14949 + Interview Questions in Maths in Class 11 Page 9 InterviewSolution

401.	If bara=2bari+barj-bark,barb=-bari+2barj-4bark,barc=bari+barj+bark then find (baraxxbarb).(barbxxbarc)
Answer» ANSWER :`-54`

Discussion

402.	Find the ratio in which the line segment joining the points (2, -1, 3) and (-1, 2, 1) is divided by the plane x + y + z = 5.
Answer» ANSWER :`1 : 3` (EXTERNALLY)

Discussion

403.	cos^(3)110^(@)+cos^(3)10^(@)+cos^(3)130^(@)=
Answer» `3//4` `3//8` `(3SQRT3)/8` `(3sqrt3)/4` ANSWER :C

Discussion

404.	A ray of light coming from the point (1,2)axis and is reflected at a point A on the coordinates passes through (6,5). Find the coordinate of A
Answer» ANSWER :`:.AIS (3.5,0)`

Discussion

405.	Let A be a matrix of rank r. Then,
Answer» `"RANK " (A^T)=R` `"rank "(A^T)LTR` `"rank " (A^T)gtr` NONE of these Answer :A

Discussion

406.	If the axes are rotated through an angle 30^(0), then find the coordinates of (0, 5) in the new system.
Answer» ANSWER :`(5/2,(5SQRT3)/2)`

Discussion

407.	The value of cosec 10^(@) + cosec 50^(@) -cosec 70^(@) is"_________"
Answer» ANSWER :6

Discussion

408.	Findlimit of the following if it exists: lim_(xto0)(x(e^(x)-1))/(1-cosx)
Answer» ANSWER :2

Discussion

409.	A particle moves in a straight line according to the law v^(2) = 4a (x sin x + cos x) wher v is the velocity of a particle at a distance x from the fixed point then the acceleration is
Answer» 2axsinx axsinx axcosx 2axcosx Answer :D

Discussion

410.	Simiplify :((1-i)^(3))/((1-i^(3))
Answer» ANSWER :`-2`

Discussion

411.	Write the given statement in symbolic form using the letter in parentheses to represent the corresponding component. Mukesh patel is a teacher (t) or a lawyer (u).
Answer» ANSWER :`t VV U`

Discussion

412.	Write the given statement in symbolic form using the letter in parentheses to represent the corresponding component. Jack went up the hill (c) and Jill went up the hill (d).
Answer» ANSWER :`C ^^ d`

Discussion

413.	Write the given statement in symbolic form using the letter in parentheses to represent the corresponding component. This is April (p) andincome tax returns must be filed (q).
Answer» <P> ANSWER :`p ^^ Q`.

Discussion

414.	Write the given statement in symbolic form using the letter in parentheses to represent the corresponding component. Accountancy is a required subject for Chartered Accountants (m) but not for engineers (n).
Answer» ANSWER :`m ^^ ~N`

Discussion

415.	( ( 1)/(r_1) + (1)/(r_2)) ((1)/(r_2) +(1)/(r_3))( (1)/(r_3)+(1)/(r_1)) =
Answer» ANSWER :`( 64 R^(3))/( a^(2) B^(2) C^(2) )`

Discussion

416.	Write the given statement in symbolic form using the letter in parentheses to represent the corresponding component. I will not drive to Jaipur (~d) but I shall go by train (t)or by plane (p).
Answer» <P> ANSWER :`~d ^^ (t VV p)`

Discussion

417.	Assume that 3.52 denotes 3.52222. If x=3.52, find 10x and 100x
Answer» SOLUTION :10X = 35.222… 100X = 352.22…

Discussion

418.	Write the given statement in symbolic form using the letter in parentheses to represent the corresponding component. I plan to take science (a) or commerce (c) in class 11.
Answer» ANSWER :a V C

Discussion

419.	Construct the matrixA = [ a _(ij)] _(3xx3) , wherea_(ij)i- j . State whether A is symmetric or skew-symmetric .
Answer» ANSWER : SINCE ` A^(T) = - A , A ` is a skew-symmetric MATRIX.

