14949 + Interview Questions in Maths in Class 11 Page 134 InterviewSolution

6651.	If bara=2bari+3barj-bark,barb=-bari+2barj-4bark, barc=bari+barj+bark then abs((baraxxbarb)· (barbxxbarc))=
Answer» 104 106 108 112 Answer :C

Discussion

6652.	Assume that P ( A ) = P ( B ). Show that A = B
Answer» ANSWER :`A= B`

Discussion

6653.	cot((pi)/4-2cot^(-1)3)=
Answer» `3` 5 7 9 Answer :C

Discussion

6654.	The vertices of Delta PQR " are " P (2, 1) , Q (-2, 3) " and " R (4, 5). Find equation of the median through the vertex R.
Answer» ANSWER :`3X - 4Y + 8 = 0 `

Discussion

6655.	A line AB of length '2l' moves with the end 'A' always on x - axis and the end 'B' on the line y = 6x find the equation of locus of middle point of AB
Answer» `9X^(2)+10Y^(2)-6xy-9l^(2)=0` `9x^(2)-10y^(2)+6xy+9l^(2)=0` `9x^(2)+10y^(2)+6xy+9l^(2)=0` `9x^(2)-10y^(2)-4xy+6l^(2)=0` ANSWER :A

Discussion

6656.	Evaluate the following limit : Lim_(x to pi/2) (1+cos 2x)/(pi-2x)^(2)
Answer» ANSWER :`1/2 `

Discussion

6657.	Solve :tan 3 theta = 1 .
Answer» ANSWER :`THETA = 1/2 NPI, N in I`

Discussion

6658.	If a le 3 cos x+ 5 sin ( x - pi//6) le b for all x , then ( a, b) is
Answer» `(-SQRT(19), sqrt(19))` (-17, 17) `(-sqrt(21), sqrt(21))` NONE of these Answer :A

Discussion

6659.	If sin(sin x + cos x) = cos (cos x - sin x) then the largest possible value of sin x is
Answer» `(1)/(sqrt(2))` 1 `sqrt(16 - PI^(2))/(4)` `(pi)/(4)` Answer :C

Discussion

6660.	A straight line through the origin O meets the parallel lines 4x+2y=9 and 2x+y+6=0 at points P and Q respectively. Then the point O divides the segment PQ in the ratio
Answer» `1 : 2` `3 : 4` `2 : 1` `4 : 3` ANSWER :B

Discussion

6661.	If the coefficients of 4^(th) and 13^(th) terms in the expansion of (a+b)^(n) are equal then find n .
Answer» ANSWER :15

Discussion

6662.	Find sum_(n=1)^(oo)(1)/(n^(2)+5n+6)
Answer» ANSWER :`=(1)/(3)`

Discussion

6663.	A tree is broken by wind, its upper part touches the ground at a point 10 metres from the foot of the tree and makes an angle of45^(@)with the ground . The entire length of the tree is
Answer» 15 metres 20 metres ` 10 ( 1+ SQRT2) ` metres ` 10 ( 1+ (sqrt3)/(2))` metres ANSWER :C

Discussion

6664.	Find the mean deviation about the mean for the following data:12,3,18,17,4,9,17,19,20,15,8,17,2,3,16,11,3,1,0,5 .
Answer» ANSWER :6.2

Discussion

6665.	Find r if""^(5)P_(r)=""^(6)P_(r-1)
Answer» ANSWER :4

Discussion

6666.	There are 8 white and 7 black balls in a bag . Three-three balls are drawn twice from the bag and balls drawn first time are not being replaced when the balls are drawn second time. Find the probability that first three balls drawn are white and second thre balls drawn are black.
Answer» SOLUTION :N/a

Discussion

6667.	If sin x sin h y = cos theta and cos x cos h y = sin theta then cos h^(2) y + cos^(2)x =
Answer» `-1` 0 1 2 Answer :D

