14949 + Interview Questions in Maths in Class 11 Page 6 InterviewSolution

251.	If A,B,C are acute angles , tan A=1/2 , tan B=1//5 , tan C=1//8 , " then " A+B+C=
Answer» `(PI)/(12)` `(pi)/(6)` `(pi)/(4)` `(pi)/(2)` Answer :C

Discussion

252.	Find th point to which the origin has to be shifted to eliminate x and y terms in the equation 14x^(2)-4xy+11y^(2)-36x+48y+41=0.
Answer» ANSWER :(1,-2)

Discussion

253.	Show that f (x) = x ^(2) is differentiable AA x in R. Hence find the derived function.
Answer» ANSWER :`A X in R`

Discussion

254.	Let y = mx and y = m^(1)x be the lines represented by the equation ax2+2hxy+by+=0. Match the following and choose the correct answer.
Answer» B,d,c,a b,c,d,a c,d,b,e b,c,e,a Answer :D

Discussion

255.	Find the acute angle between the pair of lines represented byequation (xcosalpha-ysinalpha)^(2)=(x^(2)+y^(2))sin^(2)alpha where alpha lt (pi)/(4)
Answer» ANSWER :`2ALPHA`

Discussion

256.	Consider a triangle whose sides are along x+y = 2, 3x-4y = 6 and x-y = 0.Find the mid point of the hypotenuse and the length of the hypotenuse
Answer» SOLUTION :(-2,-3), 10

Discussion

257.	If 32 tan^(8) theta=2 cos^(2) alpha-3 cos alpha and 3 cos 2 theta=1, then the general values of alpha is
Answer» `2n pi, n in Z` `NPI+-(pi)/(3), n in z` `2NPI+(pi)/(3), n in z` `2npi+-(2pi)/(3), n in z` Answer :D

Discussion

258.	A window is in the shape of a rectangle surmounted by a semi-circle. If the perimeter of the window be 20 feet then find the maximum area.
Answer» `(L^(2))/(2pi+4)` `(l^(2))/(pi+8)` `(l^(2))/(2pi+8)` `(l^(2))/(8pi+4)` ANSWER :C

Discussion

259.	Find the rth term of an A.P., sum of whose first n terms is 2n + 3n^(2).
Answer» ANSWER :6r-1

Discussion

260.	Which of the following is/are a rational number ?
Answer» `sin(tan^(-1)3+tan^(-1)""1/3)` `COS(pi/2-sin^(-1)""3/4)` `log_(2)(sin(1/4sin^(-1)""SQRT(63)/8))` `tan(1/2cos^(-1)""sqrt(5)/3)` Answer :A::B::C

Discussion

261.	If bara,barb,barc are non-coplanar vectors and (bara+2barb+barc).(bara-barb)xx(bara-barb-barc)=lamda[barabarbbarc] then lamda=
Answer» 3 5 7 8 Answer :A

Discussion

262.	Find the standard deviation from the following observations: 15,18,13,20,17,10,16,19,22,20.
Answer» Solution : Here `N=10` LET ASSUMED mean `a=16` STANDARD DEVIATION `sigma=sqrt((sumd_(i)^(2))/n-((sumd_(i))/n)^(2))` `=sqrt(128/10-(10/10)^(2))` `sigma=sqrt(12.8-1)` `=sqrt(11.8)=3.42`

Discussion

263.	If A=(2,4,1),B(-1,0,1),C=(-1,4,2), then the distance of (1,-2,1) from the plane ABC is
Answer» `2//3` `14//13` `4//3` 1 Answer :B

Discussion

264.	Statement 1: cosec^(-1)(1/2+1/(sqrt(2)))gt sec^(-1)(1/2+1/(sqrt(2))) Statement 2: cosec^(-1)x lt sec^(-1)x if 1 le x lt sqrt(2)
Answer» Both I and II are individually trueand II is the correct EXPLANATION of I Both I and II are individually TRUE but II is not the correct explanation of I I is true but II is FALSE I is false but II is true Answer :C

Discussion

265.	ABC is any triangle and P is a point on the side BC. If Q is a point such that bar(PQ)=bar(AP)+bar(PB)+bar(PC), then
Answer» `BAR(AQ)=bar(AB)+bar(BC)+bar(AC)` Q is fixed for all position of P on BC Q depends on the position of P `bar(AQ)=bar(AB)+bar(AC)-bar(BC)` ANSWER :B

Discussion

266.	Prove the following "sin"2x+2"sin"4x+"sin"6x=4cos^(2)x"sin"4x
Answer» ANSWER :`=4COS^(2)X"SIN"4x=RHS`

Discussion

267.	Find the mean and the standard deviation from the following:
Answer» ANSWER :MEAN = 22677 APPROX, `SIGMA=`RS. 25.49 approx

