28278 + Interview Questions in Maths in Class 12 Page 554 InterviewSolution

27651.	If forces of magnitudes 6 and 7 units acting in the direction I - 2j +2k and 2i - 2j - k, I + 2j + 2k and -2i + j - 2k respectively act on a particl which is displaced from P (2, -1, -3) to Q (5, -1, 1) then the work done by the forces is
Answer» 4 `-4` 7 `-7` ANSWER :A

Discussion

27652.	Find the equation of the circle which cuts the circles x^2+y^2-4x-6y+11=0 and x^2+y^2-10x-4y+21=0 orthogonally and has the diameter along the line 2x+3y=7.
Answer» ANSWER :`X^(2)+y^(2)-4x-2y+3=0`

Discussion

27653.	Integrate (e^(tan^(-1)x))/(1+x^2) with respect to x.
Answer» ANSWER :`e^(TAN^(-1)x)+C`

Discussion

27654.	Admission to the martial arts tournament is $30, but participants must purchase separate tickets for each event they with to participate in once inside . Each event is the same price as any other event . The graph below shows the total cost for a person, for admission and events , as a function of the number of events paid for . One of the following is the price of a single event. Which one is it ?
Answer» `$11` `$12` `$13` `$14` Answer :B

Discussion

27655.	Solve for x: lim_(x->-4)[(x^2-x-20)/(x+4)]
Answer» Answer :`A toP ; B to Q; C TOR; D toS`

Discussion

27656.	The sum of the least positive arguments of the distinct cube roots of the complex number (1-i sqrt3) is
Answer» `(5PI)/(3)` `(17pi)/(3)` `(23pi)/(3)` `(11pi)/(3)` ANSWER :D

Discussion

27657.	If vec(a)is a unit vector and (vec(x)-vec(a)).(vec(x)+vec(a))=8 then find \|vec(x)\|.
Answer» ANSWER :`\|VEC(X)\|=3`

Discussion

27658.	Using properties of determinants, prove that \|[sinalpha,cosalpha,cos(alpha+delta)],[sinbeta,cosbeta,cos(beta+delta)],[singamma,cosgamma,cos(gamma+delta)]\| = 0
Answer» Solution :Then split determinant into 2, USING PROPERTY 5. TAKE `cos delta` from `1^(st)` determinant and `sin delta` from `II^(nd)` as common factor.

Discussion

27659.	Find the values: log_(10)385/5+log_(10)81/32+3log_(10)5/3+log_(10)1/9
Answer» ANSWER :B

Discussion

27660.	Find a vector in the direction of vector 5hati-hatj+2hatk which has magnitude 8 units.
Answer» Answer :`=(40)/(sqrt(30))hati-(8)/(sqrt(30))hatj+(16)/(sqrt(30))HATK`

Discussion

27661.	A, B, C are aiming to shoot a baloon. A will succeed 4 times out of 5 attempts. The chance of B to shoot the baloon is 3 out of 4 and that of C is 2 out of 3. If the three aim the baloon simultaneously, then find the probability that atleast two of them hit the baloon.
Answer» ANSWER :`(5)/(6)`

Discussion

27662.	The volume of a cube is increasing at the rate of 8 cm^(3)//s. How fast is the surface area increasing when the length of an edge is 12 cm ?
Answer» ANSWER :`=(8)/(3)CM^(2)//SEC`.

