14949 + Interview Questions in Maths in Class 11 Page 74 InterviewSolution

3651.	If sec^(4) theta+ sec^(2) theta = 10 +tan^(4)theta + tan^(2) theta, then sin^(2) theta
Answer» `(2)/(3)` `(3)/(4)` `(4)/(5)` `(5)/(6)` Answer :C

Discussion

3652.	Assertion (A) : The equation Sin^(2)x+Cos^(2)y=2Sec^(2)z is only solvable sinx=1 cosy, 1 and secz=1 where x, y, z in R Reason (R) : Maximum value of Sin x and Cosy is 1 and minimum value of sec z is 1
Answer» Both A and R are true and R is correct explanation of A Both A and R are true but R is not the correct explanation of A A is FALSE, R is true A is true, R is false Answer :A

Discussion

3653.	Descibe the sample space :A coinis tossed twice . Ifit results in a head , a die is thrown , otherwise a coin is tossed .
Answer» Answer :`S=[HH1,HH2,HH3,HH4,HH5,HH6,TH1,TH2,TH3,TH4,TH5,TH6,HTH,HTT,T TH, T T T}`

Discussion

3654.	sin x = 3/5, x lies in second quadrant.
Answer» Answer :`COSEC x = 5/3, cos x =-4/5 , SEC x =- 5/4 , tan x=- 3/4, COT x =- 4/3`

Discussion

3655.	Using binomial theorem, compute (98)^5.
Answer» ANSWER :9039207968

Discussion

3656.	If there are (2n + 1) terms in the series 1, 3, 5, 7, 9, ,. .. , prove that the sum of terms at odd places and the sum of terms at even places has the ratio (n + 1)/(n).
Answer» SOLUTION :N/a

Discussion

3657.	If the three vectors 2bari -barj +bark, bari+ 2barj -3bark, 3bari + lamdabarj + 5bark are coplanar then lamda =
Answer» 4 `-4` 2 3 Answer :B

Discussion

3658.	If t_(n) = (1)/(4) (n+2) (n+3) for n=1,2,3….. then (1)/( t_1) + (1)/( t_2) + (1)/( t_3) + ….. + (1)/( t_(2003) )=
Answer» `( 4006)/( 3006)` `( 4003)/( 3007)` `( 4006)/( 3008)` `( 4006)/( 3009)` ANSWER :D

Discussion

3659.	I : If f'(a)gt0 then f is increasing at x=a II : If f is increasing at x=a then f(a) need not to be positive which of the above statements are true
Answer» only I only II both I and II neither I nor II Answer :C

Discussion

3660.	The price relatives and weights of a set of commodities are given below: If the sum of weights is 40 and the index for the set is 122, find the numerical values of x and y.
Answer» ANSWER :`x=7 and y=8`

Discussion

3661.	Evaluate the following limits : Lim_(x to 1) (x^(2)-sqrt(x))/(sqrt(x)-1)
Answer» Answer :` Lim_(X to 1) ((x^(2)-1)-(LOG x)(x-1))/(x-1)`

Discussion

3662.	The point (2,3) is first reflected in the straight line y=x and then translated through a distance of 2 units along the positive direction X-axis. The coordinates of the transformed point are
Answer» (5,4) (2,3) (5,2) (4,5) ANSWER :C

Discussion

3663.	Find the coefficient of x^5 in the expansion of (1 + 2x)^6 (1-x)^7.
Answer» ANSWER :`171`

Discussion

3664.	The product of perpendiculars from origin to the pair of lines 2x^(2)+5xy+3y^(2)+6x+7y+4=0 is
Answer» `(2)/(13)` `(4)/(sqrt26)` `(1)/(sqrt26)` `(3)/(sqrt26)` ANSWER :B

Discussion

3665.	Discuss the continuity of the functionf(x) = underset(n to oo)(Lt) (log (2 + x) - x^(2n) sin x)/(1 + x^(2n)) " at " x = 1.
Answer» ANSWER :DISCONTINUOUS at x=1

