14949 + Interview Questions in Maths in Class 11 Page 88 InterviewSolution

4351.	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

4352.	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

4353.	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

4354.	The minimum value of (x-alpha)(x-beta) is
Answer» AB `((a-b)^2)/4` 0 `-((a-b)^2)/4` ANSWER :D

Discussion

4355.	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

4356.	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

4357.	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

4358.	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

4359.	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

4360.	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

4361.	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

4362.	Find the circumcenter of the triangle whose vertices are (-2,3) , (2 , -1) , (4 , 0) .
Answer» ANSWER :`(3/2,5/2)`

Discussion

4363.	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

4364.	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

4365.	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

4366.	Sum to n terms the series whose nth terms is (1)/(4n^(2)-1)
Answer» ANSWER :`(N)/(2n+1)`

Discussion

4367.	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

4368.	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

4369.	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

4370.	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

4371.	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

4372.	Use Binomial theorem to find :(10.1)^4
Answer» ANSWER :10406.0401.

Discussion

4373.	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

4374.	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

4375.	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

4376.	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

4377.	Evaluate (n!)/((n-r)!), when n = 6, r = 2
Answer» ANSWER :30

Discussion

4378.	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

4379.	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

4380.	sin (60^(@) + theta) - sin ( 60^(@) - theta ) = sin theta.
Answer» ANSWER :`(-36)/(325), (323)/(325), ( - 36)/(323) `

Discussion

4381.	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

4382.	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

4383.	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

4384.	Find the sum of the series, 7,77,777,7777,"……….." to n tems.
Answer» ANSWER :`7/9[(10(10^(n-1)))/9-n]`

Discussion

4385.	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

4386.	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

4387.	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

4388.	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

4389.	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

4390.	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

4391.	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

4392.	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

4393.	If Np={px\|"x"inN} " then "N_3capN_5=…. .
Answer» ANSWER :`N_(15)`

Discussion

4394.	How many terms of the sequence sqrt3, 3, 3 sqrt3…… must be taken to make the sum 39 + 13 sqrt3 ?
Answer» ANSWER :6

Discussion

4395.	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

4396.	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

4397.	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

4398.	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

4399.	Check whether the statement is true or not : 32 is a multiple of 8.
Answer» ANSWER :T

Discussion

4400.	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 .

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?