14949 + Interview Questions in Maths in Class 11 Page 27 InterviewSolution

1301.	Write the component statements of the following compound statements (i) All numbers are even or odd. (ii) 18 is divisible by 2 and 9. (iii) all sides and all angles of a square are equal. (iv) this pen is black or blue.
Answer» SOLUTION :(i) p: all numbers are even. Q: all numbers are odd. (ii) p: NUMBER 18 is divisible by 2. q: number 18 is divisible by 9. (iii) p: all sides of a square are EQUAL. q: all angles of a square are equal. (iv) p: this pen is black. q : this pen is blue.

Discussion

1302.	Consider the expansion of (3x^3+2/x^2)^40 Assuming the term containing x^20 as the (r+1)^(th)term, find the coefficient of x^20 in the expansion of (3x^3+2/x^2)^40
Answer» SOLUTION :`"^40C_20."6^20`

Discussion

1303.	Obtain the equation at the line in Ex. (1) to (10) satisfying given condition : Equation of line with p=2 and sin theta = (4)/(5).
Answer» ANSWER :`3X + 4Y = 10` OR `3x + 4y - 10 = 0`

Discussion

1304.	If the sum of p terms of an AP is q and the sum of q terms is p, then show that the sum of p+q terms is -(p+ q). Alos, find the sum of first p-q terms (where, p gt q)
Answer» <P> ANSWER :`((p-q)(p+ 2Q))/(p)`

Discussion

1305.	If f:{1,2,3,....}rarr{0, pm 1, pm2, .....} isdefined byf(n)= {:{(n//2 , "if n is even"),(-((n-1)/(2)), "if n is odd"):}then f^(-1)(-100) is
Answer» 100 199 201 200 Answer :C

Discussion

1306.	L_1 : 3x+4y+8=0 , L_2 : 2x+7y-1=0 Equation of the line through B parallel to AC is
Answer» `2x+7y+21=0` `10x+35=63` `10x+35y+21=0` `2x+7y=63` ANSWER :C

Discussion

1307.	If vec(u)= vec(a)- vec(b), vec(v)= vec(a) + vec(b) and \|vec(a)\| =\|vec(b)\|=2, then \|vec(u) xx vec(v)\|=
Answer» `sqrt(16-(vec(a).vec(b))^(2))` `sqrt(16+ (vec(a).vec(b))^(2))` `2 sqrt(16-(vec(a).vec(b))^(2))` `2sqrt(16 + (vec(a).vec(b))^(2))` Answer :C

Discussion

1308.	A (-2, 2, 3) and (13, -3, 13) and L is a line through A A point P movesin the space such that 3PA = 2PB, then the locus of P is
Answer» `X^(2)+y^(2)+Z^(2)+28x-12y+10z-247=0` `x^(2)+y^(2)+z^(2)-28x+12y+10z-247=0` `x^(2)+y^(2)+z^(2)+28x-12y-10z+247=0` `x^(2)+y^(2)+z^(2)-28x+12y-10z+247=0` ANSWER :a

Discussion

1309.	A : If bara, barb, barc form a left handed orthogonal system such that bara.bara= 4, barb.barb =9, barc.barc =16 rArr [barabarbbarc]=-24 R : For left handed system [bara barb barc] < 0 , and bara.bara =abs(bara)^(2) , for orthogonal vectors bara, barb, barc, [barabarbbarc] =pm(absbara.absbarb.absbarc) The correct answer is
Answer» A,R are TRUE, R is correct explanation of A A,R are true, R is not correct explanation of A A is true, R is false A is true, R is false Answer :A

Discussion

1310.	If Sin^(4)2x+Cos^(4)2x=Sin2xCos2 then x=
Answer» `(2n+1)(PI)/(4)` `(4n+1)(pi)/(2)` `(4n+1)(pi)/(8)` `(2n+1)(pi)/(8)` Answer :C

Discussion

1311.	If f(x)=(1)/(sqrt(x+2sqrt(2x-4)))+(1)/(sqrt(x-2sqrt(2x-4))) for x gt 2, then f(11)=
Answer» `7//6` `5//6` `6//7` `5//7` ANSWER :C

Discussion

1312.	Let x_1,x_2, x_3, x_4, x_5 be the observations with mean m and standard deviation S. The standard deviation of the observations kx_1,kx_2,kx_3,kx_4,kx_5 is……….
Answer» `\|K\| + S ` `(S)/(\|k\|)` `\|k\|. S` `S` ANSWER :C

Discussion

1313.	How many committees of 5 members each can be formed with 8 officials and 4 non - official members in the following cases: each consits of 3 officials and 2 non - official members.
Answer» ANSWER :` 336`

Discussion

1314.	How many committees of 5 members each can be formed with 8 officials and 4 non - official members in the following cases: each contains at least two non-official members
Answer» ANSWER :` 456`

