14949 + Interview Questions in Maths in Class 11

1.	Find sin ""(x)/(2), cos "" (x)/(2) and tan "" (x)/(2) in each of the case: tan x = (-4)/(3) ,x in II quadrant.
Answer» Answer :`sin "" (x)/(2) = (2 SQRT5)/(5) COS "" (x)/(2) = (1)/(5) sqrt5, TAN "" (x)/(2) =2.`

Discussion

2.	A(2, 3), B(2, -3) are two points. The equation to the locus of P such that PA+PB=8 is
Answer» `16X^(2)+7Y^(2)-64x-48=0` `16x^(2)+7y^(2)-64x+48=0` `16x^(2)-7y^(2)+64x-48=0` `16x^(2)-7y^(2)+64x+48=0` ANSWER :1

Discussion

3.	Write the negation of the following simple statements. A leap year has 366 days.
Answer» ANSWER :A LEAP YEAR does not have 366 DAYS.

Discussion

4.	The minimum value of (x-alpha)(x-beta) is
Answer» AB `((a-b)^2)/4` 0 `-((a-b)^2)/4` ANSWER :D

Discussion

5.	If r% of students scored less than 33 marks, then find r, given N=50, class size=10, frequency of the rth. Percentile class =12 and cumulative frequency of the rth percentile class =22, lower limit of rth percentile class =30
Answer» ANSWER :`51.2`

Discussion

6.	If in aG.P., {a_(n)} it given that (a) 120 (b)124 (c) 128 (d) 132
Answer» 120 124 128 132 Answer :C

Discussion

7.	Bythe principleof mathematicalinduction , prove that for n le 11 .2 + 2.3 + 3.4 + …+ n(n+1) = ( n ( n +1)(n+2))/3
Answer» <P> ANSWER :p (N)

Discussion

8.	The sides of a triangle are sin alpha,cos alpha and sqrt(1+sin alpha cos alpha) for some 0 lt alpha lt pi/2. Then the greatest angle of the triangle is
Answer» `60^(@)` `150^(@)` `120^(@)` `90^(@)` ANSWER :C

Discussion

9.	An arc is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How high is it 2 m from the vertex of the parabola ?
Answer» ANSWER :`3.6` m

Discussion

10.	If in triangle ABC, sum "sin"(A)/(2)=(6)/(5) and sum II_(1)=9 (where l_(1),l_(2),l_(3))sin circumradius R is equal
Answer» `(15)/(8)` `(15)/(4)` `(15)/(2)` `(4)/(12)` Answer :A

Discussion

11.	If theta lies in the first quadrant and costheta=(8)/(17), then find the value of cos(30^(@)+theta)+cos(45^(@)-theta)+cos(120^(@)-theta).
Answer» ANSWER :`(23)/(17)((sqrt(3)-1)/(2)+(1)/(sqrt(2)))`

Discussion

12.	Find the circumcenter of the triangle whose vertices are (-2,3) , (2 , -1) , (4 , 0) .
Answer» ANSWER :`(3/2,5/2)`

Discussion

13.	Find the derivativ of the function w.r.to x tan ^(-1) (e ^(x) +1)
Answer» ANSWER :`(E ^(X))/( 1 + (e ^(x) +1 )^(2))`

Discussion

14.	How many different words can be formed by jumbling the letters in the words MISSISSIPPIin which no two S are adjacent?
Answer» ` ""^(6)C_ 4 . ""^(7)C_ 4 ` ` 6.8 ""^(8)C_ 4 ` `6.8 . ""^(7)C_4` ` 7. ""^(6) C_4.""^(8)C_4` Answer :D

Discussion

15.	sintheta=-(3)/(5)andpiltthetalt(3pi)/(2) then the value of (sectheta-cottheta)/(tantheta-cosectheta) is ………….
Answer» `(31)/(29)` `-(31)/(29)` `(30)/(29)` `-1` Answer :B

Discussion

16.	Sum to n terms the series whose nth terms is (1)/(4n^(2)-1)
Answer» ANSWER :`(N)/(2n+1)`

Discussion

17.	Let bara=bari-2barj+3bark,barb=2bari+3barj-bark,barc=lamdabari+barj+(2lamda-1)bark. If barc is parallel to the plane of bara,barb then lamda=
Answer» 1 0 `-1` 2 Answer :B

Discussion

18.	Equation of the plane passing through the point A (3, -2, -1) and parallel to the vectors (1, -2, 4) and (3, 2, -5) is
Answer» 2x+17y+8z+36=0 2x+17y+8z+36=0 2x+17y-8z-36=0 2x-17y-8z-36=0 Answer :A

Discussion

19.	If the transformed equation of a curve is X^(2) + 3XY - 2Y^(2) + 17X - 7Y - 11 = 0 when the axes are translated to the point (2,3) then find the original equation of the curve.
Answer» Answer :`X^(2) + 3xy - 2Y^(2) + 4X - y - 20 = 0`