Discussion

268.	If sintheta=(sqrt(3))/(2) and theta lies in the second quadrant, find the general solution.
Answer» ANSWER :`theta=2npi+(2PI)/(3)`

Discussion

269.	baraxxbara^(1)+barbxxbarb^(1)+barcxxbarc^(1)=
Answer» `BAR0` `BARA` `BARB` `BARC` ANSWER :A

Discussion

270.	Find the points at which the function f(x)=-(x-1)^3(x+1)^2
Answer» ANSWER :1

Discussion

271.	If alpha, beta are the roots of the equation 2x^(2) - 3x - 6 = 0, find the equation whose roots are alpha^(2) + 2 and beta^(2) + 2.
Answer» ANSWER :`4X^(2) - 49x + 118 = 0`

Discussion

272.	Find the mean, variance and standard deviation using short-cut method
Answer» ANSWER :93, 105.58, 10.27

Discussion

273.	Find the sum to n terms of the series whose nth term is 3n^(2)+2n
Answer» ANSWER :`(N)/(2) (n+1) (2n+3)`

Discussion

274.	If a polynomial of degree 'n' satisfies f(x)= f'(x) f^(11) (x) AA n in R " then "f(x)is
Answer» an ONTO FUNCTION an into function no such function is possible even function Answer :A

Discussion

275.	d/(dx)[(tanx-cotx)/(tanx+cotx)]=
Answer» `2 SIN2X` `-2SIN2X` `2 COS2X` `-2 cos 2x` Answer :A

Discussion

276.	A is a point on either of two line y+sqrt3absx=2 " at a distance of" 4/sqrt3 units from their point of intersection. The coordinates of the foot of perpendicular from A on the bisector of the angle between them are
Answer» `(-2//sqrt3,2)` (0,0) `(2//sqrt3,2)` (0,4) ANSWER :C

Discussion

277.	If cot^(-1)((1+x)/(1-x))=1/2cot^(-1)(1/x) then x=
Answer» `1/(SQRT(2))` `1/(sqrt(3))` `1/(sqrt(5))` `1/(sqrt(6))` ANSWER :B

Discussion

278.	Simplify:((-1)/(2)- (sqrt3)/(2)i)^(2)
Answer» ANSWER :`(-1)/(2) + (3)/(2)i`

Discussion

279.	Evaluate Lim_(x to a ) ((x+2)^(5/3)-(a+2)^(5/3))/(x-a)
Answer» ANSWER :`5/3 (a+2)^(2/3)`

Discussion

280.	Write the following sets in the roaster from. D= {t"/"t^(3) = t, t in R}
Answer» ANSWER :`= {-1, 0, 1}`

Discussion

281.	Expand the following expressions : (x-1/(2x))^(5)
Answer» Answer :`x^(5)-(5x^(3))/2+(5x)/2-5/(4x)+5/(16x^(3))-1/(32x^(5))`

Discussion

282.	If (sinx)/(a) = (cosx)/(b) = (tanx)/(c ) = k, then bc + (1)/(ck) + (ak)/(1+bk) is equal to
Answer» `K(a+(1)/(a))` `(1)/(k)(a+(1)/(a))` `(1)/(k^(2))` `(a)/(k)` ANSWER :B

Discussion

283.	A G.P has 2n terms. Its first term is a and last term is l then the product of all terms is…..
Answer» `(a L)^((N)/(2))` `( a l)^(n+1)` `(a l)^(n)` `(a l)^(2n)` ANSWER :C

Discussion

284.	If the equation y^(2) - 4x + 6y + 17 = 0 changed as y^(2) = 4axthen shifted origin is
Answer» (2,3) (-2,3) (-2,-3) (2,-3) ANSWER :D

Discussion

285.	underset(x to pi//2)lim (1-sin^(3)x)/(cos^(2)x)=
Answer» ANSWER :`3/2`

Discussion

286.	alpha,beta are the roots of ax^(2)+2bx+c=0 and alpha+delta,beta+delta are the roots of A x^(2)+2Bx+C=0, then what is (b^(2)-ac)//(B^(2)-AC) equal to ?
Answer» `(B//B)^(2)` `(a//A)^(2)` `(a^(2)b^(2))//(A^(2)B^(2))` `ab//AB` ANSWER :A::B

Discussion

287.	Answer the equation: inte^(4x)cos5xsin2xdx.
Answer» Answer :`(e^(4x))/(130)(4sin7x-7cos7x)-(e^(4x))/(50)(4sin3x-3cos3x)+C`

Discussion

288.	Prove that cos ^(2) A + cos ^(2) (A + 120^(@)) + cos ^(2) (A -120^(@)) = (3)/(2)
Answer» ANSWER :`3/2`

Discussion

289.	Write the first three terms in each of the following sequences defined by the following a_(n)=2n+ 5
Answer» ANSWER :`7, 9, 11`