Discussion

6668.	Differentiate the following function w.r.t. x: x^(2) cos 5x
Answer» ANSWER :`-5 X^(2) SIN 5X + 2 x cos 5x`

Discussion

6669.	Ifalpha + beta + gamma = 2 theta , " then " cos theta+ cos ( theta - alpha ) + cos (theta - beta ) + cos ( theta - gamma ) =
Answer» `4SIN ""(alpha )/(2).cos""(beta)/(2).SIN""(gamma)/(2)` `4 cos ""(alpha)/(2).cos""(beta)/(2).cos""(gamma)/(2)` `4 sin ""alpha /2.sin""beta/2.sin""gamma2` `3 sin alpha.sinbeta.singamma` ANSWER :B

Discussion

6670.	Write down the negation of following compound statements. \|x\| is equal to eighter x or -x.
Answer» ANSWER :not EQUAL to -X

Discussion

6671.	If d/(dx) (f(x))^(n)=n(f(x))^(n-1)(df(x))/(dx) then (d)/(dx) (sin^3x)=3sin^(2)x.cosx.
Answer» ANSWER :TRUE STATEMENT

Discussion

6672.	Given that, z=(1+2i)/(1-i)=((1+2i)(1+i))/((1-i)(1+i))
Answer» ANSWER :`((-1)/(2),(-3)/(2))`

Discussion

6673.	If f(x) = cos x , a = ( - pi )/(2) then the value of 'c' of Rolle's theorem in (a,b)
Answer» POSITIVE Negative Neither positive Nor Negative Irrational Answer :C

Discussion

6674.	If sin^(3) theta cos theta - cos ^(3) theta sin theta = 1 //4 " then " theta =
Answer» `THETA = (n PI)/( 2) + (pi)/(8) n in Z` `theta = ( n pi)/(2) - (pi)/(8) n in Z` `theta = (n pi)/(2) + (pi)/(4) n in Z` `theta = (n pi)/(2) - (pi)/(4) n in Z` Answer :B

Discussion

6675.	If the area enclosed by the curves f(x)=cos^(-1)(cosx) and g(x)=sin^(-1)(cosx) in x in [(9pi)/4,(15pi)/4] is api^(2),//b (where a and b are coprime), then the value of (a-b) is
Answer» ANSWER :1

Discussion

6676.	A line passing through the points (7,2) , (-3,2) then the image of the line in the x-axis is
Answer» y=4 y=9 y=-1 y=-2 Answer :D

Discussion

6677.	Find the sum of odd integers from 1 to 2001.
Answer» ANSWER :1002001

Discussion

6678.	Find the orthocentre of the triangle formed by the lines 2x-y=2,3x-2y=1,x-y=0
Answer» ANSWER :`(11,-4)`

Discussion

6679.	If \|{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}\|=5, then the value of \|{:(b_(2)c_(3)-b_(3)c_(2),a_(3)c_(2)-a_(2)c_(3),a_(2)b_(3)-a_(3)b_(2)),(b_(3)c_(1)-b_(1)c_(3),a_(1)c_(3)-a_(3)c_(1),a_(3)b_(1)-a_(1)b_(3)),(b_(1)c_(2)-b_(2)c_(1),a_(2)c_(1)-a_(1)c_(2),a_(1)b_(2)-a_(2)b_(1)):}\| is
Answer» 5 25 125 0 Answer :B

Discussion

6680.	cos theta + cos^(2) theta = 1, cos theta + cos^(2) theta = 1 + d sin^(6) theta = 1 rArr (b+c)/(a+d)=1
Answer» 2 3 4 6 Answer :B

Discussion

6681.	If D is the midpoint of the side BC of a triangle ABC then bar(AB)^(2)+bar(AC)^(2)=
Answer» `bar(AD)^(2)+bar(BD)^(2)` `2(bar(AD)^(2)+bar(BD)^(2))` `3(bar(AD)^(2)+bar(BD)^(2))` `4(bar(AD)^(2)+bar(BD)^(2))` Answer :B