Discussion

420.	The sides of a triangle lie on the line 3x+4y=0, 4x+3y=0 and x=3.Let (h,k) be the center of thecircle inscribed in DeltaABC. Thevalue of (h+k) equals.
Answer» ANSWER :4

Discussion

421.	Show that (1)/(r^(2))+(1)/(r_(1)^(2))+(1)/(r_(2)^(2))+(1)/(r_(3)^(2))=(a^(2)+b^(2)+c^(2))/(Delta^(2))
Answer» 1 0 `4RR^(2)` 1//r` ANSWER :A

Discussion

422.	Solution of cot^(2) theta + [sqrt(3) + (1)/( sqrt(3))] cot theta + 1= 0is
Answer» `n PI - (pi)/(6), n pi - (pi)/(3), AA n in Z` `(n pi)/(4), m pi, n,m in Z` `(2 n + 1) (pi)/(3), 2 m pi, n m in Z` `(2 n + 1) (pi)/(6), m pi, n, m in Z` ANSWER :A

Discussion

423.	Statement 1: The joint equation of lines y = x and y = -x is y^(2) = -x^(2), i.e., x^(2)+y^(2)=0 Statement 2 : The joint equation of lines ax+by=0 and cx+dy=0 is (ax+by)(cx+dy)=0 where a, b, c, d are constant
Answer» Both the statements are TRUE but STATEMENT 2 is the correct explanation of statement 1 Both the statements are true but statement 2 is not the correct explanation of statement 1 Statement 1 is true and statement 2 is FALSE Statement 1 is false and statement 2 is true Answer :D

Discussion

424.	List all the elements of the following sets : D= {x : x =(n)/(n+1)n in N, n le 9}
Answer» Answer :`D= {(1)/(2), (2)/(3), (3)/(4), (4)/(5), (5)/(6), (6)/(7), (7)/(8), (8)/(9), (9)/(10)}`

Discussion

425.	If roots of the equation 2x^(2)-4x+2sin theta-1=0 are of opposite sign then theta belongs to
Answer» `((PI)/6, (5PI)/6)` `(0, (pi)/6)UU((5pi)/6, pi)` `((13pi)/6, (17pi)/6)` `(0,pi)` Answer :B

Discussion

426.	If bar(a) = 2bar(i) - bar(j) + bar(k), andbar(b) = bar(i) - 3bar(j) - 5bar(k) then find \|bar(a) xx bar(b)\|.
Answer» ANSWER :`sqrt210`

Discussion

427.	Find the sum of all natural numbers between 100 and 1000 which are multiples of 5.
Answer» ANSWER :98450

Discussion

428.	If f(x) =(e^(1)/(x^(2))+1)/(e^(1)/(x^(2))-1) (x ne 0) iscontinuous at x = 0 find f(0)
Answer» ANSWER :1

Discussion

429.	f(x) =( log (1 +ax ) - log (1 - bx))/(x)is continuous at x = 0 then f(0) =
Answer» a-B ab `a/b` a + b ANSWER :D

Discussion

430.	Let f be a real valued invertible functions such that f(( 2x-3)/( x-2))= 5x- 2 ,x ne =2 . Then the value of f^(-1) (13)is ………….
Answer» ANSWER :3

Discussion

431.	The total cost C(x) in Rupees, associated with the production of x units of an item is given by C(x) = 0.005x^(3)- 0.02 x^(2)+30x+5000 Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change of total cost at any level of output.
Answer» ANSWER :3 UNITS

Discussion

432.	Match List-I with List II (##SUR_MAT_XI_V02_S_MQP_01_E01_012_Q01.png" width="80%">
Answer» `{:(""(i),(ii),(iii),(iv)),(d,c,a,B):} ` `{:(""(i),(ii),(iii),(iv)),(d,c,b.a):}` `{:(""(i),(ii),(iii),(iv)),(b,a,c,a):}` `{:(""(i),(ii),(iii),(iv)),(b,c,a,d):}` ANSWER :i-b ,ii-c,iii-a, iv-d

Discussion

433.	Solve 4cos^(2)x=3,0lexle2pi
Answer» ANSWER :`{pi/6,(5PI)/6,(7pi)/6,(11pi)/6}`

Discussion

434.	(ii) Differentiatey=x^(3)sqrt( 3x -4)
Answer» Answer :`= (3X^(2) (7x-8))/(2 SQRT( 3 X- 4))`