Discussion

20.	i) If sinalpha=3/5 where pi/2ltalphaltpi, evaluate cos3alpha and tan 2alpha(TS March-2015) ii) If cosA=7/25 and (3pi)/2ltA lt2pi , then find the value of "cot"A/2 (iii) If 0ltAltpi/4 and cosA=4/5 find the values of sin2A and cos2A
Answer» ANSWER :i) `44/125, (-24)/7` ii) `(-4)/3` III) `24/25, 7/25`

Discussion

21.	The set of all x in the interval [0, pi] for which 2 sin ^() x - 3 sin x + 1 ge 0 is ____
Answer» `[0, (pi)/(6)]CUP {(pi)/(2)}cup [(5 pi)/( 6), pi]` `[0, (pi)/(6)] cup [(5 pi)/(6) , pi]` `[0, (pi)/( 2)] cup [ (5 pi)/( 6), pi]` `(0, (pi)/(2)) cup ((5 pi)/( 6), pi )` ANSWER :A

Discussion

22.	Use Binomial theorem to find :(10.1)^4
Answer» ANSWER :10406.0401.

Discussion

23.	If A=[(2,4,-5),(3,1,-2),(0,2,-3)],find the coefficient of order 3:
Answer» -2 2 0 none of these Answer :B

Discussion

24.	The value of a for which the functionf(x)=(4a-3)(x+log5)+2(a-7)"cot"(x)/(2)"sin"^(2)(x)/(2) does not possess critical points is
Answer» `(-OO,-4//3)` `(-oo,-1)` `[1,oo)` `(2,oo)` ANSWER :A::D

Discussion

25.	How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?
Answer» ANSWER :40320

Discussion

26.	angle made with the x-axis by a straight line drawn though (1,2) so that it intersects x+y=4 at a distance sqrt6//3 from (1,2) is
Answer» `150^@` `75^@` `60^@` `15^@` ANSWER :B::D

Discussion

27.	Evaluate (n!)/((n-r)!), when n = 6, r = 2
Answer» ANSWER :30

Discussion

28.	Complete the table using calculator and use the result to estimate the limit. 1 lim_(xrarr2)(x-2)/(x^2 -x -2)
Answer» ANSWER :`vec.3`

Discussion

29.	One bag contains 5 white and 3 black balls.Another bag contains 4 white and 6 black balls, If one ball is drawn from each bag, find the probability that (i)both are white (ii)both are black(iii)one white and one black.
Answer» ANSWER :(i)`=(1)/(4)` (II)`=(9)/(40)` (iii)`(21)/(40)`

Discussion

30.	sin (60^(@) + theta) - sin ( 60^(@) - theta ) = sin theta.
Answer» ANSWER :`(-36)/(325), (323)/(325), ( - 36)/(323) `

Discussion

31.	If bara, barb, barc are non - coplanar vectors and lamda is a real number then [lamda(bara+barb)lamda^(2)barblamdabarc]=[barabarb+barcbarb] for
Answer» EXACTLY ONE VALUE of `lamda` No value of `lamda` Exactly three values of `lamda` Exactly TWO values of `lamda` Answer :B

Discussion

32.	A cylindrical, gas container is closed atthe top and open bottom. If the iron plate of the top is 5/4 times as thich as the plate forming the cylindrical sides, the ratio of the radius to the height of the cylinder using minimum material for the same cpacity is
Answer» `3:4` `5:6` `4:5` `2:3` ANSWER :C

Discussion

33.	Fill in the blanks by choosing the correct answer from the bracket overline(2i^3-i^2) = ....., i^(-5) = …..(1-2i, 1+2i, i,-i,1, -1)Also express overline(2i^3-i^2) + (12i+i^(-5)) - (overline(5-i^5)) in the form x+iy
Answer» ANSWER :1 + 2I, -I, -4 + 12I

Discussion

34.	Find the sum of the series, 7,77,777,7777,"……….." to n tems.
Answer» ANSWER :`7/9[(10(10^(n-1)))/9-n]`

Discussion

35.	The set of values of lambda in R such that sin^(2) theta + cos theta = lambda cos^(2) theta holds for some theta, is
Answer» `(-OO,1]` `(-oo,-1]` `cancleO` `[-1,oo)` ANSWER :D

Discussion

36.	Find the derivatives of the function If y= b tan ^(-1)((x )/(a) + tan ^(-1) ((y)/(x))), find (dy)/(dx).
Answer» ANSWER :`((1)/(a ) - (y)/( x ^(2) + y ^(2)))/( (1)/(b) SEC ^(2) ""(y)/(b) - (x)/(x ^(2)+ y ^(2)))`