Discussion

290.	If the angle alpha is acut, then the acute angle between the pair of staight lines x^2(costheta-sintheta)+2xycostheta+y^2(cos theta+sintheta)=0 is
Answer» `2THETA` `THETA/2` `theta/3` `theta` ANSWER :D

Discussion

291.	A bag contains a red ball, a black ball, a yellow ball and a white ball. One ball is selected randomly and note its colour and then put it into the bag. Again second ball is selected and note its colour. Write the sample space for this experiment. Hence, describe the following events : (1) A: Selected both the balls are of same colours. (2) B: Only one ball is white. (3) C: At least one ball is white. (4) D: Both the balls are of different colour. Hence, find AnnB,BuuC,AuuD,AnnD. What can we say about the events B and C ? What can we say about the events A and D?
Answer» <BR> Answer :`S={R R, RB, RY, RW, BR, BB, BY, BW, YR, YB, YY,YW, WR, WB, WY, WW}` `A={R R, WW, BB, YY}` `B={RW, BW, YW, WR, WB, WY}` `C = {RW, BW, YW, WR, WB, WY, WW}` `D={RB, RY, RW, BR, BY, BW, YR, YB, YW, WR, WB,WY}` `AnnB=phi,BuuC=C,AuuD=S,AnnD=phi,BsubC` A and D are mutually exclusive and exhanstive event.

Discussion

292.	If(r_2 -r_1 ) = 2r_2r_3 " then" angle A =
Answer» ` 60 ^(@) ` ` 90 ^(@) ` ` 30 ^(@) ` ` 45 ^(@) ` Answer :B

Discussion

293.	The solution set for the inequality2x^(2)+5x-3is
Answer» ` [-3, (-1)/(2)` ` [-3, (-1)/(2)` ` [-3, (-1)/(2)` ` [-3, (-1)/(2)` ANSWER :D

Discussion

294.	If the integersr gt 1 , n gt 2and coefficients of (3)th and (r+2) nd terms in the Binomial expansion of (1+x)^(2n) are equal ,then
Answer» N = 2r n = 3R `n=2r+1` NONE of these ANSWER :A

Discussion

295.	If a=4,b=5,c=6 then
Answer» `2A=C` `2A=2C` `3A=C` `A=3C` ANSWER :A

Discussion

296.	Find the radius and centre of the circle z bar(z)- (2 + 3i) z-(2-3i) bar(z)+ 9=0 where z is a complex variable
Answer» ANSWER :2

Discussion

297.	Evaluate the following limits : Lim_(x to 5) (log x - log 5)/(x-5)
Answer» ANSWER :`1/5`

Discussion

298.	Find the ratio in which the XZ-plane divides the line joining A(-2,3,4) and B(1,2,3)
Answer» ANSWER :`-3:2`

Discussion

299.	Match the following A(2, -3, 4), B(-5, 1, -7). The ratio in which AB divides {:("List-I", "List-II"),("(A) xy-plane", "(1) 3 :1"),("(B) yz-plane", "(2) 4:7"),("(C ) zx-plane", "(3) 2:5"):}
Answer» `{:(A,B,C),(2,3,1):}` `{:(A,B,C),(3,4,2):}` `{:(A,B,C),(2,4,1):}` `{:(A,B,C),(4,2,3):}` ANSWER :a

Discussion

300.	Equation of line common to pair of lines (p^(2)-q^(2))x^(2)+(q^(2)-r^(2))xy+(r^(2)-p^(2))y^(2)=0 and (l-m)x^(2)+(m-n)xy+(n-ly)^(y)=0 is
Answer» `x-y=0` `x+y=0` `x=2y` `2x=y` ANSWER :A

Discussion

Explore topic-wise InterviewSolutions in .

If A,B,C are acute angles , tan A=1/2 , tan B=1//5 , tan C=1//8 , " then " A+B+C=

Find th point to which the origin has to be shifted to eliminate x and y terms in the equation 14x^(2)-4xy+11y^(2)-36x+48y+41=0.

Show that f (x) = x ^(2) is differentiable AA x in R. Hence find the derived function.

Let y = mx and y = m^(1)x be the lines represented by the equation ax2+2hxy+by+=0. Match the following and choose the correct answer.

Find the acute angle between the pair of lines represented byequation (xcosalpha-ysinalpha)^(2)=(x^(2)+y^(2))sin^(2)alpha where alpha lt (pi)/(4)

Consider a triangle whose sides are along x+y = 2, 3x-4y = 6 and x-y = 0.Find the mid point of the hypotenuse and the length of the hypotenuse

If 32 tan^(8) theta=2 cos^(2) alpha-3 cos alpha and 3 cos 2 theta=1, then the general values of alpha is

A window is in the shape of a rectangle surmounted by a semi-circle. If the perimeter of the window be 20 feet then find the maximum area.

