14949 + Interview Questions in Maths in Class 11 Page 2 InterviewSolution

51.	If alpha and beta are the roots of the equation, acostheta+bsintheta=c, then match the entries of column I with the entries of column- II
Answer» <P> Solution :(A) R, (B) S, ( C) P, (D) Q

Discussion

52.	Rewrite the following statement, with 'if ... , then' in five different ways conveying the same meaning: If a natural number is even, then its square is even.
Answer» Solution :We may REWRITE it in following ways: (i) A natural NUMBER is even implies that its square is even. ltbr (II) A natural number is even only if its square is even. (iii) For a natural number to be even it is necessary that its square is even. (IV) For the square of a natural number to be even, it is sufficient that the number is even. (v) If the square of a natural number is not even, then the natural number is not even.

Discussion

53.	If sin alpha cos beta=-(1)/(2), then cos alpha sin beta may be belong to
Answer» `[-(1)/(2),(1)/(2)]` `[-(1)/(2),0]` `[0,(1)/(2)]` `[(1)/(2),1]` ANSWER :A

Discussion

54.	If f and g are real functions defined by f(x)= x^(2) + 7 and g(x)= 3x + 5. Then, find each of the following (f(t)- f(5))/(t-5), if t ne 5
Answer» ANSWER :`t+ 5`

Discussion

55.	Verify the following : (-1, 2, 1), (1, -2, 5), (4, -7, 8) and (2, -3, 4) are the vertices of a parallelogram.
Answer» ANSWER :1

Discussion

56.	If A=((coshtheta,sinhtheta),(sinhtheta,coshtheta)) and ninN then A^(n)=
Answer» `((coshntheta,sinhntheta),(sinntheta,coshntheta))` `((-coshntheta,sinhntheta),(sinntheta,coshntheta))` `((ncoshtheta,nsinhtheta),(nsinhtheta,ncoshtheta))` Does not EXIST ANSWER :A

Discussion

57.	If x = theta -(1)/(theta) , y = theta + (1)/(theta) then (dy)/(dx) =
Answer» x/y y/x `-x//y` `-y//x` ANSWER :A

Discussion

58.	If f(x)=((x-a)(x-b))/(x) and (f(x))/((x-y)(x-z))+(f(y))/((y-z)(y-x))+(f(z))/((z-x)(z-y))=(k)/(xyz) then k=
Answer» a b ab 3ab Answer :C

Discussion

59.	Cot A +Cot B +cot C =
Answer» ` ( a^(2)+B^(2) +C^(2))/( 2DELTA) ` ` ( a^(2)+b^(2) +c^(2))/( 4Delta) ` ` ( a+b +c)/( 3Delta) ` ` ( a^(2)+b^(2) +c^(2))/( 3Delta) ` ANSWER :B

Discussion

60.	Represent the complex numbers2-2i
Answer» ANSWER :`2 SQRT2 [COS ((-pi)/(4))+ ISIN (-(pi)/(4))]`

Discussion

61.	Find length of perpendicular from origin to the lines passes from points ( cos theta , sin theta ) and ( cos phi , sin phi).
Answer» ANSWER :`\| COS ((THETA - PHI)/( 2))\|`

Discussion

62.	Evaluate the following limits : Lt_(xto0)(2^(2x)-1)/x
Answer» ANSWER :`LOG4`

Discussion

63.	If tan alpha, tan beta, tan lambda are the roots of the equation x^(3) - px^(2) - r = 0 then the value of (1+tan^(2) alpha) (1+tan^(2) beta)(1+tan^(2)lambda) =
Answer» `1+(p-r)^(2)` `2+(p-r)^(2)` `3+(p+r)^(2)` `1-(p-r)^(2)` ANSWER :A

Discussion

64.	A point moves so that square of its distance from the point (3,-2) is numerically equal to its distance from the line 5x - 12 y = 3. The equation of its locus is ..........
Answer» ANSWER :`13x^2+13y^2-83x+64y+172=0`

Discussion

65.	Two sides of a triangle are along the coordinate axes and the medians through the vertice (other than the origin ) are mutually perpendicurlar. The number of such triangles is //are
Answer» ZERO two four Infinite Answer :C