Discussion

3666.	If A,B,C and D are angles of a quadrilateral and sinA/2sinB/2sinC/2sinD/2=1/4,prove that A=B=C=D=pi//2
Answer» Solution :`(2sinA/2sinB/2)(2sinC/2sinD/2)=` `rArr {cos(A-B)/2 - cos(A+B)/2}{cos(C-D)/2-cos(C+D)/2}=1` Since, `A+B=2pi-(C+D)`, the above EQUATION becomes, `rArr {cos(A-B)/2 -cos(A+B)/2}{cos(C-D)/2 + cos(A+B)/2}=1` `rArr cos^(2)(A+B)/2 -cos(A+B)/2{cos(A-B)/2-cos(C-D)2}+1-cos(A-B)/2cos(C-D)/2=0` This is a QUADRATIC equation in `cos(A+B)/2` which has real ROOTS. `rArr {cos(A-B)/2-cos(C-D)/2}^(2)-4{1-cos(A-B)/2.cos(C-D)} ge 0` `(cos(A-B)/2 +cos(C-D)/2)^(2) ge 4` `rArr cos(A-B)/2 + cos(C-D)/2 ge`, Now both `cos(A-B)/2` and `cos(C-D)/2 le 1` `rArr cos(A-B)/2=1` and `cos(C-D)/2=1` `rArr (A-B)/2 =0 = (C-D)/2` `A=B, C=D` Similarly, A=C,B=D `rArr A=B=C=D=pi/2`

Discussion

3667.	Convert the products into sum or difference. If angles are given in degrees, evaluate from tables. sin ""(A +B)/(2) cos ""(A -B)/(2)
Answer» ANSWER :`1/2 [SIN A + sin B]`

Discussion

3668.	If the sum of thereciprocals of the intercepts made by a variable straight line on the axes of coordinates is a constant, then prove that the line always passes through a fixed point.
Answer» ANSWER :`(1/k,1/k)`

Discussion

3669.	If bare_(1),bare_(2) and bare_(3) are mutually perpendicular unit vectors then what is the magnitude of bare_(1)+bare_(2) + bare_(3)?
Answer» ANSWER :`SQRT3`

Discussion

3670.	The pair of lines 9x^(2)+y^(2)+6xy-9=0 are
Answer» PARALLEL and COINCIDENT Parallel but not coincident Imaginary Coincident only ANSWER :B

Discussion

3671.	Let f(x){:{(2x+a",",x ge -1),(bx^(2)+3,x lt -1):} and g(x)={:{(x+4",",0 le x le 4),(-3x-2,-2 lt x lt 0):} If the domain of g(f(x)) is [-1, 4], then
Answer» `a =1, B GT 5` `a=2, b gt 7` `a=2, b gt 10` `a=0, b in R` Answer :D

Discussion

3672.	If f(x) = \|{:(sinx,sina, sin b),(cos x , cos a, cos b),(tanx,tana,tanb):}\|,where 0 lt a lt b lt ( pi )/(2), then the equation f'(x) = 0 has, in the interval (a,b)
Answer» ATLEAST ONE ROOT ATMOST one root no root exactly one root Answer :A

Discussion

3673.	Find the derivative of the w.r.to x. x ^(x) + e ^(e ^(x))
Answer» ANSWER :`X ^(x) (1 + LOG x) + E ^(e^(x)).e ^(x)`

Discussion

3674.	Find the mean deviation about the mean for the data in
Answer» ANSWER :157.92

Discussion

3675.	If f: R to C is defined by f(x) =e^(2ix) AA x in R, then f is (where C denotes the set of all complex numbers)
Answer» One-one Onto One-one and Onto neither one-one nor Onto Answer :D

Discussion

3676.	IfA+ B+C= pi//2 , " then " tan 2A + tan 2B+ tan 2C=
Answer» SIN2A SIN2B SIN 2C Cot2A Cot2B Cot2C Cos2A COS2B Cos2C Tan2A Tan2B Tan2C Answer :D

Discussion

3677.	Let f:R-{(3)/(2) } toR.f(x)= (3x+ 5)/(2x-3)Let f_2 (x)=f(f(x)) , f_3 (x) = f(f_2(x)) ,.....f_x(x)= f(f_(n-1) (x)),"then"f_(2008)(x)+f_(2009)(x)=
Answer» `(2X^(2)-5)/(2x-3)` `(2x^(2)-5)/(2x+3)` `(2x^(2)-5)/(2x+3)` `(2x^(2)+5)/(2x-3)` ANSWER :D