Discussion

1315.	How many committees of 5 members each can be formed with 8 officials and 4 non - official members if a particular official members is never included.
Answer» ANSWER :` 462`

Discussion

1316.	How many committees of 5 members each can be formed with 8 officials and non - official members in the following cases: a particular non-official members is always included?
Answer» ANSWER :` 330 `

Discussion

1317.	(cos h(x))/(1-tan h x) + (sin h(x))/(1-cot h(x)) =
Answer» `SIN H(X) + COT h(x)` `tan h (x) + cot h (x)` `tan h (x) - cot h(x)` `sin h(x) + COS h(x)` Answer :D

Discussion

1318.	(d)/(dx) {Tan ^(-1)"" (sqrt(1+ x ^(2))+ sqrt(1- x ^(2)))/( sqrt(1+ x ^(2))- sqrt(1- x ^(2)))}=
Answer» ANSWER :`(-X)/( SQRT (1 - x ^(4)))`

Discussion

1319.	The value of 'c' of Lagrange's mean value theorem for f(x) = x^(3) - 5x^(2) - 3xin [ 1,3] is
Answer» 2 `5//4` 3 `7//3` ANSWER :D

Discussion

1320.	If x, y, z are perpendicular distances from circumcentre to the sides of Delta^("le")ABC respectively then (xyz)/(abc){(a)/(x)+(b)/(y)+(c)/(z)}=
Answer» 1 `(1)/(2)` `(1)/(3)` `(1)/(4)` ANSWER :D

Discussion

1321.	Express the following in the form a+bi (8+7i) (8-7i)
Answer» ANSWER :`113+0i`

Discussion

1322.	Find the component statements of the following compound statements: Chandigarh is the capital of Haryana and U.P.
Answer» ANSWER :p: Chandigarh is capital of hariyana Q: CHANIGARH is capital of U.P.

Discussion

1323.	Find the derivative of the following functions:( i)Sinx.cos x
Answer» ANSWER :COS 2X

Discussion

1324.	In the space A(bar(a)) is a point and bar(b) is a vector.If P(bar(r )) is any point such that bar(r ) xx bar(b) = bar(a) xx bar(b) then show that locus of P is a straight line.
Answer» <P> ANSWER :LOCUS of P is a STRAIGHT LINE.

Discussion

1325.	Find (a, b) if Lt_(xtooo){sqrt(x^(2)-x+1)-ax-b}=0
Answer» ANSWER :`(-1,1//2)`

Discussion

1326.	The solution set of sintheta+costheta=2 is ………
Answer» `kpi,kinZ` `2kpi+(PI)/(2),kinZ` `PHI` `(2k+1)(pi)/(2),kinZ` ANSWER :C

Discussion

1327.	If cosecx=1+cotx, then x=2npi,2npi+(pi)/(2),ninZ.
Answer» ANSWER :TRUE

Discussion

1328.	Describe the sample space for the indicated experiments. A coin is tossed and then a die is rolled only in case a head is shown on the coin
Answer» Answer :{H1, H2, H3, H4, H5, H6, T}

Discussion

1329.	Find the derivative of the w.r.to x. (sin x ) ^(log x) + x ^( sin x)
Answer» ANSWER :`[COS X LOG x+ (SIN x )/(x)]`

Discussion

1330.	A letter is chosen at random from the 'ASSASSINATION'. Find the probability that letter is (i) a vowel (ii) a consonant.
Answer» ANSWER :(i) `6/13` (II) `7/13`

Discussion

1331.	Find which one is true.If A and B are two matrices such that A+B and BA are both defined then:
Answer» A and B are two MATRICES not NECESSARILY of same ORDER A and B are SQUARE matrices of same order Number of COLUMNS of A is equal to the number of rows of B A= B. Answer :A::B::C::D

Discussion

1332.	If tan^(3)x+3gt3 tan x +tan^(2)xthen
Answer» `X in (npi+(pi)/3, N pi +(pi)/2)uu(npi -(pi)/3, npi+(pi)/4), NIN Z` `x in (n pi+(pi)/4, npi+(pi)/2)uu(npi-(pi)/4, n pi+(pi)/4),n in Z` `x in (n pi -(pi)/6, n pi+(pi)/2)uu(n pi -(pi)/4, npi +(pi)/4), n in Z` `x in (n pi -(pi)/3, n pi+(pi)/2)uu(n pi -(pi)/4, npi +(pi)/4), n in Z` Answer :A

Discussion

1333.	Differentiate the following functions w.r.t. x. f(x) = sqrt( x^2 +1)
Answer» ANSWER :`(X)/( SQRT (x^2 +1) )`

Discussion

1334.	If 0^(@)lt theta lt 90^(@) and cos theta=(4)/(5) find the values of "cosec"(180^(@)+theta)
Answer» ANSWER :`(-5)/(3)`

