28278 + Interview Questions in Maths in Class 12 Page 15 InterviewSolution

701.	If x, y are any two non-zero real numbers, a_(ij) =xi + yj, A = (a_(ij))_(m xxn) and P, Q are two n xx n matrices such that A = xP + yQ, then
Answer» <P>P is singular and Q is non-singular P + Q is symmetric and P-Q is skew symmetric Both P + Q and P -Q are singular Both P + Q and P -Q are non-singular Answer :B

Discussion

702.	Let [x] denote the greatest integer less than or equal to x, Then the number of points where the function y=[x]+1\|1-x\|,-1 le x le 3 is not differentiable, is
Answer» 1 2 3 4 Answer :D

Discussion

703.	EvaluateDelta = {:\|(3,2,3) ,( 2,2,3),( 3,2,3)\|:}
Answer» ANSWER :`K= DELTA `

Discussion

704.	The area of the region bounded by the curves y=2^(x),y=2x-x^(2) and the lines x=0,x=2 is
Answer» Answer :`(3)/(L n 2)- (4)/(3)`

Discussion

705.	If f(x)={(sqrtx(1+xsin""1/x)","xgt0,),(-sqrt-x(1+xsin""1/x)","xlt0,),(0","""","x=0,):} , thenf(x) is
Answer» continuous as WELL as differentiable at x = 0 continuous but not differentiable at x = 0 differentiable but not continuous at x = 0 NEITHER continuous nor differentiable at x = 0 Answer :B

Discussion

706.	The reaction involved during the removal of temporary hardness of water is:
Answer» `2CaCl_(2)+(NaPO_(3))_(6)rarrNa_(2)(Ca_(2)(PO_(3))_(6))+4NaCl` `CaCl_(2)+Na_(2)CO_(3)rarrCaCO_(3)darr+2NaCl` `MgSO_(4)+Na_(2)Al_(2)Si_(2)O_(8)xH_(2)OrarrMgAl_(2)Si_(2)O_(7)xH_(2)O+Na_(2)SO_(4)` `Ca(HCO_(3))_(2)overset(Delta)rarrCaCO_(3)+H_(2)O+CO_(2)darr` Answer :d

Discussion

707.	int_(0)^(pi//2) (dx)/(1 + sin^(2)x)=
Answer» `(PI)/(2sqrt(2))` `(pi)/(SQRT(2))` `pi/2` 0 Answer :A

Discussion

708.	If A^(-1)=[[3,-1,1],[-15,6,-5],[5,-2,2]] and B=[[1,2,-2],[-1,3,0],[0,-2,1]]find(AB)^-1
Answer» SOLUTION :Initiatly find `B^(-1):B^(-1)=(adjB)/(\|B\|)=[[3,2,6],[1,1,2],[2,2,5]]` Then `(AB)^(-1)=B^(-1)A^(-1)=[[9,-3,5],[-2,1,0],[1,0,2]]`

Discussion

709.	Pick out the compound proposition which is a taugology.
Answer» <P>`(P^(^^)Q)to p` `p to q` `p to q` `p^(^^)q to ~p` ANSWER :A

Discussion

710.	If A = [{:(-2),(4),(5):}] and B = [1,3-6], verify that (AB)^(1)= B^(1) A^(1)
Answer» ANSWER :`(AB)^(1) = B^(1) A^(1)`

Discussion

711.	Find the number of terms in the expansion of (x - 2y + 3z)^10
Answer» SOLUTION :N/A

Discussion

712.	Consider the parabola y^(2)=12x and match the following lists :
Answer» Solution :`atoq,btos,c to p,d tor`. The equation of tangent having slope m is `y=mx+(3)/(m)` The line 3x-y+1=0 is tangent for m=3. The equation of NORMAL having slope m is `y=mx-6m-3m^(3)`. The line 2x-y-36=0 is normal for m=2. The CHORD of of contact w.r.t any POINT on the directrix isthe FOCAL chord which passes through the focus (3,0). The line 2x-y-6=0 passes through the focus. Chord which subtend right angle at the vertex are CONCURRENT at point `(4xx3,0),i.e.,(12,0)`. The line x-2y-12=0 passes through the point (12,0).