Find the rth term of an A.P., sum of whose first n terms is 2n + 3n^(2).

Which of the following is/are a rational number ?

If bara,barb,barc are non-coplanar vectors and (bara+2barb+barc).(bara-barb)xx(bara-barb-barc)=lamda[barabarbbarc] then lamda=

Find the standard deviation from the following observations: 15,18,13,20,17,10,16,19,22,20.

If A=(2,4,1),B(-1,0,1),C=(-1,4,2), then the distance of (1,-2,1) from the plane ABC is

Statement 1: cosec^(-1)(1/2+1/(sqrt(2)))gt sec^(-1)(1/2+1/(sqrt(2))) Statement 2: cosec^(-1)x lt sec^(-1)x if 1 le x lt sqrt(2)

ABC is any triangle and P is a point on the side BC. If Q is a point such that bar(PQ)=bar(AP)+bar(PB)+bar(PC), then

Prove the following "sin"2x+2"sin"4x+"sin"6x=4cos^(2)x"sin"4x

Find the mean and the standard deviation from the following:

If sintheta=(sqrt(3))/(2) and theta lies in the second quadrant, find the general solution.

baraxxbara^(1)+barbxxbarb^(1)+barcxxbarc^(1)=

Find the points at which the function f(x)=-(x-1)^3(x+1)^2

If alpha, beta are the roots of the equation 2x^(2) - 3x - 6 = 0, find the equation whose roots are alpha^(2) + 2 and beta^(2) + 2.

Find the mean, variance and standard deviation using short-cut method

Find the sum to n terms of the series whose nth term is 3n^(2)+2n

If a polynomial of degree 'n' satisfies f(x)= f'(x) f^(11) (x) AA n in R " then "f(x)is

d/(dx)[(tanx-cotx)/(tanx+cotx)]=

A is a point on either of two line y+sqrt3absx=2 " at a distance of" 4/sqrt3 units from their point of intersection. The coordinates of the foot of perpendicular from A on the bisector of the angle between them are

If cot^(-1)((1+x)/(1-x))=1/2cot^(-1)(1/x) then x=

Simplify:((-1)/(2)- (sqrt3)/(2)i)^(2)

Evaluate Lim_(x to a ) ((x+2)^(5/3)-(a+2)^(5/3))/(x-a)

Write the following sets in the roaster from. D= {t"/"t^(3) = t, t in R}

Expand the following expressions : (x-1/(2x))^(5)

If (sinx)/(a) = (cosx)/(b) = (tanx)/(c ) = k, then bc + (1)/(ck) + (ak)/(1+bk) is equal to

A G.P has 2n terms. Its first term is a and last term is l then the product of all terms is…..

If the equation y^(2) - 4x + 6y + 17 = 0 changed as y^(2) = 4axthen shifted origin is

underset(x to pi//2)lim (1-sin^(3)x)/(cos^(2)x)=

alpha,beta are the roots of ax^(2)+2bx+c=0 and alpha+delta,beta+delta are the roots of A x^(2)+2Bx+C=0, then what is (b^(2)-ac)//(B^(2)-AC) equal to ?

Answer the equation: inte^(4x)cos5xsin2xdx.

Prove that cos ^(2) A + cos ^(2) (A + 120^(@)) + cos ^(2) (A -120^(@)) = (3)/(2)

Write the first three terms in each of the following sequences defined by the following a_(n)=2n+ 5

If the angle alpha is acut, then the acute angle between the pair of staight lines x^2(costheta-sintheta)+2xycostheta+y^2(cos theta+sintheta)=0 is

If(r_2 -r_1 ) = 2r_2r_3 " then" angle A =

The solution set for the inequality2x^(2)+5x-3is

If the integersr gt 1 , n gt 2and coefficients of (3)th and (r+2) nd terms in the Binomial expansion of (1+x)^(2n) are equal ,then

If a=4,b=5,c=6 then

Find the radius and centre of the circle z bar(z)- (2 + 3i) z-(2-3i) bar(z)+ 9=0 where z is a complex variable

Evaluate the following limits : Lim_(x to 5) (log x - log 5)/(x-5)

Find the ratio in which the XZ-plane divides the line joining A(-2,3,4) and B(1,2,3)

Match the following A(2, -3, 4), B(-5, 1, -7). The ratio in which AB divides {:("List-I", "List-II"),("(A) xy-plane", "(1) 3 :1"),("(B) yz-plane", "(2) 4:7"),("(C ) zx-plane", "(3) 2:5"):}

Equation of line common to pair of lines (p^(2)-q^(2))x^(2)+(q^(2)-r^(2))xy+(r^(2)-p^(2))y^(2)=0 and (l-m)x^(2)+(m-n)xy+(n-ly)^(y)=0 is