Discussion

1335.	If the straight line 3x+4y=8 is equidistant from (2,3) and (-4,a) then the value of a is
Answer» `15/2` `15/3` `15/4` `15` ANSWER :A

Discussion

1336.	Find the value of alpha and p if the equation xcosalpha+ysinalpha=p is the normal form of the line sqrt(3x)+y+2=0.
Answer» ANSWER :`ALPHA=(7pi)/6 " and " p=1`

Discussion

1337.	Differentiate the following functions with respect to x from definition. (i) x^2
Answer» ANSWER :`(d)/( DX) (x^2) = 2X`

Discussion

1338.	If in aDelta ABC, r_1= 2r_2= 3r_3,then the perimeter of the triangle is equal to
Answer» ` 3A ` ` 3B ` ` 3C ` ` 3 (a+b+c) ` Answer :B

Discussion

1339.	If A=tan6^(@) tan42^(@), B=cot66^(@) cot78^(@) then
Answer» `A=2B` `A=B` `B=2A` `3A=2B` ANSWER :B

Discussion

1340.	The minimum and maximum values of cos x + 3sqrt(2)sin(x+(pi)/(4)) + 6 are
Answer» 1, 11 11, -1 6, 5 5, 6 Answer :A

Discussion

1341.	Find the condition that the equation ax^(2) + 2hxy + by^(2) + 2gx + 2fy + c = 0 to takethe form aX^(2) + 2hXY + bY^(2) = 0when the axes are translated.
Answer» `(2\|C\|)/(sqrt(h^(2)-ab))` `(\|c\|)/(sqrt(h^(2)-ab))` `(3\|c\|)/(sqrt(h^(2)-ab))` `(4\|c\|)/(sqrt(h^(2)-ab))` ANSWER :A

Discussion

1342.	Prove that the locus of mid-point of focal chords of parabola y^(2)=4ax "is" y^(2)=2a(x-a).
Answer»

Discussion

1343.	If p implies(qvvr) has validity F then validity of statement p, q and r is …….respectively.
Answer» F,T,T T,T,F T,F,F F,F,F Answer :C

Discussion

1344.	By shifting origin at (-2,3) find new transformed form at the equation y+3x=2.
Answer» ANSWER :`y+3x=5`

Discussion

1345.	sin(pi/10)sin((13pi)/10)=
Answer» 1 `-1//2` `1//2` `-1//4` ANSWER :D

Discussion

1346.	If A=[(3,2,1),(0,4,2),(1,2,3)]and B=[(3,2,0),(4,8,0),(-1,6,2)],then
Answer» B=-4A B=4A 2A `-3A Answer :A

Discussion

1347.	If piltxlt2pi then (sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqrt(1-cosx))
Answer» `TAN(pi/4+x/2)` `tan(pi/4-x/2)` `tan(pi/4+x)` `tan(pi/4-x)` ANSWER :B

Discussion

1348.	If z=x+iy, where x and y are real numbers and \|x\|+\|y\| lt= k\|z\| then k=.....
Answer» 1 2 `SQRT(2)` `sqrt(3)` Answer :C

Discussion

1349.	Find the number of terms in the following expansions. (ii) ( 5x-(1)/(x^3) )^(17)
Answer» ANSWER :`=18`

Discussion

1350.	If w is a complex cube root unity then \|{:(1,1+w,1+w^(2)),(1+w,1+w^(2),1),(1+w^(2),1,1+w):}\|=
Answer» `-2` 4 0 2 Answer :B

Discussion

Explore topic-wise InterviewSolutions in .

Write the component statements of the following compound statements (i) All numbers are even or odd. (ii) 18 is divisible by 2 and 9. (iii) all sides and all angles of a square are equal. (iv) this pen is black or blue.

Consider the expansion of (3x^3+2/x^2)^40 Assuming the term containing x^20 as the (r+1)^(th)term, find the coefficient of x^20 in the expansion of (3x^3+2/x^2)^40

Obtain the equation at the line in Ex. (1) to (10) satisfying given condition : Equation of line with p=2 and sin theta = (4)/(5).