Discussion

713.	If ab=(ab)/3on Q^(+) , then 3(1/5**1/2)is .......
Answer» `5/160` `1/30` `3/160` `3/60` SOLUTION :N/A

Discussion

714.	Let F be the set of all on-to functions from a set A = {a_(1), a_(2), a_(3), a_(4), a_(5), a_(6)} to another set B = {b_(1), b_(2), b_(3), b_(4), b_(5)}. If a function f is selected from F at random, then find the probability that the selected function f is such that f^(-1) (b_(1)) = {a_(1)}
Answer» ANSWER :`(2)/(15)`

Discussion

715.	Prove that the segment of the tangent to the hyperbola y = (c )/(x)which is contained between the coordinate axes is bisected at the point of tangency.
Answer» `1:1` `1:2` `1:3` NONE of these Answer :A

Discussion

716.	Which of the following species have highest magnetic moment (by using spin only formula ) :-
Answer» `Cu^+` `CR^(2+)` `Mn^(2+)` `CO^(3+)`

Discussion

717.	If vec a. vec a = 0 and vec a. vec b = 0 the what can be concluded about the vector vec b?
Answer» ANSWER :VECTOR `VECB` can be any vector

Discussion

718.	The solution of 3e^(x) cos^(2) y dx + (1 + e^(x)) cot y dy = 0 is
Answer» `TAN y = c (E^(x) -1)^(3)` `tan y = c (e^(x) + 1)^(3)` `tan y = c (e^(x) -1)^(2)` `cos y = c (e^(x) -1)^(3)` Answer :A

Discussion

719.	Find the coordinates of the centre of gravity of the figure bounded by the straight line y= (2)/(pi)x and the sinusoid y = sin x (x ge 0)
Answer» ANSWER :`(12-pi^(2))/(12-3pi)`

Discussion

720.	A person observes the angle of elevation of a building as pi//6. The person proceeds towards the building with a speed of 25 (sqrt(3) - 1) m/minutes. After 2 minutes, he observes the angle of elevation as pi//4. The height (in m) of the building is ___________.
Answer» ANSWER :`50.00`

Discussion

721.	Let a, b and c be such that a + b + c= 0 and P=a^(2)/(2a^(2)+ bc) + b^(2)/(2b^(2) + ca) + c^(2)/(2c^(2) + ab)is defined. What isthe value of P.
Answer» ANSWER :1

Discussion

722.	If ""^(n-1)C_(3)+^(n-1)C_(4) gt ""^(n)C_(3) then n is just greater than integer
Answer» 5 6 4 7 Answer :D

Discussion

723.	Evaluate the following integrals. int_(0)^(pi/2)(sin^(2)x)/(1+sinxcosx)dx
Answer» ANSWER :`(PI)/(3SQRT3)`

Discussion

724.	Let A = [(0,0,-1),(0,-1,0),(-1,0,0)]. The only correct statement about the matrix A is :
Answer» A is ZERO matrix `A = (-1)= I , ` whereI is a unit matrix `A^(-1)` does not exist `A^(2)=I ` ANSWER :D

Discussion

725.	int(dx)/(e^x+e^-x)=_____.
Answer» SOLUTION :`INT(DX)/(e^x+e^-x)=int(e^xdx)/(1+e^(2X))=int(DT)/(1+t^2)` (where `e^x=trArre^xdx=dt)=tan6-1t+c`

Discussion

726.	Show that int_0^(pi/2)(cosx-sinx)/(1+sinxcosx)dx=0
Answer» SOLUTION :`int_0^(pi/2)(cosx-sinx)/(1+sinxcosx)DX` =`int_0^(pi/2)(COS(pi/2-x)-SIN(pi/2-x))/(1+sin(pi/2-x)cos(pi/2-x))dx` =`int_0^(pi/2)(cosx-sinx)/(1+sinxcosx)dx`