Discussion

27663.	If x^(2) - (5m - 2)x + 4m^(2) + 10m + 25 is a perfect square then m = The roots of the equation x^(2)+2ax+a^(2)+b^(2)=0 are
Answer» RATIONAL and equal rational and not equal irrational imaginary Answer :C

Discussion

27664.	Solvethe followinglinear differential equation (dy)/(dx)+(y)/((1-x)sqrt(x))=1-sqrt(x)
Answer» ANSWER :`2/3xsqrt(X)+x+c`

Discussion

27665.	Evaluate int_(0)^(pi//2) sin^(4) x. cos^(2) x dx.
Answer» ANSWER :`pi/32`

Discussion

27666.	Show that the area enclosed between the curve y^(2)=12(x+3) and y^(2)=20(5-x) is 64sqrt((5)/(3))
Answer» ANSWER :`(20)/(3)`

Discussion

27667.	The ratio in whichthe line joining (2,-4,3)and (-4,5,-6) is divided by the plane 3x+2y+z-4 = 0is
Answer» `2:1` `4:3` `-1:4` `2:3` ANSWER :C

Discussion

27668.	Water is running into an underground right circular conical reservoir, which is 10m deep and radius of the base is 5m. If the rate of change in the volume of water in the reservoir is (3)/(sqrt2) pi m^(3)//min, then the rate (in m/min) at which water rises in it, when the water level is 4m is
Answer» `3//2` `3//8` `1//8` `1//4` ANSWER :A

Discussion

27669.	If oneof therootsof18x^3 + 81x^2+ 121 x+60=0isequalto halfthe sumof theothertwothenone of itsrootsis
Answer» `-3/2` `3/2` `2/3` `-2/3` ANSWER :A

Discussion

27670.	Find the area of the region bounded by the curves y =x^(2) +2, y =x, x =0 and x =3.
Answer» ANSWER :`(21)/(2)`

Discussion

27671.	Integrate the following functions x log2x
Answer» SOLUTION :`int x log 2x DX` =`log2x xx x^2/2 - int 1/(2x) (2xx1) x^2/2 dx` =`x^2/2 log 2x - 1/2 int x dx` =`x^2/2 log 2x-x^2/4 +C`

Discussion

27672.	If \|(x^(2)+3x,x+1,x-3),(x-1,2-x,x+4),(x-3,x-3,3x)\|=a_(0)+a_(1)x+a_(2)x^(2)+a_(3)x^(3)+a_(4)x^(4), then (a_(1)+a_(3))+2(a_(0)+a_(2)+a_(4))=
Answer» `-1` 0 1 `-29` ANSWER :A

Discussion

27673.	Range of f(x)=(1)/(1-2cosx) is :
Answer» `[(1)/(3),1]` `[-1,(1)/(3)]` `(-OO,-1]UU[(1)/(3),oo)` `[-(1)/(3),1]` Answer :B

Discussion

27674.	If the system of equations lamdax_(1)+x_(2)+x_(3)+lamdax_(2)+x_(3)=1,x_(1)+x_(2)+lamdax_(3)=1 is inconsistent then lamda equals
Answer» 5 `-2//3` `-3` `-2` ANSWER :D

Discussion

27675.	Find the general solution of the differential equation (dy)/(dx) + y cot x = 2x + x^(2).cot x.
Answer» Answer :`y = X^(2) - (PI^(2))/(4 SIN x)(sin x NE 0)`

Discussion

27676.	(Manufacturing problem) A manufacturer has three machines I, II and III installed in his factory. Machines I and II are capable of being operated for at most 12 hours whereas machine III must be operated for atleast 5 hours a day. She produces only two items M and N eachrequiring the use of all the three machines. The number of hoursrequired for producing 1 unit of each of M and N on the three machines are given in the following table : She makes a profit of Rs. 600 and Rs. 400 on items M and N respectively. How many of each should she produce so as to maximise her profit assuming that she can sell all the items that she produced? What will be the maximum profit ?
Answer» ANSWER :The manufacturer has to PRODUCE 4units of each items. The maximum profit of Rs. 4000 will be at (4, 4).