Discussion

6682.	The value of alpha^(3)/2cosec^(2)(1/2tan^(-1)""alpha/beta)+beta^(3)/2sec^(2)(1/2tan^(-1)(beta/alpha)) is equal to
Answer» `(ALPHA-BETA)(alpha^(2)+beta^(2))` `(alpha-beta)(alpha^(2)+beta^(2))` `(alpha+beta)(alpha^(2)+beta^(2))` `(alpha-beta)(alpha^(2)-beta^(2))` ANSWER :C

Discussion

6683.	Find the area of the parallelogram whose sides are 3x+4y+5=0, 3x+4y-2=0,2x+3y+1=0, 2x+3y-7=0
Answer» ANSWER :56 SQ. UNITS

Discussion

6684.	The number of values of x for which \|\|\|x^(2) -x+4\| -2\| =3\|=x^(2)+x- 12is …………………
Answer» ANSWER :1

Discussion

6685.	If cosA=(3)/(4) then 32sin((A)/(2))sin((5A)/(2)) = ……………
Answer» `-11` `-SQRT(11)` `sqrt(11)` 11 Answer :D

Discussion

6686.	If n (A) =10, n (B) =6 and n (C ) =5 for three disjoint sets A,B,C, then n (A uu B uuC)equals
Answer» 11 21 1 9 Answer :B

Discussion

6687.	Compute the missing frequencies in the following distribution , given that is sum f_(i)= 100 and the median is 32{:("Marks",0-10,10-20,20-30,30-40,40-50,50-60),("Number of students "," "9," "?, " "26, " "30, " " ?, " "10):}
Answer» ANSWER :`9 . 16`

Discussion

6688.	Consider the lines L _(1) : (x +1)/( 3) = (y+2)/(1) = (z+1)/(2), L_(2): (x-2)/(1) = (y+2)/(2) = (z-3)/(3) The shortest distance between L _(1) and L _(2) is
Answer» 0 `(17)/(sqrt3)` `(41)/(5SQRT3)` `(17)/(5sqrt3)` Answer :D

Discussion

6689.	If 25, x - 6 and x - 12 are in G.Pthen x = .......... or ......... .
Answer» ANSWER :21

Discussion

6690.	A box without lid having maximum volume is made out of square metel sheet of edge 60 cms by cutting equal square pieces from the four corners and turing up the projecting pieces tomake the sides of the box . The height of the box is
Answer» 60 10 15 12 Answer :B

Discussion

6691.	Find equation of the line perpendicular to the linex - 7y + 5 = 0 and having x intercept 3.
Answer» ANSWER :`y + 7X = 21`

Discussion

6692.	Solve the equation sin^(4)x + cos^(4)x =7/2 sinx.cosx.
Answer» Solution :`SIN^(4)x+COS^(4)x=7/2sinx.cosx rArr (sin^(2)x +cos^(2)x)^(2) =7/2sinx.cosx` `rArr 1-1/2(SIN2X)^(2)=7/4(sin2x) rArr 2SIN^(2)2x+7sin2x-4=0` `rArr (2sin2x-1)(sin2x+4) =0 rArr sin2x =1/2` or `sin2x = -4` (Which is not possible)`rArr 2x = npi+(-1)^(n)pi/6 , n in I` i.e, `x=(npi)/(2)+(-1)^(n)pi/12, n in I` ANS.

Discussion

6693.	The difference betweentworootsof theequation x^3 -13 x^2 + 15 x+189=0is2thentherootsof theequation are
Answer» 2 1 ` SQRT(2)` `2 sqrt(2)` ANSWER :A

Discussion

6694.	A and B are events such that P(A)= 0.42, P(B)= 0.48 and P(A and B)= 0.16, Determine (i) P(not A), (ii) P(not B) and (iii) P(A or B).
Answer» ANSWER :(i) 0.58, (II) 0.52, (III) 0.74

Discussion

6695.	Perpendicular distance from origin to the plane barr.barm = bara.barm is
Answer» `ABS(bara.barm)/absbarm` `abs(bara.barm)/ABSBARA` `(bara.barm)/absbara` `(bara.barm)/absbarm` ANSWER :A

Discussion

6696.	Let f : (-1, 1) to R be a differentiable function with f(0) = -1 and f'(0) = 1 . Let g(x) = [f(2f(x)+ 2)]^2 . Then g'(0) is equal to
Answer» `-2` `4` `-4` `0` ANSWER :B

Discussion

6697.	If f(x) = sqrt(x + 2sqrt(2x - 4)) + sqrt(x - 2sqrt(2x - 4)), then f'(3) = f'(6) =
Answer» 0 `1` `2` `1/2` ANSWER :D

Discussion

6698.	A single letter is selected at random from the word 'Probability' . Find the probability that it is a vowel.
Answer» ANSWER :`=(4)/(11)`.