Discussion

66.	A variable line passes through a fixed point P. The algebraic sum of the perpendiculars drawn from the points (2, 0), (0, 2) and (1, 1) on the line is zero. Find the coordinates of the point P.
Answer» <P> ANSWER :REQUIRED POINT `P = (1,1)`

Discussion

67.	If y = Tan^(-1)((4 sin 2x)/(cos 2x - 6 sin^2 x)) "then " (dy)/(dx) "at" x = 0is
Answer» 10 12 6 8 Answer :D

Discussion

68.	Solve: sin 5x - sin 3x - sin x =0, 0^(@) lt x lt 360^(@).
Answer» ANSWER :`(23pi)/(12),`

Discussion

69.	If sinxgt-1/2 then x lies between
Answer» `2NPI-(pi)/3lt x lt 2n pi +(4pi)/3, n in Z` `2np -(pi)/6lt x lt 2npi+(7pi)/6, n in Z` `2npi-(pi)/6 lt XLT 2npi+(5PI)/6, n in Z` `2npi-(pi)/3lt xlt 2npi+(2PI)/3, n in Z` Answer :B

Discussion

70.	bara,barb,barc are non-coplanar and barl=(barbxxbarc)/([bara barb barc]),barm=(barcxxbara)/([bara barb barc]),barn=(baraxxbarb)/([bara barb barc]) then (bara+barb+barc).(barl+barm+barn)=
Answer» 0 1 2 3 Answer :C

Discussion

71.	In Delta ABC, b cos (C+ theta)+c cos (B- theta)=
Answer» ` a cos THETA ` `a SIN theta` ` a TAN theta ` ` a cot theta ` ANSWER :A

Discussion

72.	The plane x/1 + y/2 + (z)/(-1) = 1 meets the co-ordinate axes in the points A, B and C respectively. Area of triange ABC is
Answer» `3/2` `(2sqrt2)/(3)` `(SQRT3)/(2)` `(SQRT6)/(2)` ANSWER :A

Discussion

73.	Convert the following complex numbers into polar form 1 - i
Answer» Answer :`sqrt2[COS((-pi)/4) + ISIN((-pi)/4)]`

Discussion

74.	If bar(alpha)=2bar(i)+3bar(j), bar(beta)=4bar(i)+bar(j), bar(gamma)=5bar(i)+dbar(j) are three vectors having their initial point at origin. If their extremities are collinear, then d =
Answer» 0 1 2 3 Answer :A

Discussion

75.	Evaluate : 2 sin 15 ^(@) cos 15 ^(@)
Answer» ANSWER :`1/2`

Discussion

76.	Find the value of sin^(2)52(1^(@))/(2)-cos^(2)7(1^(@))/(2)
Answer» ANSWER :`(-1)/(2sqrt(2))`

Discussion

77.	The value of sqrt(3)cosec20^(@)-sec20^(@) is …………
Answer» `-4` 1 2 4 Answer :D

Discussion

78.	bara is perpendicular to barb,barc. If abs(bara)=2,abs(barb)=3,abs(barc)=4(barb,barc)=(2pi)/3 then abs(barabarbbarc])=
Answer» `12sqrt3` 12 `6sqrt3` 6 Answer :A

Discussion

79.	If tantheta+tan2theta+tantheta. tan2theta=1 then theta =
Answer» `(npi)/(3)+(pi)/(9)` `(npi)/(3)+(pi)/(12)` `npi+(-1)^(n)(pi)/(6)` `npi+(pi)/(4)` ANSWER :B

Discussion

80.	Solve the following equations cos^(2) theta = (3)/(4), theta in [0, pi]
Answer» ANSWER :`{(PI)/(6), (5PI)/(6)}`

Discussion

81.	Prove that using the Mathematical induction sin(alpha)sin(alpha+ pi/6)+ sin(alpha+(2pi)/(6))+.....+ sin (alpha + ((n-1)pi)/(6))=(sin(alpha + ((n-1)pi)/(12))xx "sin" ((npi)/(12)))/(sin((pi)/(12)))
Answer» <P> Answer :`rArr p(K+1)` is TURE whenever p(k) is TRUE.