Discussion

27677.	Prove that in any DeltaABC,cos A=(b^(2)+c^(2)-a^(2))/(2bc) where a, b and c are the magnitudes of the sides opposite to the vertices A, B and C respectively.
Answer» Answer :`cos A=(B^(2)+C^(2)-a^(2))/(2BC)`

Discussion

27678.	If k_(1) and k_(2) (k_(1) gt k_(2)) are two non-zero integral values of k for which the cubic equation x^(3)+3x^(2)+k=0 has all integer roots, then the value of k_(1)-k_(2) is equal to_______
Answer» Solution :`X^(3)+3x^(2)+k=0 to ALPHA, beta, GAMMA` `alpha+beta+gamma=-3, alpha beta +beta gamma+gamma alpha=0, alpha beta gamma=-k` `alpha^(2)+beta^(2)+gamma^(2)=9` `becausealpha,beta, gamma epsilonIimpliesalpha^(2)=9, beta^(2)=0, gamma^(2)=0` or `alpha^(2)=4, beta^(2)=4, gamma^(2)=1` `alpha^(2)=4, beta^(2)=4, gamma^(2)=1` Possible roots: `+-3, 0, 0, +-2, +-2, +-1` But `alpha beta+beta gamma +gamma alpha=0` So, possible roots are `3, 0, 0, -3, 0, 0, 2, 2, -1, -2, -2 , 1` Possible non-zero valuesof `k` are `-4` and 4

Discussion

27679.	The value of 1/(sqrt(10) - sqrt(9)) - 1/(sqrt(11) - sqrt(10)) + 1/(sqrt(12) - sqrt(11)) - .... - 1/(sqrt(121) - sqrt(120)) is equal to
Answer» a. `-10` B. 11 c. 14 d. -8 Answer :D

Discussion

27680.	An oxide of certain element 'X' is x_(4)O_(6)"has" (400)/(7))% by mass of 'X' then find atomic mass of 'X'?
Answer» ANSWER :`32.00`

Discussion

27681.	The value of the determinant : \|(1,cos(beta-alpha),cos(gamma-alpha)),(cos(alpha-beta),1,cos(gamma-beta)),(cos(alpha-gamma),cos(beta-gamma),1)\| is :
Answer» `4 sinalphasinbetasingamma` `2cosalphacosbetacosgamma` `4 cosalphacosbetacosgamma` ANSWER :D

Discussion

27682.	The area of the region bounded by the curve sqrtx+sqrty=sqrta(x,ygt0) and the coondinate axes is
Answer» ANSWER :`(a^(2))/(6)`

Discussion

27683.	Statement-1 e^(x)+e^(-x) gt 2 +x^2 is an increasing function on R.
Answer» Statement-1 TRUE statement -1 is True,Statement -2is True statement -2 is a CORRECT explanation for Statement-3 Statement-1 True statement -1 is True,Statement -2is True statement -2 is not a correct explanation for Statement-3 Statement-1 True statement -1 is True,Statement -2is False Statement-1 is False ,Statement -2 is True Solution :We have `f(x)=e^x+e^(-x)-2-x^2` `rArr f(x)=e^x-e^(-x)-2X` `rArr f(x)= e^x+e^(-x)-2=((e^x-1)^2)/(e^x)gt 0 `for all `x ne 0`ltbr gt `rArr ` f(x) in INCREASING in R `rArr f(x) gtf(0) " for all " x in R , x ne 0 ` `f(x) gt 0 "for all " x (ne 0) in R` `f (x) gt f(0) " for all " x ne 0 ` `e^x+e^(-x)-2-x^2 LT 0 " for all " x ne 0 ` `rArr e^x+e^(-x) gt 2+ x^2 " for all " x ne 0` Hence both the statements are true statement-2 is a correct explanation of statment-1

Discussion

27684.	Form the differential equation of the family of circles in the second quadrant and touching the coordinate axes.
Answer» ANSWER :`(X + y)^(2) [(y')^(2) + 1] = [x + y y']^(2)`

Discussion

27685.	If the normal at the point P intersects the x-axis at (9, 0) then the eccentricity of the hyperbola is
Answer» `SQRT(5/2)` `sqrt(3/2)` `sqrt(2)` `sqrt(3)` ANSWER :B