Discussion

3678.	Identify the Quantifiers in the following statements: for all negative integers x,x^(3) is also a negative integers.
Answer» ANSWER :UNIVERSAL QUANTIFIER is USED

Discussion

3679.	The radius of a sphere increases at the rate of 0.03 cm/sec. Find the rate of increase in the volume of the sphere when the radius is 5 cm.
Answer» ANSWER :`15pi`

Discussion

3680.	Find the value of (a^2 + sqrt(a^2 - 1))^4 + (a^2 - sqrt(a^2 - 1))^4 .
Answer» ANSWER :`2a^8` + `12a^6` - `10a^4` -`4a^2` + 2

Discussion

3681.	Evaluate the following limits : Lim_( x to 0) ((1+x)^(m)-1)/((1+x)^(n)-1)
Answer» ANSWER :`m/n`

Discussion

3682.	The points D, E, F are the midpoints of the sides bar(BC), bar(CA),bar(AB) " of " Delta ABCrespectively. If A=(-2,3,4), D =(1,-4,2),E =(-5,2,-3) then F=
Answer» (-8,9,-1) (4,-3,9) (-2,-5,-5) (-6,1,3) ANSWER :B

Discussion

3683.	Find the sumto n terms series 1^(2) + (1^(2) + 2^(2)) (1^(2) + 2^(2) + 3^(2)) +. . . . .
Answer» ANSWER :`(N(n+1)^2(n+2))/12`

Discussion

3684.	If 4 n alpha = pi, then the numerical value of tan alpha tan 2 alpha tan 3 alpha….tan (2n - 1) alpha is equal to
Answer» -1 0 1 2 Answer :C

Discussion

3685.	If A -={2x //x in N } B -= {4x//x in N } , then A uuB=
Answer» `{2,4,6,8,10,12,14,16,18,20….}` `{4,8,12,16,20….}` `{2,4,6,8,10,12,14,16,18,20}` `{4,8,12,16,20}` ANSWER :A

Discussion

3686.	Assertion (A): If S be the area of a circle having radius x and A the area of an euilateral triangle having side pix at any isntant, then (dA)/(dt) gt (ds)/(dt) Reason (R ) : A gt S
Answer» BothA and R are true and R is the correct EXPLANATION of A Both A and R are true R is not the correct explanation of A A is true but R is false A is false but R is true ANSWER :A

Discussion

3687.	Find the range of the following functions given by f(x)= \|x-3\|
Answer» ANSWER :`[0, OO)`

Discussion

3688.	If the tangents of the angles A and B of triangle ABC satisfy the equation abx^(2)-c^(2)x+ab=0, then
Answer» `tanA=a//B` `tanB=b//a` `cocS=0` `SIN^(2)A+sin^(2)B+sin^(2)C=2` ANSWER :A::B::D

Discussion

3689.	Find the derivative of the w.r.t.x e ^(x) (x - (1)/(x)) ^(3)
Answer» ANSWER :`E ^(X)`

Discussion

3690.	Find the 4^(th)term in the expansion of (x-2y)^12.
Answer» ANSWER :`1760` `x^9` `Y^3`

Discussion

3691.	Radian value of 47^@ 30' is ......
Answer» ANSWER :`(19.pi)/72`

Discussion

3692.	Write the negative of the proposition : "If a number is divisible by 15, then it is divisible by 5 or 3".
Answer» Answer :A NUMBER is DIVISIBLE by 15 and it is not divisible by 5 and 3.