If the sum of p terms of an AP is q and the sum of q terms is p, then show that the sum of p+q terms is -(p+ q). Alos, find the sum of first p-q terms (where, p gt q)

If f:{1,2,3,....}rarr{0, pm 1, pm2, .....} isdefined byf(n)= {:{(n//2 , "if n is even"),(-((n-1)/(2)), "if n is odd"):}then f^(-1)(-100) is

L_1 : 3x+4y+8=0 , L_2 : 2x+7y-1=0 Equation of the line through B parallel to AC is

If vec(u)= vec(a)- vec(b), vec(v)= vec(a) + vec(b) and |vec(a)| =|vec(b)|=2, then |vec(u) xx vec(v)|=

A (-2, 2, 3) and (13, -3, 13) and L is a line through A A point P movesin the space such that 3PA = 2PB, then the locus of P is

If Sin^(4)2x+Cos^(4)2x=Sin2xCos2 then x=

If f(x)=(1)/(sqrt(x+2sqrt(2x-4)))+(1)/(sqrt(x-2sqrt(2x-4))) for x gt 2, then f(11)=

Let x_1,x_2, x_3, x_4, x_5 be the observations with mean m and standard deviation S. The standard deviation of the observations kx_1,kx_2,kx_3,kx_4,kx_5 is……….

How many committees of 5 members each can be formed with 8 officials and 4 non - official members in the following cases: each consits of 3 officials and 2 non - official members.

How many committees of 5 members each can be formed with 8 officials and 4 non - official members in the following cases: each contains at least two non-official members

How many committees of 5 members each can be formed with 8 officials and 4 non - official members if a particular official members is never included.

How many committees of 5 members each can be formed with 8 officials and non - official members in the following cases: a particular non-official members is always included?

(cos h(x))/(1-tan h x) + (sin h(x))/(1-cot h(x)) =

(d)/(dx) {Tan ^(-1)"" (sqrt(1+ x ^(2))+ sqrt(1- x ^(2)))/( sqrt(1+ x ^(2))- sqrt(1- x ^(2)))}=

The value of 'c' of Lagrange's mean value theorem for f(x) = x^(3) - 5x^(2) - 3xin [ 1,3] is

If x, y, z are perpendicular distances from circumcentre to the sides of Delta^("le")ABC respectively then (xyz)/(abc){(a)/(x)+(b)/(y)+(c)/(z)}=

Express the following in the form a+bi (8+7i) (8-7i)

Find the component statements of the following compound statements: Chandigarh is the capital of Haryana and U.P.

Find the derivative of the following functions:( i)Sinx.cos x

In the space A(bar(a)) is a point and bar(b) is a vector.If P(bar(r )) is any point such that bar(r ) xx bar(b) = bar(a) xx bar(b) then show that locus of P is a straight line.

Find (a, b) if Lt_(xtooo){sqrt(x^(2)-x+1)-ax-b}=0

The solution set of sintheta+costheta=2 is ………

If cosecx=1+cotx, then x=2npi,2npi+(pi)/(2),ninZ.

Describe the sample space for the indicated experiments. A coin is tossed and then a die is rolled only in case a head is shown on the coin

Find the derivative of the w.r.to x. (sin x ) ^(log x) + x ^( sin x)

A letter is chosen at random from the 'ASSASSINATION'. Find the probability that letter is (i) a vowel (ii) a consonant.

Find which one is true.If A and B are two matrices such that A+B and BA are both defined then:

If tan^(3)x+3gt3 tan x +tan^(2)xthen

Differentiate the following functions w.r.t. x. f(x) = sqrt( x^2 +1)

If 0^(@)lt theta lt 90^(@) and cos theta=(4)/(5) find the values of "cosec"(180^(@)+theta)

If the straight line 3x+4y=8 is equidistant from (2,3) and (-4,a) then the value of a is

Find the value of alpha and p if the equation xcosalpha+ysinalpha=p is the normal form of the line sqrt(3x)+y+2=0.

Differentiate the following functions with respect to x from definition. (i) x^2

If in aDelta ABC, r_1= 2r_2= 3r_3,then the perimeter of the triangle is equal to

If A=tan6^(@) tan42^(@), B=cot66^(@) cot78^(@) then

The minimum and maximum values of cos x + 3sqrt(2)sin(x+(pi)/(4)) + 6 are

Find the condition that the equation ax^(2) + 2hxy + by^(2) + 2gx + 2fy + c = 0 to takethe form aX^(2) + 2hXY + bY^(2) = 0when the axes are translated.

Prove that the locus of mid-point of focal chords of parabola y^(2)=4ax "is" y^(2)=2a(x-a).

If p implies(qvvr) has validity F then validity of statement p, q and r is …….respectively.

By shifting origin at (-2,3) find new transformed form at the equation y+3x=2.

sin(pi/10)sin((13pi)/10)=

If A=[(3,2,1),(0,4,2),(1,2,3)]and B=[(3,2,0),(4,8,0),(-1,6,2)],then

If piltxlt2pi then (sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqrt(1-cosx))

If z=x+iy, where x and y are real numbers and |x|+|y| lt= k|z| then k=.....

Find the number of terms in the following expansions. (ii) ( 5x-(1)/(x^3) )^(17)

If w is a complex cube root unity then |{:(1,1+w,1+w^(2)),(1+w,1+w^(2),1),(1+w^(2),1,1+w):}|=