Discussion

6699.	Sum of the power of a and b in expansion (a+b)^n is n .
Answer» ANSWER :TRUE STATEMENT

Discussion

6700.	Define loss of kinetic energy in inelastic collision
Answer» Solution :In perfectly inelastic collision, the loss in kinetic energy during collision is transformed to another form of energy like SOUND, thermal, heat, light etc. LET `KE_i` be the TOTAL kinetic energy before collision and `KE_f` be the total kinetic energy after collision. Total kinetic energy before collision, `KE_i = 1/2 m_1u_1^2 + m_2 u_2^2 "" ...(1)` Total kinetic energy after collision, `KE_f = 1/2 (m_1 + m_2) v^2 "" ...(2)` Then the loss of kinetic energy is Loss of KE ,` Delta Q = KE_f - KE_i` ` =1/2 (m_1 + m_2) v^2 - 1/2 m_1 u_1^2 + 1/2 m_2 u_2^2 "" ...(3)` SUBSTITUTING equation ` v = (m_1u_1 + m_2 u_2)/(m_1 + m_2)` in equation (3), and on simplifying (expand v by using the algebra `(a + b)^2 =a ^2 + b^2 + 2ab` we get Loss of KE , ` DeltaQ = 1/2 ((m_1 m_2)/(m_1 + m_2)) (u_1 - u_2)^2`

Discussion

Explore topic-wise InterviewSolutions in .

If bara=2bari+3barj-bark,barb=-bari+2barj-4bark, barc=bari+barj+bark then abs((baraxxbarb)· (barbxxbarc))=

Assume that P ( A ) = P ( B ). Show that A = B

cot((pi)/4-2cot^(-1)3)=

The vertices of Delta PQR " are " P (2, 1) , Q (-2, 3) " and " R (4, 5). Find equation of the median through the vertex R.

A line AB of length '2l' moves with the end 'A' always on x - axis and the end 'B' on the line y = 6x find the equation of locus of middle point of AB

Evaluate the following limit : Lim_(x to pi/2) (1+cos 2x)/(pi-2x)^(2)

Solve :tan 3 theta = 1 .

If a le 3 cos x+ 5 sin ( x - pi//6) le b for all x , then ( a, b) is

If sin(sin x + cos x) = cos (cos x - sin x) then the largest possible value of sin x is

A straight line through the origin O meets the parallel lines 4x+2y=9 and 2x+y+6=0 at points P and Q respectively. Then the point O divides the segment PQ in the ratio

If the coefficients of 4^(th) and 13^(th) terms in the expansion of (a+b)^(n) are equal then find n .

Find sum_(n=1)^(oo)(1)/(n^(2)+5n+6)

A tree is broken by wind, its upper part touches the ground at a point 10 metres from the foot of the tree and makes an angle of45^(@)with the ground . The entire length of the tree is

Find the mean deviation about the mean for the following data:12,3,18,17,4,9,17,19,20,15,8,17,2,3,16,11,3,1,0,5 .

Find r if""^(5)P_(r)=""^(6)P_(r-1)

There are 8 white and 7 black balls in a bag . Three-three balls are drawn twice from the bag and balls drawn first time are not being replaced when the balls are drawn second time. Find the probability that first three balls drawn are white and second thre balls drawn are black.

