y-z=3` are orthogonal The function `f(x)="In"(e^(-2)+e^(x))` is monotonic increasing`AA x in R` If g is the INVERSE of the function, `f(x)="In"(e^(-2)+e^(x))" then " g(x)="In"(e^(x)-e^(-2))` Answer :A::B

Discussion

26862.	A die marked 1,2,3 in red and 4,5,6 in green is tossed. Let A be the event "the number is even" and B be the event."the number is red".Are A and B are independent?
Answer» SOLUTION :S={1,2,3,4,5,6},A={2,4,6} and B={1,2,3}THEREFORE `AnnB`={2}`rArr` P`(AnnB)`=1/6 P(A) =3/6=1/2 and P(B) =3/6=1/2therefore P(A) P(B)=1/2xx1/2=1/4`ne` P`(AnnB)` Thus,A and B are not independent.

Discussion

26863.	Image of sphere x^(2)+y^(2)+z^(2)=9 in plane 2x+3y+4z-29=0 is
Answer» `X^(2)+y^(2)+Z^(2)-8x-12y-16z+107=0` `x^(2)+y^(2)+z^(2)+8x-12y-16z+107=0` `x^(2)+y^(2)+z^(2)-8x+12y-16z+107=0` `x^(2)+y^(2)+z^(2)-8x-12y+16z+107=0` ANSWER :A

Discussion

26864.	Find the values of the following integrals int(sinhx+(1)/(sqrt(x^(2)-1)))dx,\|x\|gt1
Answer» ANSWER :`coshx+log\|X+sqrt(x^(2)-1)\|C`

Discussion

26865.	Find the value of integral int_(0)^(t)int(\|cos2x\|+\|sin2x\|)dx,"where "npilttlt(npi+(pi)/(4)).
Answer» ANSWER :`(2)/(PI)`

Discussion

26866.	If planes ax+by+cz+d=0 and a'x+b'y+c'z+d'=0 are perpendicular, then
Answer» `aa'+bb'+cc'+dd'=0` `aa'+bb'+cc'=0` `(a)/(a')=(B)/(b')=(C )/(c')` `(a)/(a')+(b)/(b')+(c )/(c')=0` ANSWER :B

Discussion

26867.	If alpha=5vec(i) -3vec(k) and beta= 2vec(i)-vec(j)+2vec(k) , then find the value of alpha . beta
Answer»

Discussion

26868.	If y^(2) = ax^(2) + bx + c where a, b c are contants then y^(3)(d^(2)y)/(dx^(2))=?
Answer» A CONSTANT A FUNCTION of X A function of y NONE of these Answer :A

Discussion

26869.	Let alpha != beta satisfy alpha^(2)+1=6alpha, beta^(2)+=6beta . Then, the quadraticequation whose roots are (alpha)/(alpha+1),(beta)/(beta+1) is
Answer» `8X^(2)+8x+1=0` `8x^(2)-8x-1=0` `8x^(2)+8x+1=0` `8x^(2)+8x-1=0` ANSWER :C

Discussion

26870.	Find the values of a and b such that the function defined by f(x)={{:(5," if "x le 2),(ax+b," if "2 lt x lt 10),(21," if "x ge 10):} is a continuous function.
Answer» `a=3, b=1` `a=1, b=1` `a=1, b=2` `a=2, b=1` ANSWER :`D`

Discussion

26871.	If the pole of a line w.r.t to the circle x^(2)+y^(2)=a^(2) lies on the circle x^(2)+y^(2)=a^(4) then the line touches the circle
Answer» `x^(2)+y^(2)=2` `x^(2)+y^(2)=1` `x^(2)+y^(2)=3` `x^(2)+y^(2)=4` Answer :B

Discussion

26872.	In a bank, principal increases continuously at the rate of 5% per year. An amount of Rs 1000 is deposited with this bank, how much will it worth after 10 years (e^(0.5) = 1.648).
Answer» ANSWER :RS 1648

Discussion

26873.	Obtain the following integrals : int (x)/(x^(4)-1)dx
Answer» ANSWER :`:. I=(1)/(4){log\|x^(2)-1\|-log\|x^(2)+1\|}+C`