Discussion

82.	Show that sin A= (sin 3A) /(1+2 cos 2A). Hence find the value of sin 15^(@).
Answer» ANSWER :`(sqrt3-1)/(2SQRT2)`

Discussion

83.	Find delta and dy for y = log x when x = 3, delta x = 0.003.
Answer» ANSWER :0.001.

Discussion

84.	Evaluate lim_(xto0)(sinax+bx)/(ax+sinbx)a,b,a+bne0.
Answer» ANSWER :1

Discussion

85.	Given , cos2^(m)thetacos2^(m+1)theta......cos2^ntheta=(sin2^(n+1)theta)/(2^(n-m+1)sin2^(m) theta)where 2^mtheta ne kpi,n,m,k in l solve the following cos""(pi)/11cos""(2pi)/11cos""(3pi)/11.....cos""(10pi)/11 is equal to
Answer» `-1/32` `1/512` `1/1024` `-1/1024` ANSWER :C

Discussion

86.	In Delta ABC, if cos A cos B+ sin A sin B sin C=1, then the triangle is
Answer» equilateral right ANGLED isosceles right angled isosceles Answer :D

Discussion

87.	Let f(x)= sin^(2)""x/2+cos^(2)""x/2 and g(x)=sec^(2)x-tan^(2)x. The two functions are equal over the set
Answer» `phi` R `R-{x\|x=(2n+1) pi/2, N in Z}` `R-{0}` Answer :C

Discussion

88.	Determine whether p,q and "If p, then q " are true or false in each case given below :p : 5
Answer» <P> ANSWER :`{:(p,Q,p =>q),(T,T,T):}`

Discussion

89.	OACB is a parallelogram with bar(OC)=bar(a), bar(AB)=bar(b)" then "bar(OA)=
Answer» `(BAR(a)+bar(B))/2` `bar(a)+bar(b)` `(bar(a)-bar(b))/2` `bar(a)-bar(b)` ANSWER :C

Discussion

90.	Find the square root of the complex number 5+12i
Answer» ANSWER :`(3+ 2I) or -(3+ 2i)`

Discussion

91.	Match the statements/ expressions in Column I with the statements/ expressions in Column II.
Answer» ANSWER :d

Discussion

92.	If f(x)= sgn(x^(2) -2x+ 3)then the value of f(x) is
Answer» ANSWER :1

Discussion

93.	Two cards are selected randomly from four cards denoted as A, B, C, D without replacement. Describle the sample space for this experiment.
Answer» Answer :`S={AB,AC,AD,BC,BD,CD}`

Discussion

94.	If Tan^(-1)("tan"(5pi)/4)=alpha and Tan^(-1)(-"tan"(2pi)/3)=beta then
Answer» `alpha-BETA=(7pi)/12` `alpha+beta=(7pi)/12` `2alpha+3 beta=(7pi)/12` `4alpha=3beta` ANSWER :B

Discussion

95.	Let p be " Ananya is beautiful, " and let q be " Ananya is 165 centimetres tall. " Under what conditions is the statement, "Ananya is beautiful and 165 centimetress tall." true ?
Answer» Answer :Only if ANANYA is both beautiful and 165 CM TALL.

Discussion

96.	Let p be " Ananya is beautiful, " and let q be " Ananya is 165 centimetres tall. " Under what conditions is the statement, " " Ananya is beautiful and 165 centimetres tall, " false ?
Answer» ANSWER :If Ananyais not BEAUTIFUL and or not 165 CM TALL.

Discussion

97.	Let p be " Ananya is beautiful, " and let q be " Ananya is 165 centimetres tall. " Under what conditions is the statement," Ananya is beautiful or 165 centimetres tall," false ?
Answer» ANSWER :Only if ANANYA is NEITHER BEAUTIFUL nor 165 cmtall .

Discussion

98.	The negation of the following statement is ………..The green plants takes CO_(2) in and gives out O_(2)
Answer» Plant do not take `CO_(2)` is and do not give out `O_(2)` PLANTS do not take `CO_(2)` or do not give out `O_(2)` Plants take in `CO_(2)` and do not give out`O_(2)` Plants take in `CO_(2)` or do not give out `O_(2)` ANSWER :B

Discussion

99.	A straight line (x)/(a)+(y)/(b)=1 meets the axes in A, B.Aline perpendicular to AB meets the axes in P and Q. The locus of point intersection of AQ and BP is
Answer» `X(x-a)+y(y-b)=0 ` `x(x+a)+y(y+b)=0` `x(x+a)+y(y-b)=0` `x(x-a)+y(y+b)=0` ANSWER :A

Discussion

100.	In.^(2n)C_(3) :.^(n)C_(3) = 11 : 1then n is
Answer» ANSWER :6

Discussion

Explore topic-wise InterviewSolutions in .