Discussion

727.	sin^(-1)(3 x/2) + cos^(-1 ) ( 3 x/2)= ……..
Answer» `(3 PI)/(2)` `6X` `3X` `(pi)/(2)` ANSWER :D

Discussion

728.	If \|z+barz\|+\|z-barz\|=2 , then z lies on
Answer» a straight LINES a square a CIRCLE NONE Answer :A

Discussion

729.	Integral part of (8 + 3sqrt7)^n is
Answer» an even NUMBER an ODD number an even or an odd number depending upon the value of n nothing can be SAID Answer :B

Discussion

730.	Rectangle ABCDliesin thestandard(x,y )coordinatinateplanewithcornersatA (4,2),B (6,-1) ,C(1,4), andD(-1,-1),and isrepresentedby the2xx4matrix[(4,6,1,-1),(2,-1,-4,-1)] ABCDis thentranslated, withthe cornersofthetranslatedrectanglerepresentedby thematrix [(1,3,-2,-4),(n,-3,-6,-3)] whatis thevalueof n ?
Answer» `0` `-1` `-2` `-3` ANSWER :A

Discussion

731.	Obtain the following integrals : int sqrt(5-2x+x^(2))dx
Answer» ANSWER :`(x-1)/(2) * SQRT(x^(2)-2x+5)+2log\|(x-1)+sqrt(x^(2)-2x+4)\|+C`

Discussion

732.	If veca=hati+hatj+thatk, vecb =hati+2hatj+3hatk then the value of 't for which (veca+vecb) and (veca-vecb) are perpendicular are
Answer» `pm2` `PM 2 sqrt3` `pm 3 SQRT2` `pm 3` Answer :B

Discussion

733.	Solve the following : [[x,1,3],[1,x,1],[3,6,3]]=0
Answer» Solution :`[[x,1,3],[1,x,1],[3,6,3]]`=0 or, `x[[x,1],[6,3]]-1[[1,1],[3,3]]+3[[1,x],[3,6]]`=0 or, x(3x-6)-0+3(6-3x)=0 `3x^2-6x+18-9x=0` or, `3x^2-15x+18=0` `x^2-5x+6=0` or, (x-3)(x-2)=0 `therefore` x=3 0r, x=2

Discussion

734.	Using the Lagrange formula prove the inequality x/(1+x) lt "in" (1+x) lt x " at " x gt 0
Answer» ANSWER :`(1+X)=x/(XI)(1ltxilt1+x)`

Discussion

735.	The value of e^(itheta)+e^(-itheta) is …...... .
Answer» ` 2 COS THETA` `cos theta` `2 SIN theta` `sin theta` ANSWER :A

Discussion

736.	The equation of one asymptote of the hyperbola 14x^(2)+38y+20y^(2)+x-7y-91=0" is "7x+5y-3=0. Then the other asymptote is
Answer» a,b,C b,c,a c,a,b c,b,a Answer :B

Discussion

737.	Let theta in (0,pi//2) . If the eccentricity of the hyperbola x^(2) cos^(2) theta - y^(2) = 6 cos^(2) theta is sqrt(3)times the eccentricity of the ellipse x^(2) + y^(2) cos^(2) theta= 3 theta cos^(2)theta then theta is equal to
Answer» `pi//6` `pi//4` `COS^(-1)(1//sqrt(3))` `pi//3` ANSWER :B

Discussion

738.	int_(0)^(pi//6) cos^4 3 theta.sin^2 6 theta d theta equals to
Answer» `pi/96` `5/192` `5pi/256` `5pi/192` ANSWER :D

Discussion

739.	Whichof the following is not an odd function ?
Answer» ln `((X ^(4)+x^(2)+1)/((x^(2)+x+1)^(2)))` SGN (sgn(x)) sin (tan x) `f (x),` where `f (x)+ f ((1)/(x)) =f(x) f ((1)/(x))AA x in R-{0} and f(2) =33` Answer :D