Discussion

26874.	Solve the differential equation (x dy - y dx) y sin ((y)/(x)) = (y dx + x dy) x cos ((y)/(x)).
Answer» ANSWER :`SEC ((y)/(X)) = C XY`

Discussion

26875.	Let 2 planes are being contained by the vectors alpha hati+3hatj-hatk, hati+(alpha-1)hatj+2hatk and 3hati+5hatj+2hatk. If the angle between these 2 planes is theta, then the value of cos^(2)theta is equal to
Answer» `(15)/(17)` `(289)/(717)` `(289)/(2151)` `(17)/(2151)` ANSWER :C

Discussion

26876.	A plano-convex lens (focal length f_2, refractive indexmu_(2), radius of curvature R) fits exactly into a plano-concave lens (focal lengthf_(1) refractive index mu_1, radius of curvature R). Their plane surfaces are parallel to each other. Then, the focal length of the combination will be :
Answer» `f_(1)-f_(2)` `(R)/(mu_(2)-mu_(1)` `(2f_1f_(2))/(f_(1)-f_(2)` `f_(1)+f_(2)` SOLUTION :NA

Discussion

26877.	Solvethe equation 15x^3- 23x^2+ 9x-1=0
Answer» ANSWER :`1,1/3,1/5`

Discussion

26878.	D, E and F are the mid points of the sides BC, CA and AB respectively of Delta ABC. 'O' is any point Match List-I to List-II. {:(,"List I",,"List II"),((I),"OA + OB + OC is equal to......",(a),OD + OE + OF),((II),"AD + BE + CF is equal to",(b),O),((III),OE + OF + "DO is",(c),OA),((IV),AD + (2)/(3)BE + (1)/(3)"CF equal",(d),(1)/(2)C):} The correct match is
Answer» `I RARR a, II rarr B, III rarr c, IV rarr d` `I rarr a, II rarr c, III rarr d, IV rarr d` `I rarr c, II rarr d, III rarr a, IV rarr b` `I rarr c, II rarr a, III rarr b, IV rarr d` Answer :A

Discussion

26879.	A die is thrown. If E is the event the number appearing is a multiple of 3' and F be theevent the number appearing is even then
Answer» E and FARE mutally exclusive E and F are dependent E and F' are independent None of these SOLUTION :N/A

Discussion

26880.	The total revenue in Rupees received from the sale of x units of a product is give by R(x)=13x^(2)+26x+15. Find the marginal revenue when x = 7.
Answer» ANSWER :RS. 208

Discussion

26881.	Find the vector equation of the plane vecr=hati-hatj+lambda(hati+hatj+hatk)+mu(hati-2hatj+3hatk) in scalar product form. Reduce it to normal form.
Answer» ANSWER :`vecr.(5hati-2hatj-3hatk)=7`, `vecr.((5)/(SQRT(38))HATI-(2)/(sqrt(38))HATJ-(3)/(sqrt(38))hatk)=(7)/(sqrt(38))`

Discussion

26882.	The solution of x cos. (y)/(x) (y dx + x dy) = y sin.(y)/(x) (x dy - y dx) is
Answer» `C xy Cos((2y)/(X)) = 1` `c xy Cos((y)/(x)) = 1` `xy Cos((y)/(x)) = c` `c y Cos((y)/(x)) = 2X` ANSWER :C

Discussion

26883.	Lets have first derivative at c such that f'(c) = 0 and f'(c) gt 0, AA x in (c- delta c), also f'(c)gt 0, AA x in (c,c+delta), then c is a point of
Answer» LOCAL maximum Local minimum Point of INFLECTION ABSOLUTE maximum Answer :C

Discussion

26884.	Which of the following is the universal quantifier ?
Answer» `in` `SUB` `AA` `EE` ANSWER :C

Discussion

26885.	Let f(x) be a function which is differentiable any number of times and f(2x^(2)-1)=2x^(3)f(x), AA x in R. Then f^((2010))(0)= (Here f^((n))(x)=n^(th) order derivative of f at x)
Answer» `-1` 1 0 data is insufficient Solution :Replace x by `-x` `therefore""f(2x^(2)-1)=-2x^(3)f(-x)` `""2x^(3)f(x)=-2x^(3)f(-x)` `RARR""f(-x)=-f(x)` `therefore"f(x) or ODD function"` `therefore""f^((n))(0)=0`, when n is EVEN