Discussion

435.	The perpendicular distance from origin to the line x/(p sec alpha)+y/(p cosec alpha)=1 is
Answer» <P>`\| p sin 2alpha\|` `\|p cos 2 ALPHA\|` `\|p tan 2alpha\|` `\|p\|` ANSWER :D

Discussion

436.	The radius of a right circular cylinder increases at the rate of 0.1 cm/min. and the height decreases at the rate of 0.2 cm/min. The rate of change of the volume of the cylinder. In cm^(3) /min. when the radius is 2 cm and the height is3cm is
Answer» `-2P` `-(8pi)/(5)` `-(3PI)/(5)` `(2PI)/(5)` ANSWER :D

Discussion

437.	If 180^(@) lt theta lt 270^(@) , sin theta =-3//5 , thencos theta //2=
Answer» `-1/sqrt10` `1/sqrt10` `1/10` 10 Answer :A

Discussion

438.	Which of the following sets are finite or infinite : {x : x in R, 0 lt x lt 1}
Answer» ANSWER :it is an INFINITE SET

Discussion

439.	Sketch the region represented by x + y le 1.
Answer» ANSWER :`x+y=1`

Discussion

440.	If cosalpha+cosbeta=0=sinalpha+sinbeta, then prove that cos2alpha+cos2beta=-2cos(alpha+beta).
Answer» ANSWER :`-2COS(alpha+beta)`

Discussion

441.	A plane P contains the lineL 1 : y/b + z/c =1, x =0 and is parallel to the line L _(2) : x/a - z/c = 1, y =0.. Equation of the plane P is
Answer» `x/a - y/b +z/c + 1=0` `x/a + y/b + z/c -1=0` `x/a + y/b - z/c -1 =0` `x/a - y/b -z/c + 1=0` ANSWER :D

Discussion

442.	A plane P contains the lineL1 : y/b + z/c =1, x =0 and is parallel to the line L _(2) : x/a - z/c = 1, y =0. If shortest distance between the lines L _(1) and L _(2) is 1/4 then the value of (1)/(a ^(2)) + (1)/(b ^(2)) + (1)/(c ^(2)) equals
Answer» 16 64 128 192 Answer :B

Discussion

443.	A plane P contains the lineL 1 : y/b + z/c =1, x =0 and is parallel to the line L _(2) : x/a - z/c = 1, y =0. Distance of image of A (a,0,0)in the plane P from M ((-5)/(3) , (8)/(3) , (11)/(3)) , where a=b=c=1, is equal to
Answer» 1 2 3 4 Answer :C

Discussion

444.	(i) int(dx)/(sqrt(a^(2)-x^(2)))=(1)/(a)sin^(-1)((x)/(a))+c (ii) int(dx)/(a^(2)+x^(2))=tan^(-1)((x)/(a))+c (iii) int(x+1)/(x^(2)+2x+1)dx=(1)/(2)log\|(x^(2)+2x+1)\| (iv) int(dx)/(x(x-1))dx=log\|(x-1)/(x)\|+c State which pair of the statement given above is true.
Answer» (III) and (IV) (i) and (II) (i) and (iii) (ii) and (iv) ANSWER :A

Discussion

445.	If the angles made by the normal of the plane 2x + 3y - 4z - 16=0 with the coordinates axes X, Y, Z are Cos ^(-1) k _(1), Cos ^(-1) k _(2), Cos^(-1) k _(3),then k _(1), k _(2), k _(3) respectively are
Answer» `(2) /(sqrt29) , (3)/(sqrt29) , (4)/(sqrt29)` `(2)/(sqrt29), - (3)/(sqrt29) , (4)/(sqrt29)` `(2)/(sqrt29) , (3)/(sqrt29), - (4)/(sqrt29)` `1/2, 1/3, -1/4` ANSWER :C

Discussion

446.	Let f(x) = nx + n - [nx+n]+ tan"" (pix)/( 2), where [x] is the greatest integer le x and n in N.It is
Answer» a PERIODIC function of period 1 a periodic function of period 4 not periodic a periodic function of period 2 Answer :D