Discussion

740.	A 20 kg car moving at a speed of 0.5m//s to the right collides head on with a 35 kg car at rest. After cllision, the 35kg car is observed to move to the right with a speed of 0.2m//s. Find coefficient of restitution 'e' and fill 100e in the OMR sheet.
Answer» SOLUTION :`20xx0.5=35xx0.2+20xx"V"` `10-7=20" v"` `"v "=+(3)/(20)"m"//"s"=0.15" m"//"s"` `E=(0.2-(0.15))/(0.5-0)=(1)/(10)`

Discussion

741.	If A = [( 1, cos theta , 1,),( - cos theta ,1,cos theta ),( -1 , - cos theta ,1)] where0 lethetale2 pithen …..
Answer» `(2,OO)` `(2,4)` [2,4] [-2,2] ANSWER :C

Discussion

742.	Consider the function h(x)=(g^(2)(x))/(2)+3x^(3)-5, where g(x) is a continuous and differentiable function. It is given that h(x) is a monotonically increasing function and g(0) = 4. Then which of the following is not true ?
Answer» `g^(2)(1)gt10` `h(5)GT3` `h((5)/(2))lt2` `g^(-1)lt22` Solution :`h(X)=(g^(2)(x))/(2)+3x^(3)-5` `h'(x)gt0` `rArr""g(x)g'(x)gt-9x^(2)` `rArr""int_(0)^(1)g(x)g'(x)dxgt-int_(0)^(1)9x^(2)dx` `rArr""((g(1))^(2)-(g(x))^(2))/(2)gt-3(1-0)` `rArr""(g(1))^(2)-16gt-6` `rArr""(g(1))^(2)gt10` `""int_(-1)^(0)g(x)g'(x)dx gt -int_(-1)^(0)9x^(2)dx` `rArr""((g(0))^(2)-(g(-1))^(2))/(2)gt-3(0-(-1))` `rArr""16-(g(-1))^(2)gt-6` `rArr""(g(-1))^(2)lt22` `""h(5)gth(0)` `rArr""h(5)gt(g^(2)(0))/(2)+3(0)-5=3`

Discussion

743.	Find the sum of the infinite series 1-(4)/(5)+(4.7)/(5.10)-(4.7.10)/(5.10.15)+………
Answer» SOLUTION :N/A

Discussion

744.	For every pair of continuous functions f,g:[0,1] to R such that max {f(x) : x in [0,1]} =" max " {g(x) :x in [0,1]}, the correct statement(s) is (are).
Answer» `(f( C))^(2) + 3F( c) = (g(c ))^(2) + 3G( c)` for some `c in [0,1]` `(f( c))^(2) + f( c) = (g( c))^(2) + 3g (c )` for some `c in [0,1]` `(f(c ))^(2) + 3f (c ) = (g( c))^(2) + g( c)` for some `c in [0,1]` `(f( c))^(2) = (g( c))^(2)` for some `c in [0,1]` Answer :A::D

Discussion

745.	If the sum of deviation of values from an average is 125 and mean deviation is 8.33, then the number of terms is
Answer» 10 15 9 12 Answer :B

Discussion

746.	Evaluate : int (sqrt(1 + sin x))/( 1 + cos x) e^(-(x)/(2))dx
Answer» ANSWER :`- E^((x)/(2)) sec""(x)/(2) + C `

Discussion

747.	Statement-1 : f(x) = x^(7) + x^(6) - x^(5) + 3 is an onto function. and Statement -2 : f(x) is a continuous function.
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-2 is NOT a correct explanation for Statement-1. Statement -1 is FALSE, Statement -2 is False Statement -1 is False, Statement -2 is True Answer :B

Discussion

748.	Verify A(adjA)=(adjA) A=\|A\| I in following examples (3) and (4) [{:(2,3),(-4,-6):}]
Answer» ANSWER :`[{:(0,0),(0,0):}]`