Discussion

27686.	If \|x^(2)\| + \|x\| + 12 = 0, then x =
Answer» 3 or - 4 -3 or -4 `+-3` or `+-4` No solution Answer :D

Discussion

27687.	bar(alpha)=2hati+3hatj-hatk,bar(beta)=-hati+2hatj-4hatk and bar(gamma)=hati+hatj+hatk then (bar(alpha)xx bar(beta))*(bar(alpha)xx bar(gamma)) = …………..
Answer» 60 64 74 `-74` ANSWER :D

Discussion

27688.	4 A person is known to speak truth 2 out of 3 times. He throws a die and reports that it is 1. Find the probability that it is actually 1.
Answer» ANSWER :`(2)/(7)`

Discussion

27689.	If a_(1), a_(2),………, a_(50) are in G.P, then (a_(1) - a_(3) + a_(5) - ....... + a_(49))/(a_(2) - a_(4) + a_(6) - ....... + a_(50)) =
Answer» 0 1 `a_(1)/a_(2)` `a_(25)/a_(24)` ANSWER :C

Discussion

27690.	Find k if the following pairs of circles are orthogonal x^2+y^2+2by-k=0 x^2+y^2+2ax+8=0
Answer» ANSWER :k=8

Discussion

27691.	If A,B are square matrices of same order and B is a skew -symmetric matrix , show that A'BA is skew symmetric.
Answer» ANSWER :`=-A'BA`

Discussion

27692.	A line perpendicular to the X-axis cuts the circle x^(2)+y^(2)=9 at A and the ellipse 4x^(2)+9y^(2)=36 at B such that A and B lie in the same quadrant. If theta is the greatest acute angle between the tangents drawn to the curves at A and B, then tan theta=
Answer» `1/12` `1/(2sqrt(6))` `5/24` `5/(4sqrt(6))` ANSWER :B

Discussion

27693.	Letz_(1),z_(2),z_(3) be complex numbers, such that (i)\|z_(1)\|=\|z_(2)\| = \|z_(3)\|=1 (ii) z_(1) +z_(2) +z_(3) ne 0 z_(1)^(2) +z_(2)^(2) +z_(3)^(2) =0prove that for all integersn ge 2 , \|z_(1)^(n) +z_(2)^(n)\| in { 0,1,2,3}
Answer»

Discussion

27694.	If A=[[0,-1],[1,0]], then the incorrect option among the following is
Answer» `A^(3)-I=A(A-I)` `(A^(3)+I)=A(A^(3)-I)` `A^(4)-I=A^(2)+I` `A^(2)+I=A(A^(2)-I)` ANSWER :D

Discussion

27695.	If y=x for xgt0,y=0, for x=0,y=-x,xlt0, then at x=0, y is :
Answer» not CONTINUOUS DIFFERENTIABLE continuous but not differentiable NONE of these. ANSWER :C

Discussion

27696.	Using differentials, find the approximate value of log_(e)(4.01), given that log_(e)4 = 1.3863.
Answer» ANSWER :1.39

Discussion

27697.	If PSP^(1) is a focal chord of a parabola y^(2)=4ax and SL is its semi latusrectum then SP SL and SP^(1) are in
Answer» A.P. G.P. H.P. A.G.P. Answer :C

Discussion

27698.	Prove that the function f given by f(x) = log sin x is increasing on (0, (pi)/(2)) and decreasing on ((pi)/(2),pi).
Answer» ANSWER :`F'(X)LT 0`

Discussion

27699.	If f(x) is continuous for all x, wheref(x)={:{((x^(2)-7x+12)/((x-2)^(2))", for "x!=2),(k ", for" x = 2 ):}, then k=
Answer» 7 -7 `pm7` NONE of these Answer :A

Discussion

27700.	The longest side of a triangle is 3 times the shortest side and the third side is 2 cm shorter than the longest side. If the perimeter of the triangle is at least 61 cm, find the minimum length of the shortest side.
Answer» ANSWER :The minimum LENGTH of the SHORTEST side =x=9 cm

Discussion

Explore topic-wise InterviewSolutions in .