Discussion

3693.	Find the value of tan(Cos^(-1)4/5 + Tan^(-1) 2/3)
Answer» `17/6` `7/16` `16/7` `6/17` ANSWER :A

Discussion

3694.	Find the range and domain of the function defined by f(x)= (1)/(2- sin 3x)
Answer» ANSWER :`D_(F)= R, R_(f) = [(1)/(3), 1]`

Discussion

3695.	The range off(x)=[1+sinx]+[2+sin""x/2]+[3+sin""x/2]+...+[n+sin""x/n]AA x in [0, pi], where [.] where denotes the greatest integer function, is
Answer» `{(N^(2)+n-2)/(2),(n(n+1))/(2)}` `{(n(n+1))/(2)}` `{(n^(2)+n-2)/(2), (n(n+1))/(2), (n^(2)+n+2)/(2)}` `{(n(n+1))/(2),(n^(2)+n+2)/(2)}` ANSWER :D

Discussion

3696.	-i
Answer» SOLUTION :MULTIPLICATIVE INVERSE of `-i=(1)/(-i)` `""=(1)/(-i)xx(i)/(i)=(i)/(-i^(2))= (i)/(- (-1))=i`

Discussion

3697.	If 1+sin x sin ^(2)""(x)/(2) = 0 then x is
Answer» 1 2 3 no solution Answer :D

Discussion

3698.	ABC is a triangular park with AB=AC=100 meters. A clock tower is situated at the mid point of BC. The angles of elevation of the tower at A and B are cot^(1) (3.2) and "cosec "^(-1)(2.6) respectively. The height of the tower is
Answer» 35 m 25 m 30 m 20 m Answer :B

Discussion

3699.	If rr_(2)=r_(1)r_(3)then find B.
Answer» ANSWER :` 90 ^(@) `

Discussion

3700.	Equation of the parabola with focus (0,-3) and the directrix y=3 is:(a)x^(2)=-12y(b)x^(2)=12y(c)x^(2)=3y(d)x^(2)=-3y
Answer» `X^(2)=-12Y` `x^(2)=12y` `x^(2)=3Y` `x^(2)=-3y` ANSWER :A

Discussion

Explore topic-wise InterviewSolutions in .

If sec^(4) theta+ sec^(2) theta = 10 +tan^(4)theta + tan^(2) theta, then sin^(2) theta

Assertion (A) : The equation Sin^(2)x+Cos^(2)y=2Sec^(2)z is only solvable sinx=1 cosy, 1 and secz=1 where x, y, z in R Reason (R) : Maximum value of Sin x and Cosy is 1 and minimum value of sec z is 1

Descibe the sample space :A coinis tossed twice . Ifit results in a head , a die is thrown , otherwise a coin is tossed .

sin x = 3/5, x lies in second quadrant.

Using binomial theorem, compute (98)^5.

If there are (2n + 1) terms in the series 1, 3, 5, 7, 9, ,. .. , prove that the sum of terms at odd places and the sum of terms at even places has the ratio (n + 1)/(n).

If the three vectors 2bari -barj +bark, bari+ 2barj -3bark, 3bari + lamdabarj + 5bark are coplanar then lamda =

If t_(n) = (1)/(4) (n+2) (n+3) for n=1,2,3….. then (1)/( t_1) + (1)/( t_2) + (1)/( t_3) + ….. + (1)/( t_(2003) )=

I : If f'(a)gt0 then f is increasing at x=a II : If f is increasing at x=a then f(a) need not to be positive which of the above statements are true

The price relatives and weights of a set of commodities are given below: If the sum of weights is 40 and the index for the set is 122, find the numerical values of x and y.

Evaluate the following limits : Lim_(x to 1) (x^(2)-sqrt(x))/(sqrt(x)-1)

The point (2,3) is first reflected in the straight line y=x and then translated through a distance of 2 units along the positive direction X-axis. The coordinates of the transformed point are

Find the coefficient of x^5 in the expansion of (1 + 2x)^6 (1-x)^7.

The product of perpendiculars from origin to the pair of lines 2x^(2)+5xy+3y^(2)+6x+7y+4=0 is

Discuss the continuity of the functionf(x) = underset(n to oo)(Lt) (log (2 + x) - x^(2n) sin x)/(1 + x^(2n)) " at " x = 1.

If A,B,C and D are angles of a quadrilateral and sinA/2sinB/2sinC/2sinD/2=1/4,prove that A=B=C=D=pi//2

Convert the products into sum or difference. If angles are given in degrees, evaluate from tables. sin ""(A +B)/(2) cos ""(A -B)/(2)

If the sum of thereciprocals of the intercepts made by a variable straight line on the axes of coordinates is a constant, then prove that the line always passes through a fixed point.