Discussion

37.	Line x+y= 4divides bar(AB) joining A(-2,3) and B(1,5) in ratio 1: lambda form A then lambda= …...
Answer» `3:2` `2:3` `1:3` `-2:3` ANSWER :B

Discussion

38.	Find the distance of the line 4x - y = 0 from the point P (4,1) measured along the line making an angle 135^@ with the positive x - axis.
Answer» ANSWER :`3sqrt2` UNITS

Discussion

39.	Express (1+i)/sqrt3+i in the form x + iy. Hence, find the polar form of (1+i)/sqrt3+i
Answer» ANSWER :`(sqrt3+1)/4 + I (sqrt3-1)/4`

Discussion

40.	The y-intercept cut from circle x^(2)+y^(2)+2x+4y-5=0 is
Answer» 6 units 8 units 10 units None of these ANSWER :A

Discussion

41.	If (sqrt(1 +x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2))=3thenx=
Answer» `(-1)/(t^2 (1 + SQRT(1 - t^4)))` `(t^2 (sqrt(1 - t^4) - 1))/(t^6)` `(1)/(t^2 (1 + sqrt(1 - t^4)))` `(1 - sqrt(1 - t^4))/(t^6)` ANSWER :A::B

Discussion

42.	A quadratic equation whose roots are tan22 1^(@)/2 and cot22 1^(@)/2 is
Answer» `X^(2)-2sqrt2x+1=0` `2X^(2)-sqrt2x+1=0` `x^(2)+2sqrt2x-1=0` `x^(2)-2sqrt2x-1=0` ANSWER :A

Discussion

43.	If Np={px\|"x"inN} " then "N_3capN_5=…. .
Answer» ANSWER :`N_(15)`

Discussion

44.	How many terms of the sequence sqrt3, 3, 3 sqrt3…… must be taken to make the sum 39 + 13 sqrt3 ?
Answer» ANSWER :6

Discussion

45.	A die is thrown twice . Find the probability that the sum of the two numbers obtains is 5 or 7?
Answer» ANSWER :`(5)/(18)`

Discussion

46.	Fill in the blanks to make each of the following a true statement : (A - B) cup (B- A)="…………."
Answer» ANSWER :`= (A CUP B)- (A CAP B)`

Discussion

47.	Find the value of cos^(2)112^((1^(0))/(2))-sin^(2)52^((1^(0))/(2)) cos^(2)52^((1^(0))/(2))-sin^(2)22^((1^(0))/(2))
Answer» ANSWER :`(SQRT(3)+1)/(4sqrt(2))`

Discussion

48.	If the distance between the foci of a hyperbola is 16 and itseccentricity is sqrt(2), then obtain the equation of the hyperbola.
Answer» ANSWER :`x^(2) - y^(2) - 32` , is required EQUATION of HYPERBOLA.

Discussion

49.	Check whether the statement is true or not : 32 is a multiple of 8.
Answer» ANSWER :T

Discussion

50.	A, B and C are mutually exclusive and exhaustive events. If P(B)=(3)/(2)P(A) and P(C)=(1)/(2)P(B), then find P(A).
Answer» ANSWER :`(4)/(13)`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Find sin ""(x)/(2), cos "" (x)/(2) and tan "" (x)/(2) in each of the case: tan x = (-4)/(3) ,x in II quadrant.

A(2, 3), B(2, -3) are two points. The equation to the locus of P such that PA+PB=8 is

Write the negation of the following simple statements. A leap year has 366 days.

The minimum value of (x-alpha)(x-beta) is

If r% of students scored less than 33 marks, then find r, given N=50, class size=10, frequency of the rth. Percentile class =12 and cumulative frequency of the rth percentile class =22, lower limit of rth percentile class =30

If in aG.P., {a_(n)} it given that (a) 120 (b)124 (c) 128 (d) 132

Bythe principleof mathematicalinduction , prove that for n le 11 .2 + 2.3 + 3.4 + …+ n(n+1) = ( n ( n +1)(n+2))/3

The sides of a triangle are sin alpha,cos alpha and sqrt(1+sin alpha cos alpha) for some 0 lt alpha lt pi/2. Then the greatest angle of the triangle is

An arc is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How high is it 2 m from the vertex of the parabola ?

If in triangle ABC, sum "sin"(A)/(2)=(6)/(5) and sum II_(1)=9 (where l_(1),l_(2),l_(3))sin circumradius R is equal

If theta lies in the first quadrant and costheta=(8)/(17), then find the value of cos(30^(@)+theta)+cos(45^(@)-theta)+cos(120^(@)-theta).

Find the circumcenter of the triangle whose vertices are (-2,3) , (2 , -1) , (4 , 0) .

Find the derivativ of the function w.r.to x tan ^(-1) (e ^(x) +1)

How many different words can be formed by jumbling the letters in the words MISSISSIPPIin which no two S are adjacent?

sintheta=-(3)/(5)andpiltthetalt(3pi)/(2) then the value of (sectheta-cottheta)/(tantheta-cosectheta) is ………….