If forces of magnitudes 6 and 7 units acting in the direction I - 2j +2k and 2i - 2j - k, I + 2j + 2k and -2i + j - 2k respectively act on a particl which is displaced from P (2, -1, -3) to Q (5, -1, 1) then the work done by the forces is

Find the equation of the circle which cuts the circles x^2+y^2-4x-6y+11=0 and x^2+y^2-10x-4y+21=0 orthogonally and has the diameter along the line 2x+3y=7.

Integrate (e^(tan^(-1)x))/(1+x^2) with respect to x.

Solve for x: lim_(x->-4)[(x^2-x-20)/(x+4)]

The sum of the least positive arguments of the distinct cube roots of the complex number (1-i sqrt3) is

If vec(a)is a unit vector and (vec(x)-vec(a)).(vec(x)+vec(a))=8 then find |vec(x)|.

Using properties of determinants, prove that |[sinalpha,cosalpha,cos(alpha+delta)],[sinbeta,cosbeta,cos(beta+delta)],[singamma,cosgamma,cos(gamma+delta)]| = 0

Find the values: log_(10)385/5+log_(10)81/32+3log_(10)5/3+log_(10)1/9

Find a vector in the direction of vector 5hati-hatj+2hatk which has magnitude 8 units.

A, B, C are aiming to shoot a baloon. A will succeed 4 times out of 5 attempts. The chance of B to shoot the baloon is 3 out of 4 and that of C is 2 out of 3. If the three aim the baloon simultaneously, then find the probability that atleast two of them hit the baloon.

The volume of a cube is increasing at the rate of 8 cm^(3)//s. How fast is the surface area increasing when the length of an edge is 12 cm ?

If x^(2) - (5m - 2)x + 4m^(2) + 10m + 25 is a perfect square then m = The roots of the equation x^(2)+2ax+a^(2)+b^(2)=0 are

Solvethe followinglinear differential equation (dy)/(dx)+(y)/((1-x)sqrt(x))=1-sqrt(x)

Evaluate int_(0)^(pi//2) sin^(4) x. cos^(2) x dx.

Show that the area enclosed between the curve y^(2)=12(x+3) and y^(2)=20(5-x) is 64sqrt((5)/(3))

The ratio in whichthe line joining (2,-4,3)and (-4,5,-6) is divided by the plane 3x+2y+z-4 = 0is

Water is running into an underground right circular conical reservoir, which is 10m deep and radius of the base is 5m. If the rate of change in the volume of water in the reservoir is (3)/(sqrt2) pi m^(3)//min, then the rate (in m/min) at which water rises in it, when the water level is 4m is

If oneof therootsof18x^3 + 81x^2+ 121 x+60=0isequalto halfthe sumof theothertwothenone of itsrootsis

Find the area of the region bounded by the curves y =x^(2) +2, y =x, x =0 and x =3.

Integrate the following functions x log2x

If |(x^(2)+3x,x+1,x-3),(x-1,2-x,x+4),(x-3,x-3,3x)|=a_(0)+a_(1)x+a_(2)x^(2)+a_(3)x^(3)+a_(4)x^(4), then (a_(1)+a_(3))+2(a_(0)+a_(2)+a_(4))=

Range of f(x)=(1)/(1-2cosx) is :

If the system of equations lamdax_(1)+x_(2)+x_(3)+lamdax_(2)+x_(3)=1,x_(1)+x_(2)+lamdax_(3)=1 is inconsistent then lamda equals

Find the general solution of the differential equation (dy)/(dx) + y cot x = 2x + x^(2).cot x.