Discussion

26886.	Let f(x) =x^(3)-3(7-a)X^(2)-3(9-a^(2))x+2 The values of parameter a if f(x) has points of extrema which are opposite in sign are
Answer» `pi` (-3,3) `(-OO,(58)/(14))` none of these Solution :`f(X)=x^(3)-3(7-a)x^(2)-3(9-a^(2))x+2` f(X)=`3x^(2)-6(7-a)x-3(9-a^(2))` for real root `Dge0` or `49+a^(2)-14a+9-a^(2)ge0 or ale58/14` when point of minma is negativepoint of maxima is also negative Hence EQUATION f(x) =`3xA^(2)-6(7-a)x-3(9-a^(2))` =0 has both roots negative sum or roots =`2(7-a)lta or a gt 7 ` which is not possible as form (1) `ale58/14` When pointof maxima is POSITIVE point of minima is also positive ltrbgt Hence equation `f(x) =3x6(2)-6(7-a)x-3(9-a^(2))=0` has both roots positive sum roots =`2(7-a)gt0 or alt7` Also product of roots is positive or `-(9-a^(2))gt0 or a^(32)gt9 or a in (-oo,-3)cup(3,oo)` From (1),(2) and (3) in `(-oo,-3)cup(3,58//14)` For points of extrema of opposite sign equation (1) has roots of opposite sign Thus `a in (-3,3).

Discussion

26887.	The reflection of the point (alpha,beta,gamma) in the xy - plane is ..........
Answer» `(ALPHA,BETA,0)` `(0,0,GAMMA)` `(-alpha,-beta,gamma)` `(alpha,beta,-gamma)` ANSWER :D

Discussion

26888.	Iff(x) = x^(4) - 12x^(3) + 17x^(2) - 9x + 7then f(x + 3) =
Answer» `x^(4) - 37X^(2) - 123x +110 ` `x^(4) - 25x^(2) - 73X -85 ` `x^(4) - 13x^(3) - 12x^(2) -15 ` `x^(4) - 47x^(2) - 125X +165 ` ANSWER :1

Discussion

26889.	Consider the lines given by L_(1):x+3y-5=0 L_(2):3x-ky-1=0 L_(3):5x+2y-12=0 Match the following lists.
Answer» SOLUTION :Given LINES are `L_(1): x+3y-5 = 0` `L_(2): 3x-ky-1 = 0` `L_(3): 5x+2y-12 = 0` `L_(1) " and " L_(3)` intersect at (2, 1) `therefore L_(1), L_(2), L_(3)` are concurrent if 6-k-1 = 0 or k=5 `"For " L_(1), L_(2)` to be parallel `(1)/(3) = (3)/(-k) RARR k = -9` `"For " L_(2), L_(3)` to be parallel `(3)/(5) = (-k)/(2) rArr k = (-6)/(5)` Thus, for k = 5, lines are concurrent and for `k = -9, (-6)/(5),` at least two lines are parallelk. So, for these values of k, lines will not FORM triangle. Obviously, for `k ne 5, -9, (-6)/(5),` lines form triangle.

Discussion

26890.	Find the principal argument Arg z.
Answer» ANSWER :`(7pi)/(12)`

Discussion

26891.	Out of 20 consecutive integers two are drawn at random. Then find the probability that the sum is even.
Answer» ANSWER :`(9)/(38)`

Discussion

26892.	Equations of tangents to the hyperbola 4x^(2)-3y^(2)=24 which makes an angle 30^(@) with y-axis are
Answer» `sqrt3x+y= pm SQRT10` `sqrt3x-y= pm 10` `sqrt3x-y= pm 5` `sqrt3x-y= pm SQRT5` ANSWER :A