Sum to n terms the series whose nth terms is (1)/(4n^(2)-1)

Let bara=bari-2barj+3bark,barb=2bari+3barj-bark,barc=lamdabari+barj+(2lamda-1)bark. If barc is parallel to the plane of bara,barb then lamda=

Equation of the plane passing through the point A (3, -2, -1) and parallel to the vectors (1, -2, 4) and (3, 2, -5) is

If the transformed equation of a curve is X^(2) + 3XY - 2Y^(2) + 17X - 7Y - 11 = 0 when the axes are translated to the point (2,3) then find the original equation of the curve.

i) If sinalpha=3/5 where pi/2ltalphaltpi, evaluate cos3alpha and tan 2alpha(TS March-2015) ii) If cosA=7/25 and (3pi)/2ltA lt2pi , then find the value of "cot"A/2 (iii) If 0ltAltpi/4 and cosA=4/5 find the values of sin2A and cos2A

The set of all x in the interval [0, pi] for which 2 sin ^() x - 3 sin x + 1 ge 0 is ____

Use Binomial theorem to find :(10.1)^4

If A=[(2,4,-5),(3,1,-2),(0,2,-3)],find the coefficient of order 3:

The value of a for which the functionf(x)=(4a-3)(x+log5)+2(a-7)"cot"(x)/(2)"sin"^(2)(x)/(2) does not possess critical points is

How many words, with or without meaning, can be formed using all the letters of﻿ the word EQUATION, using each letter exactly once?﻿

angle made with the x-axis by a straight line drawn though (1,2) so that it intersects x+y=4 at a distance sqrt6//3 from (1,2) is

Evaluate (n!)/((n-r)!), when n = 6, r = 2

Complete the table using calculator and use the result to estimate the limit. 1 lim_(xrarr2)(x-2)/(x^2 -x -2)

One bag contains 5 white and 3 black balls.Another bag contains 4 white and 6 black balls, If one ball is drawn from each bag, find the probability that (i)both are white (ii)both are black(iii)one white and one black.

sin (60^(@) + theta) - sin ( 60^(@) - theta ) = sin theta.

If bara, barb, barc are non - coplanar vectors and lamda is a real number then [lamda(bara+barb)lamda^(2)barblamdabarc]=[barabarb+barcbarb] for

A cylindrical, gas container is closed atthe top and open bottom. If the iron plate of the top is 5/4 times as thich as the plate forming the cylindrical sides, the ratio of the radius to the height of the cylinder using minimum material for the same cpacity is

Fill in the blanks by choosing the correct answer from the bracket overline(2i^3-i^2) = ....., i^(-5) = …..(1-2i, 1+2i, i,-i,1, -1)Also express overline(2i^3-i^2) + (12i+i^(-5)) - (overline(5-i^5)) in the form x+iy

Find the sum of the series, 7,77,777,7777,"……….." to n tems.

The set of values of lambda in R such that sin^(2) theta + cos theta = lambda cos^(2) theta holds for some theta, is

Find the derivatives of the function If y= b tan ^(-1)((x )/(a) + tan ^(-1) ((y)/(x))), find (dy)/(dx).

Line x+y= 4divides bar(AB) joining A(-2,3) and B(1,5) in ratio 1: lambda form A then lambda= …...

Find the distance of the line 4x - y = 0 from the point P (4,1) measured along the line making an angle 135^@ with the positive x - axis.

Express (1+i)/sqrt3+i in the form x + iy. Hence, find the polar form of (1+i)/sqrt3+i

The y-intercept cut from circle x^(2)+y^(2)+2x+4y-5=0 is

If (sqrt(1 +x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2))=3thenx=

A quadratic equation whose roots are tan22 1^(@)/2 and cot22 1^(@)/2 is

If Np={px|"x"inN} " then "N_3capN_5=…. .

How many terms of the sequence sqrt3, 3, 3 sqrt3…… must be taken to make the sum 39 + 13 sqrt3 ?

A die is thrown twice . Find the probability that the sum of the two numbers obtains is 5 or 7?

Fill in the blanks to make each of the following a true statement : (A - B) cup (B- A)="…………."

Find the value of cos^(2)112^((1^(0))/(2))-sin^(2)52^((1^(0))/(2)) cos^(2)52^((1^(0))/(2))-sin^(2)22^((1^(0))/(2))

If the distance between the foci of a hyperbola is 16 and itseccentricity is sqrt(2), then obtain the equation of the hyperbola.

Check whether the statement is true or not : 32 is a multiple of 8.

A, B and C are mutually exclusive and exhaustive events. If P(B)=(3)/(2)P(A) and P(C)=(1)/(2)P(B), then find P(A).

How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?