Prove that in any DeltaABC,cos A=(b^(2)+c^(2)-a^(2))/(2bc) where a, b and c are the magnitudes of the sides opposite to the vertices A, B and C respectively.

If k_(1) and k_(2) (k_(1) gt k_(2)) are two non-zero integral values of k for which the cubic equation x^(3)+3x^(2)+k=0 has all integer roots, then the value of k_(1)-k_(2) is equal to_______

The value of 1/(sqrt(10) - sqrt(9)) - 1/(sqrt(11) - sqrt(10)) + 1/(sqrt(12) - sqrt(11)) - .... - 1/(sqrt(121) - sqrt(120)) is equal to

An oxide of certain element 'X' is x_(4)O_(6)"has" (400)/(7))% by mass of 'X' then find atomic mass of 'X'?

The value of the determinant : |(1,cos(beta-alpha),cos(gamma-alpha)),(cos(alpha-beta),1,cos(gamma-beta)),(cos(alpha-gamma),cos(beta-gamma),1)| is :

The area of the region bounded by the curve sqrtx+sqrty=sqrta(x,ygt0) and the coondinate axes is

Statement-1 e^(x)+e^(-x) gt 2 +x^2 is an increasing function on R.

Form the differential equation of the family of circles in the second quadrant and touching the coordinate axes.

If the normal at the point P intersects the x-axis at (9, 0) then the eccentricity of the hyperbola is

If |x^(2)| + |x| + 12 = 0, then x =

bar(alpha)=2hati+3hatj-hatk,bar(beta)=-hati+2hatj-4hatk and bar(gamma)=hati+hatj+hatk then (bar(alpha)xx bar(beta))*(bar(alpha)xx bar(gamma)) = …………..

4 A person is known to speak truth 2 out of 3 times. He throws a die and reports that it is 1. Find the probability that it is actually 1.

If a_(1), a_(2),………, a_(50) are in G.P, then (a_(1) - a_(3) + a_(5) - ....... + a_(49))/(a_(2) - a_(4) + a_(6) - ....... + a_(50)) =

Find k if the following pairs of circles are orthogonal x^2+y^2+2by-k=0 x^2+y^2+2ax+8=0

If A,B are square matrices of same order and B is a skew -symmetric matrix , show that A'BA is skew symmetric.

A line perpendicular to the X-axis cuts the circle x^(2)+y^(2)=9 at A and the ellipse 4x^(2)+9y^(2)=36 at B such that A and B lie in the same quadrant. If theta is the greatest acute angle between the tangents drawn to the curves at A and B, then tan theta=

Letz_(1),z_(2),z_(3) be complex numbers, such that (i)|z_(1)|=|z_(2)| = |z_(3)|=1 (ii) z_(1) +z_(2) +z_(3) ne 0 z_(1)^(2) +z_(2)^(2) +z_(3)^(2) =0prove that for all integersn ge 2 , |z_(1)^(n) +z_(2)^(n)| in { 0,1,2,3}

If A=[[0,-1],[1,0]], then the incorrect option among the following is

If y=x for xgt0,y=0, for x=0,y=-x,xlt0, then at x=0, y is :

Using differentials, find the approximate value of log_(e)(4.01), given that log_(e)4 = 1.3863.

If PSP^(1) is a focal chord of a parabola y^(2)=4ax and SL is its semi latusrectum then SP SL and SP^(1) are in

Prove that the function f given by f(x) = log sin x is increasing on (0, (pi)/(2)) and decreasing on ((pi)/(2),pi).

If f(x) is continuous for all x, wheref(x)={:{((x^(2)-7x+12)/((x-2)^(2))", for "x!=2),(k ", for" x = 2 ):}, then k=

The longest side of a triangle is 3 times the shortest side and the third side is 2 cm shorter than the longest side. If the perimeter of the triangle is at least 61 cm, find the minimum length of the shortest side.