Discussion

749.	The locus of the point, the sum of the squares of whose distances from n fixed points A_(i)(x_(i),y_(i))i=1,2,3....n. is equal to K^(2)is a circle.
Answer» passing through the origin with centre at origin with centre at a point of mean position of the given POINTS None of these Solution :Let `(x,y)` be any point on the locus, then `underset(i=1)overset(N)(Sigma)([x-x_(i)]^(2)+[y-y_(i)]^(2))=k^(2)impliesn(x^(2)+y^(2))-2x underset(i=1)overset(n)(Sigma)x_(i)-2yunderset(i=1)overset(n)(Sigma)y_(i)+underset(i=1)overset(n)(Sigma)x_(i)^(2)+underset(i=1)overset(n)(Sigma)y_(i)^(2)-K^(2)=0` `implies x^(2)+y^(2)-2((1)/(n)underset(i=1)overset(n)(Sigma)x_(i))x-2((1)/(n)underset(i=1)overset(n)(Sigma)y_(i))y+(1)/(n)(underset(i=1)overset(n)(Sigma)x_(i)^(2)+underset(i=1)overset(n)(Sigma)y_(i)^(2)-K^(2))=0` which is a CIRCLE with centre `((1)/(n)underset(i=1)overset(n)(Sigma)x_(i),(1)/(n)underset(i=1)overset(n)(Sigma)y_(i))` the point of mean position of the given points.

Discussion

750.	If 1,z_1z_2,……z_(n-1) are the n^th roots of unity, then (1-z_1)(1-z_2)…..(1-z_(n-1))=.
Answer» 0 `n-1` n 1 Answer :C

Discussion

Explore topic-wise InterviewSolutions in .

If x, y are any two non-zero real numbers, a_(ij) =xi + yj, A = (a_(ij))_(m xxn) and P, Q are two n xx n matrices such that A = xP + yQ, then

Let [x] denote the greatest integer less than or equal to x, Then the number of points where the function y=[x]+1|1-x|,-1 le x le 3 is not differentiable, is

EvaluateDelta = {:|(3,2,3) ,( 2,2,3),( 3,2,3)|:}

The area of the region bounded by the curves y=2^(x),y=2x-x^(2) and the lines x=0,x=2 is

If f(x)={(sqrtx(1+xsin""1/x)","xgt0,),(-sqrt-x(1+xsin""1/x)","xlt0,),(0","""","x=0,):} , thenf(x) is

The reaction involved during the removal of temporary hardness of water is:

int_(0)^(pi//2) (dx)/(1 + sin^(2)x)=

If A^(-1)=[[3,-1,1],[-15,6,-5],[5,-2,2]] and B=[[1,2,-2],[-1,3,0],[0,-2,1]]find(AB)^-1

Pick out the compound proposition which is a taugology.

If A = [{:(-2),(4),(5):}] and B = [1,3-6], verify that (AB)^(1)= B^(1) A^(1)

Find the number of terms in the expansion of (x - 2y + 3z)^10

Consider the parabola y^(2)=12x and match the following lists :

If a**b=(ab)/3on Q^(+) , then 3**(1/5**1/2)is .......

Let F be the set of all on-to functions from a set A = {a_(1), a_(2), a_(3), a_(4), a_(5), a_(6)} to another set B = {b_(1), b_(2), b_(3), b_(4), b_(5)}. If a function f is selected from F at random, then find the probability that the selected function f is such that f^(-1) (b_(1)) = {a_(1)}

Prove that the segment of the tangent to the hyperbola y = (c )/(x)which is contained between the coordinate axes is bisected at the point of tangency.

Which of the following species have highest magnetic moment (by using spin only formula ) :-

If vec a. vec a = 0 and vec a. vec b = 0 the what can be concluded about the vector vec b?

The solution of 3e^(x) cos^(2) y dx + (1 + e^(x)) cot y dy = 0 is

Find the coordinates of the centre of gravity of the figure bounded by the straight line y= (2)/(pi)x and the sinusoid y = sin x (x ge 0)

A person observes the angle of elevation of a building as pi//6. The person proceeds towards the building with a speed of 25 (sqrt(3) - 1) m/minutes. After 2 minutes, he observes the angle of elevation as pi//4. The height (in m) of the building is ___________.