Discussion

26893.	Show that sqrt3" cosec "20^(@)-sec 20^(@)=4
Answer» 4 2 1 3 Answer :A

Discussion

26894.	Which of the following is NOT true e?
Answer» `{(PTOQ)^^(qtor)}to(ptor)` is a TAUTOLOGY `(p^^~q)harr(ptoq)` is a tautology `~(PHARRQ)-=(p^^~q)vv(~p^^q)` `pto(q^^r)-=(ptoq)^^(ptor)` ANSWER :C

Discussion

26895.	If a + xb + yc = 0,a xx b + b xx c + c xx a = 6 (bxxc) then the locus of the point (x,y) is
Answer» `x^(2) + y^(2) = 1` `x + y - 5 = 0` `2X + 6y = 5 ` `x + y + 6 = 0` Answer :B

Discussion

26896.	The probability of a shooter hitting a target is (3)/(4). How many minimum number of times must "he" // "she" fire so that the probability of hitting the target at least once is more than 0.99?
Answer» ANSWER :4

Discussion

26897.	Iff: NtoN, f(x)= 2x +3then …….
Answer» fisnotone -one F isonto `f^(-1)(X)=(x-3)/(2)` `f^(-1)`not defined ANSWER :D

Discussion

26898.	Differentiate w.r.t x f (x) sin 3xsin^(3)x
Answer» SOLUTION :y = sin 3X ` sin ^(3) x` ` (dy)/(dx) = sin 3 x d/(dx) (sin^(3) x) + sin^(3) x d/(dx) (sin 3x)` = (sin 3x) ( ` 3 sin^(2) x . Cos x) + sin^(3) (3 cos 3x)` ` 3 sin^(2) x (sin 3x cos x + cos 3x sin x) ` ` 3 sin^(2) x sin 4X`

Discussion

26899.	The locus represented by xy + yz = 0 is .........
Answer» A PAIR of PERPENDICULAR LINES A pair of parallel lines A pair of parallel planes A pair of perpendicular planes Answer :D

Discussion

26900.	If the two circles x^(2)+y^(2)+2gx+c=0 and x^(2)+y^(2)-2fy-c=0 have equal radius then locus of (g,f) is
Answer» `x^(2)+y^(2)=c^(2)` `x^(2)-y^(2)=2C` `x-y^(2)=c^(2)` `x^(2)+y^(2)=2c^(2)` ANSWER :B

Discussion

Explore topic-wise InterviewSolutions in .

Evaluate the following integrals int_1^2e^(4x+1)dx

What is the maximum slope of the curve y=-x^(3)+3x^(2)+2x-27 ? Also find the point.

int (1)/(sqrt(sin^(2) x cos^(2) x - sin^(4) x))dx=

What is the maximum value of the function sin x + cos x?

Let x_(1), x_(2) be the roots of x^(2)-3x +a=0 and x_(3), x_(4) be the roots of x^(2)-12x+b=0. If x_(1) lt x_(2) lt x_(3) lt x_(4) and x_(1), x_(2), x_(3) , x_(4) are in G.P., then ab equals

Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is 4r/3. Also, find maximum volume in terms of volume of the sphere.

Evaluate(i) int(xe^(x))/((x+1)^(2))dx(ii) int x^3e^(-x) dx

Show that * on R-{-1} defined by (a*b) =(a)/(b+1) is neither commutative nor associative

Expand :3sqrt(3) in ascending powers of (1)/(3)

Which of the followingstatement(s) is/are incorrect ?

A die marked 1,2,3 in red and 4,5,6 in green is tossed. Let A be the event "the number is even" and B be the event."the number is red".Are A and B are independent?

Image of sphere x^(2)+y^(2)+z^(2)=9 in plane 2x+3y+4z-29=0 is

Find the values of the following integrals int(sinhx+(1)/(sqrt(x^(2)-1)))dx,|x|gt1

Find the value of integral int_(0)^(t)int(|cos2x|+|sin2x|)dx,"where "npilttlt(npi+(pi)/(4)).

If planes ax+by+cz+d=0 and a'x+b'y+c'z+d'=0 are perpendicular, then

If alpha=5vec(i) -3vec(k) and beta= 2vec(i)-vec(j)+2vec(k) , then find the value of alpha . beta

If y^(2) = ax^(2) + bx + c where a, b c are contants then y^(3)(d^(2)y)/(dx^(2))=?