If sin x sin h y = cos theta and cos x cos h y = sin theta then cos h^(2) y + cos^(2)x =

Differentiate the following function w.r.t. x: x^(2) cos 5x

Ifalpha + beta + gamma = 2 theta , " then " cos theta+ cos ( theta - alpha ) + cos (theta - beta ) + cos ( theta - gamma ) =

Write down the negation of following compound statements. |x| is equal to eighter x or -x.

If d/(dx) (f(x))^(n)=n(f(x))^(n-1)(df(x))/(dx) then (d)/(dx) (sin^3x)=3sin^(2)x.cosx.

Given that, z=(1+2i)/(1-i)=((1+2i)(1+i))/((1-i)(1+i))

If f(x) = cos x , a = ( - pi )/(2) then the value of 'c' of Rolle's theorem in (a,b)

If sin^(3) theta cos theta - cos ^(3) theta sin theta = 1 //4 " then " theta =

If the area enclosed by the curves f(x)=cos^(-1)(cosx) and g(x)=sin^(-1)(cosx) in x in [(9pi)/4,(15pi)/4] is api^(2),//b (where a and b are coprime), then the value of (a-b) is

A line passing through the points (7,2) , (-3,2) then the image of the line in the x-axis is

Find the sum of odd integers from 1 to 2001.

Find the orthocentre of the triangle formed by the lines 2x-y=2,3x-2y=1,x-y=0

cos theta + cos^(2) theta = 1, cos theta + cos^(2) theta = 1 + d sin^(6) theta = 1 rArr (b+c)/(a+d)=1

If D is the midpoint of the side BC of a triangle ABC then bar(AB)^(2)+bar(AC)^(2)=

The value of alpha^(3)/2cosec^(2)(1/2tan^(-1)""alpha/beta)+beta^(3)/2sec^(2)(1/2tan^(-1)(beta/alpha)) is equal to

Find the area of the parallelogram whose sides are 3x+4y+5=0, 3x+4y-2=0,2x+3y+1=0, 2x+3y-7=0

The number of values of x for which |||x^(2) -x+4| -2| =3|=x^(2)+x- 12is …………………

If cosA=(3)/(4) then 32sin((A)/(2))sin((5A)/(2)) = ……………

If n (A) =10, n (B) =6 and n (C ) =5 for three disjoint sets A,B,C, then n (A uu B uuC)equals

Compute the missing frequencies in the following distribution , given that is sum f_(i)= 100 and the median is 32{:("Marks",0-10,10-20,20-30,30-40,40-50,50-60),("Number of students "," "9," "?, " "26, " "30, " " ?, " "10):}

Consider the lines L _(1) : (x +1)/( 3) = (y+2)/(1) = (z+1)/(2), L_(2): (x-2)/(1) = (y+2)/(2) = (z-3)/(3) The shortest distance between L _(1) and L _(2) is

If 25, x - 6 and x - 12 are in G.Pthen x = .......... or ......... .

A box without lid having maximum volume is made out of square metel sheet of edge 60 cms by cutting equal square pieces from the four corners and turing up the projecting pieces tomake the sides of the box . The height of the box is

Find equation of the line perpendicular to the linex - 7y + 5 = 0 and having x intercept 3.

Solve the equation sin^(4)x + cos^(4)x =7/2 sinx.cosx.

The difference betweentworootsof theequation x^3 -13 x^2 + 15 x+189=0is2thentherootsof theequation are

A and B are events such that P(A)= 0.42, P(B)= 0.48 and P(A and B)= 0.16, Determine (i) P(not A), (ii) P(not B) and (iii) P(A or B).

Perpendicular distance from origin to the plane barr.barm = bara.barm is

Let f : (-1, 1) to R be a differentiable function with f(0) = -1 and f'(0) = 1 . Let g(x) = [f(2f(x)+ 2)]^2 . Then g'(0) is equal to

If f(x) = sqrt(x + 2sqrt(2x - 4)) + sqrt(x - 2sqrt(2x - 4)), then f'(3) = f'(6) =

A single letter is selected at random from the word 'Probability' . Find the probability that it is a vowel.

Sum of the power of a and b in expansion (a+b)^n is n .

Define loss of kinetic energy in inelastic collision