Let a, b and c be such that a + b + c= 0 and P=a^(2)/(2a^(2)+ bc) + b^(2)/(2b^(2) + ca) + c^(2)/(2c^(2) + ab)is defined. What isthe value of P.

If ""^(n-1)C_(3)+^(n-1)C_(4) gt ""^(n)C_(3) then n is just greater than integer

Evaluate the following integrals. int_(0)^(pi/2)(sin^(2)x)/(1+sinxcosx)dx

Let A = [(0,0,-1),(0,-1,0),(-1,0,0)]. The only correct statement about the matrix A is :

int(dx)/(e^x+e^-x)=_____.

Show that int_0^(pi/2)(cosx-sinx)/(1+sinxcosx)dx=0

sin^(-1)(3 x/2) + cos^(-1 ) ( 3 x/2)= ……..

If |z+barz|+|z-barz|=2 , then z lies on

Integral part of (8 + 3sqrt7)^n is

Obtain the following integrals : int sqrt(5-2x+x^(2))dx

If veca=hati+hatj+thatk, vecb =hati+2hatj+3hatk then the value of 't for which (veca+vecb) and (veca-vecb) are perpendicular are

Solve the following : [[x,1,3],[1,x,1],[3,6,3]]=0

Using the Lagrange formula prove the inequality x/(1+x) lt "in" (1+x) lt x " at " x gt 0

The value of e^(itheta)+e^(-itheta) is …...... .

The equation of one asymptote of the hyperbola 14x^(2)+38y+20y^(2)+x-7y-91=0" is "7x+5y-3=0. Then the other asymptote is

Let theta in (0,pi//2) . If the eccentricity of the hyperbola x^(2) cos^(2) theta - y^(2) = 6 cos^(2) theta is sqrt(3)times the eccentricity of the ellipse x^(2) + y^(2) cos^(2) theta= 3 theta cos^(2)theta then theta is equal to

int_(0)^(pi//6) cos^4 3 theta.sin^2 6 theta d theta equals to

Whichof the following is not an odd function ?

A 20 kg car moving at a speed of 0.5m//s to the right collides head on with a 35 kg car at rest. After cllision, the 35kg car is observed to move to the right with a speed of 0.2m//s. Find coefficient of restitution 'e' and fill 100e in the OMR sheet.

If A = [( 1, cos theta , 1,),( - cos theta ,1,cos theta ),( -1 , - cos theta ,1)] where0 lethetale2 pithen …..

Consider the function h(x)=(g^(2)(x))/(2)+3x^(3)-5, where g(x) is a continuous and differentiable function. It is given that h(x) is a monotonically increasing function and g(0) = 4. Then which of the following is not true ?

Find the sum of the infinite series 1-(4)/(5)+(4.7)/(5.10)-(4.7.10)/(5.10.15)+………

For every pair of continuous functions f,g:[0,1] to R such that max {f(x) : x in [0,1]} =" max " {g(x) :x in [0,1]}, the correct statement(s) is (are).

If the sum of deviation of values from an average is 125 and mean deviation is 8.33, then the number of terms is

Evaluate : int (sqrt(1 + sin x))/( 1 + cos x) e^(-(x)/(2))dx

Statement-1 : f(x) = x^(7) + x^(6) - x^(5) + 3 is an onto function. and Statement -2 : f(x) is a continuous function.

Verify A(adjA)=(adjA) A=|A| I in following examples (3) and (4) [{:(2,3),(-4,-6):}]

The locus of the point, the sum of the squares of whose distances from n fixed points A_(i)(x_(i),y_(i))i=1,2,3....n. is equal to K^(2)is a circle.

If 1,z_1z_2,……z_(n-1) are the n^th roots of unity, then (1-z_1)(1-z_2)…..(1-z_(n-1))=.

If ab=(ab)/3on Q^(+) , then 3(1/5**1/2)is .......