Discussion

447.	A straight line through the fixed point (3,4) cuts the coordinate axes at A and B. If the area of the triangle formed by the line and the coordinate axes is least then the the ratio of intercepts is …….. And the min area is ……..
Answer» `3:4,12` `1:2,12` `1:1,9` `3:4,12` ANSWER :A

Discussion

448.	Find the slope of a line perpendicular to the line whose slope is 1/(3)
Answer» ANSWER :-3

Discussion

449.	Let U = {1, 2, 3, 4, 5, 6}, A = {2, 3} and B = {3, 4, 5}. Find A′, B′ ,A′∩ B′, A ∪ B and hence show that (A ∪ B )′ = A′ ∩ B′.
Answer» Answer :`(A cup B)'= {1, 6}= A' CAP B'`

Discussion

450.	If the median AD of DeltaABC, makes an angle theta with AB then sin(A-theta)=
Answer» `(B sin theta)/(C)` `(c sin theta)/(b)` `(a)/(CSIN theta)` `(c)/(b sin theta)` ANSWER :B

Discussion

Explore topic-wise InterviewSolutions in .

If bara=2bari+barj-bark,barb=-bari+2barj-4bark,barc=bari+barj+bark then find (baraxxbarb).(barbxxbarc)

Find the ratio in which the line segment joining the points (2, -1, 3) and (-1, 2, 1) is divided by the plane x + y + z = 5.

cos^(3)110^(@)+cos^(3)10^(@)+cos^(3)130^(@)=

A ray of light coming from the point (1,2)axis and is reflected at a point A on the coordinates passes through (6,5). Find the coordinate of A

Let A be a matrix of rank r. Then,

If the axes are rotated through an angle 30^(0), then find the coordinates of (0, 5) in the new system.

The value of cosec 10^(@) + cosec 50^(@) -cosec 70^(@) is"_________"

Findlimit of the following if it exists: lim_(xto0)(x(e^(x)-1))/(1-cosx)

A particle moves in a straight line according to the law v^(2) = 4a (x sin x + cos x) wher v is the velocity of a particle at a distance x from the fixed point then the acceleration is

Simiplify :((1-i)^(3))/((1-i^(3))

Write the given statement in symbolic form using the letter in parentheses to represent the corresponding component. Mukesh patel is a teacher (t) or a lawyer (u).

Write the given statement in symbolic form using the letter in parentheses to represent the corresponding component. Jack went up the hill (c) and Jill went up the hill (d).

Write the given statement in symbolic form using the letter in parentheses to represent the corresponding component. This is April (p) andincome tax returns must be filed (q).

Write the given statement in symbolic form using the letter in parentheses to represent the corresponding component. Accountancy is a required subject for Chartered Accountants (m) but not for engineers (n).

( ( 1)/(r_1) + (1)/(r_2)) ((1)/(r_2) +(1)/(r_3))( (1)/(r_3)+(1)/(r_1)) =

Write the given statement in symbolic form using the letter in parentheses to represent the corresponding component. I will not drive to Jaipur (~d) but I shall go by train (t)or by plane (p).

Assume that 3.52 denotes 3.52222. If x=3.52, find 10x and 100x

Write the given statement in symbolic form using the letter in parentheses to represent the corresponding component. I plan to take science (a) or commerce (c) in class 11.

Construct the matrixA = [ a _(ij)] _(3xx3) , wherea_(ij)i- j . State whether A is symmetric or skew-symmetric .

The sides of a triangle lie on the line 3x+4y=0, 4x+3y=0 and x=3.Let (h,k) be the center of thecircle inscribed in DeltaABC. Thevalue of (h+k) equals.

Show that (1)/(r^(2))+(1)/(r_(1)^(2))+(1)/(r_(2)^(2))+(1)/(r_(3)^(2))=(a^(2)+b^(2)+c^(2))/(Delta^(2))

Solution of cot^(2) theta + [sqrt(3) + (1)/( sqrt(3))] cot theta + 1= 0is

Statement 1: The joint equation of lines y = x and y = -x is y^(2) = -x^(2), i.e., x^(2)+y^(2)=0 Statement 2 : The joint equation of lines ax+by=0 and cx+dy=0 is (ax+by)(cx+dy)=0 where a, b, c, d are constant

List all the elements of the following sets : D= {x : x =(n)/(n+1)n in N, n le 9}

If roots of the equation 2x^(2)-4x+2sin theta-1=0 are of opposite sign then theta belongs to

If bar(a) = 2bar(i) - bar(j) + bar(k), andbar(b) = bar(i) - 3bar(j) - 5bar(k) then find |bar(a) xx bar(b)|.