If bare_(1),bare_(2) and bare_(3) are mutually perpendicular unit vectors then what is the magnitude of bare_(1)+bare_(2) + bare_(3)?

The pair of lines 9x^(2)+y^(2)+6xy-9=0 are

Let f(x){:{(2x+a",",x ge -1),(bx^(2)+3,x lt -1):} and g(x)={:{(x+4",",0 le x le 4),(-3x-2,-2 lt x lt 0):} If the domain of g(f(x)) is [-1, 4], then

If f(x) = |{:(sinx,sina, sin b),(cos x , cos a, cos b),(tanx,tana,tanb):}|,where 0 lt a lt b lt ( pi )/(2), then the equation f'(x) = 0 has, in the interval (a,b)

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

Find the mean deviation about the mean for the data in

If f: R to C is defined by f(x) =e^(2ix) AA x in R, then f is (where C denotes the set of all complex numbers)

IfA+ B+C= pi//2 , " then " tan 2A + tan 2B+ tan 2C=

Let f:R-{(3)/(2) } toR.f(x)= (3x+ 5)/(2x-3)Let f_2 (x)=f(f(x)) , f_3 (x) = f(f_2(x)) ,.....f_x(x)= f(f_(n-1) (x)),"then"f_(2008)(x)+f_(2009)(x)=

Identify the Quantifiers in the following statements: for all negative integers x,x^(3) is also a negative integers.

The radius of a sphere increases at the rate of 0.03 cm/sec. Find the rate of increase in the volume of the sphere when the radius is 5 cm.

Find the value of (a^2 + sqrt(a^2 - 1))^4 + (a^2 - sqrt(a^2 - 1))^4 .

Evaluate the following limits : Lim_( x to 0) ((1+x)^(m)-1)/((1+x)^(n)-1)

The points D, E, F are the midpoints of the sides bar(BC), bar(CA),bar(AB) " of " Delta ABCrespectively. If A=(-2,3,4), D =(1,-4,2),E =(-5,2,-3) then F=

Find the sumto n terms series 1^(2) + (1^(2) + 2^(2)) (1^(2) + 2^(2) + 3^(2)) +. . . . .

If 4 n alpha = pi, then the numerical value of tan alpha tan 2 alpha tan 3 alpha….tan (2n - 1) alpha is equal to

If A -={2x //x in N } B -= {4x//x in N } , then A uuB=

Assertion (A): If S be the area of a circle having radius x and A the area of an euilateral triangle having side pix at any isntant, then (dA)/(dt) gt (ds)/(dt) Reason (R ) : A gt S

Find the range of the following functions given by f(x)= |x-3|

If the tangents of the angles A and B of triangle ABC satisfy the equation abx^(2)-c^(2)x+ab=0, then

Find the derivative of the w.r.t.x e ^(x) (x - (1)/(x)) ^(3)

Find the 4^(th)term in the expansion of (x-2y)^12.

Radian value of 47^@ 30' is ......

Write the negative of the proposition : "If a number is divisible by 15, then it is divisible by 5 or 3".

Find the value of tan(Cos^(-1)4/5 + Tan^(-1) 2/3)

Find the range and domain of the function defined by f(x)= (1)/(2- sin 3x)

The range off(x)=[1+sinx]+[2+sin""x/2]+[3+sin""x/2]+...+[n+sin""x/n]AA x in [0, pi], where [.] where denotes the greatest integer function, is

-i

If 1+sin x sin ^(2)""(x)/(2) = 0 then x is

ABC is a triangular park with AB=AC=100 meters. A clock tower is situated at the mid point of BC. The angles of elevation of the tower at A and B are cot^(1) (3.2) and "cosec "^(-1)(2.6) respectively. The height of the tower is

If rr_(2)=r_(1)r_(3)then find B.

Equation of the parabola with focus (0,-3) and the directrix y=3 is:(a)x^(2)=-12y(b)x^(2)=12y(c)x^(2)=3y(d)x^(2)=-3y