Let alpha != beta satisfy alpha^(2)+1=6alpha, beta^(2)+=6beta . Then, the quadraticequation whose roots are (alpha)/(alpha+1),(beta)/(beta+1) is

Find the values of a and b such that the function defined by f(x)={{:(5," if "x le 2),(ax+b," if "2 lt x lt 10),(21," if "x ge 10):} is a continuous function.

If the pole of a line w.r.t to the circle x^(2)+y^(2)=a^(2) lies on the circle x^(2)+y^(2)=a^(4) then the line touches the circle

In a bank, principal increases continuously at the rate of 5% per year. An amount of Rs 1000 is deposited with this bank, how much will it worth after 10 years (e^(0.5) = 1.648).

Obtain the following integrals : int (x)/(x^(4)-1)dx

Solve the differential equation (x dy - y dx) y sin ((y)/(x)) = (y dx + x dy) x cos ((y)/(x)).

Let 2 planes are being contained by the vectors alpha hati+3hatj-hatk, hati+(alpha-1)hatj+2hatk and 3hati+5hatj+2hatk. If the angle between these 2 planes is theta, then the value of cos^(2)theta is equal to

A plano-convex lens (focal length f_2, refractive indexmu_(2), radius of curvature R) fits exactly into a plano-concave lens (focal lengthf_(1) refractive index mu_1, radius of curvature R). Their plane surfaces are parallel to each other. Then, the focal length of the combination will be :

Solvethe equation 15x^3- 23x^2+ 9x-1=0

A die is thrown. If E is the event the number appearing is a multiple of 3' and F be theevent the number appearing is even then

The total revenue in Rupees received from the sale of x units of a product is give by R(x)=13x^(2)+26x+15. Find the marginal revenue when x = 7.

Find the vector equation of the plane vecr=hati-hatj+lambda(hati+hatj+hatk)+mu(hati-2hatj+3hatk) in scalar product form. Reduce it to normal form.

The solution of x cos. (y)/(x) (y dx + x dy) = y sin.(y)/(x) (x dy - y dx) is

Lets have first derivative at c such that f'(c) = 0 and f'(c) gt 0, AA x in (c- delta c), also f'(c)gt 0, AA x in (c,c+delta), then c is a point of

Which of the following is the universal quantifier ?

Let f(x) be a function which is differentiable any number of times and f(2x^(2)-1)=2x^(3)f(x), AA x in R. Then f^((2010))(0)= (Here f^((n))(x)=n^(th) order derivative of f at x)

Let f(x) =x^(3)-3(7-a)X^(2)-3(9-a^(2))x+2 The values of parameter a if f(x) has points of extrema which are opposite in sign are

The reflection of the point (alpha,beta,gamma) in the xy - plane is ..........

Iff(x) = x^(4) - 12x^(3) + 17x^(2) - 9x + 7then f(x + 3) =

Consider the lines given by L_(1):x+3y-5=0 L_(2):3x-ky-1=0 L_(3):5x+2y-12=0 Match the following lists.

Find the principal argument Arg z.

Out of 20 consecutive integers two are drawn at random. Then find the probability that the sum is even.

Equations of tangents to the hyperbola 4x^(2)-3y^(2)=24 which makes an angle 30^(@) with y-axis are

Show that sqrt3" cosec "20^(@)-sec 20^(@)=4

Which of the following is NOT true e?

If a + xb + yc = 0,a xx b + b xx c + c xx a = 6 (bxxc) then the locus of the point (x,y) is

The probability of a shooter hitting a target is (3)/(4). How many minimum﻿ number of times must "he" // "she" fire so that the probability of hitting the target at least﻿ once is more than 0.99?

Iff: NtoN, f(x)= 2x +3then …….

Differentiate w.r.t x f (x) sin 3xsin^(3)x

The locus represented by xy + yz = 0 is .........

If the two circles x^(2)+y^(2)+2gx+c=0 and x^(2)+y^(2)-2fy-c=0 have equal radius then locus of (g,f) is

The probability of a shooter hitting a target is (3)/(4). How many minimum number of times must "he" // "she" fire so that the probability of hitting the target at least once is more than 0.99?