Find the sum of all natural numbers between 100 and 1000 which are multiples of 5.

If f(x) =(e^(1)/(x^(2))+1)/(e^(1)/(x^(2))-1) (x ne 0) iscontinuous at x = 0 find f(0)

f(x) =( log (1 +ax ) - log (1 - bx))/(x)is continuous at x = 0 then f(0) =

Let f be a real valued invertible functions such that f(( 2x-3)/( x-2))= 5x- 2 ,x ne =2 . Then the value of f^(-1) (13)is ………….

The total cost C(x) in Rupees, associated with the production of x units of an item is given by C(x) = 0.005x^(3)- 0.02 x^(2)+30x+5000 Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change of total cost at any level of output.

Match List-I with List II (##SUR_MAT_XI_V02_S_MQP_01_E01_012_Q01.png" width="80%">

Solve 4cos^(2)x=3,0lexle2pi

(ii) Differentiatey=x^(3)sqrt( 3x -4)

The perpendicular distance from origin to the line x/(p sec alpha)+y/(p cosec alpha)=1 is

The radius of a right circular cylinder increases at the rate of 0.1 cm/min. and the height decreases at the rate of 0.2 cm/min. The rate of change of the volume of the cylinder. In cm^(3) /min. when the radius is 2 cm and the height is3cm is

If 180^(@) lt theta lt 270^(@) , sin theta =-3//5 , thencos theta //2=

Which of the following sets are finite or infinite : {x : x in R, 0 lt x lt 1}

Sketch the region represented by x + y le 1.

If cosalpha+cosbeta=0=sinalpha+sinbeta, then prove that cos2alpha+cos2beta=-2cos(alpha+beta).

A plane P contains the lineL 1 : y/b + z/c =1, x =0 and is parallel to the line L _(2) : x/a - z/c = 1, y =0.. Equation of the plane P is

A plane P contains the lineL1 : y/b + z/c =1, x =0 and is parallel to the line L _(2) : x/a - z/c = 1, y =0. If shortest distance between the lines L _(1) and L _(2) is 1/4 then the value of (1)/(a ^(2)) + (1)/(b ^(2)) + (1)/(c ^(2)) equals

A plane P contains the lineL 1 : y/b + z/c =1, x =0 and is parallel to the line L _(2) : x/a - z/c = 1, y =0. Distance of image of A (a,0,0)in the plane P from M ((-5)/(3) , (8)/(3) , (11)/(3)) , where a=b=c=1, is equal to

(i) int(dx)/(sqrt(a^(2)-x^(2)))=(1)/(a)sin^(-1)((x)/(a))+c (ii) int(dx)/(a^(2)+x^(2))=tan^(-1)((x)/(a))+c (iii) int(x+1)/(x^(2)+2x+1)dx=(1)/(2)log|(x^(2)+2x+1)| (iv) int(dx)/(x(x-1))dx=log|(x-1)/(x)|+c State which pair of the statement given above is true.

If the angles made by the normal of the plane 2x + 3y - 4z - 16=0 with the coordinates axes X, Y, Z are Cos ^(-1) k _(1), Cos ^(-1) k _(2), Cos^(-1) k _(3),then k _(1), k _(2), k _(3) respectively are

Let f(x) = nx + n - [nx+n]+ tan"" (pix)/( 2), where [x] is the greatest integer le x and n in N.It is

A straight line through the fixed point (3,4) cuts the coordinate axes at A and B. If the area of the triangle formed by the line and the coordinate axes is least then the the ratio of intercepts is …….. And the min area is ……..

Find the slope of a line perpendicular to the line whose slope is 1/(3)

Let U = {1, 2, 3, 4, 5, 6}, A = {2, 3} and B = {3, 4, 5}. Find A′, B′ ,A′∩ B′, A ∪ B and hence show that (A ∪ B )′ = A′ ∩ B′.

If the median AD of DeltaABC, makes an angle theta with AB then sin(A-theta)=