If alpha and beta are the roots of the equation, acostheta+bsintheta=c, then match the entries of column I with the entries of column- II

Rewrite the following statement, with 'if ... , then' in five different ways conveying the same meaning: If a natural number is even, then its square is even.

If sin alpha cos beta=-(1)/(2), then cos alpha sin beta may be belong to

If f and g are real functions defined by f(x)= x^(2) + 7 and g(x)= 3x + 5. Then, find each of the following (f(t)- f(5))/(t-5), if t ne 5

Verify the following : (-1, 2, 1), (1, -2, 5), (4, -7, 8) and (2, -3, 4) are the vertices of a parallelogram.

If A=((coshtheta,sinhtheta),(sinhtheta,coshtheta)) and ninN then A^(n)=

If x = theta -(1)/(theta) , y = theta + (1)/(theta) then (dy)/(dx) =

If f(x)=((x-a)(x-b))/(x) and (f(x))/((x-y)(x-z))+(f(y))/((y-z)(y-x))+(f(z))/((z-x)(z-y))=(k)/(xyz) then k=

Cot A +Cot B +cot C =

Represent the complex numbers2-2i

Find length of perpendicular from origin to the lines passes from points ( cos theta , sin theta ) and ( cos phi , sin phi).

Evaluate the following limits : Lt_(xto0)(2^(2x)-1)/x

If tan alpha, tan beta, tan lambda are the roots of the equation x^(3) - px^(2) - r = 0 then the value of (1+tan^(2) alpha) (1+tan^(2) beta)(1+tan^(2)lambda) =

A point moves so that square of its distance from the point (3,-2) is numerically equal to its distance from the line 5x - 12 y = 3. The equation of its locus is ..........

Two sides of a triangle are along the coordinate axes and the medians through the vertice (other than the origin ) are mutually perpendicurlar. The number of such triangles is //are

A variable line passes through a fixed point P. The algebraic sum of the perpendiculars drawn from the points (2, 0), (0, 2) and (1, 1) on the line is zero. Find the coordinates of the point P.

If y = Tan^(-1)((4 sin 2x)/(cos 2x - 6 sin^2 x)) "then " (dy)/(dx) "at" x = 0is

Solve: sin 5x - sin 3x - sin x =0, 0^(@) lt x lt 360^(@).

If sinxgt-1/2 then x lies between

bara,barb,barc are non-coplanar and barl=(barbxxbarc)/([bara barb barc]),barm=(barcxxbara)/([bara barb barc]),barn=(baraxxbarb)/([bara barb barc]) then (bara+barb+barc).(barl+barm+barn)=

In Delta ABC, b cos (C+ theta)+c cos (B- theta)=

The plane x/1 + y/2 + (z)/(-1) = 1 meets the co-ordinate axes in the points A, B and C respectively. Area of triange ABC is

Convert the following complex numbers into polar form 1 - i

If bar(alpha)=2bar(i)+3bar(j), bar(beta)=4bar(i)+bar(j), bar(gamma)=5bar(i)+dbar(j) are three vectors having their initial point at origin. If their extremities are collinear, then d =

Evaluate : 2 sin 15 ^(@) cos 15 ^(@)

Find the value of sin^(2)52(1^(@))/(2)-cos^(2)7(1^(@))/(2)

The value of sqrt(3)cosec20^(@)-sec20^(@) is …………

bara is perpendicular to barb,barc. If abs(bara)=2,abs(barb)=3,abs(barc)=4(barb,barc)=(2pi)/3 then abs(barabarbbarc])=

If tantheta+tan2theta+tantheta. tan2theta=1 then theta =

Solve the following equations cos^(2) theta = (3)/(4), theta in [0, pi]

Prove that using the Mathematical induction sin(alpha)sin(alpha+ pi/6)+ sin(alpha+(2pi)/(6))+.....+ sin (alpha + ((n-1)pi)/(6))=(sin(alpha + ((n-1)pi)/(12))xx "sin" ((npi)/(12)))/(sin((pi)/(12)))

Show that sin A= (sin 3A) /(1+2 cos 2A). Hence find the value of sin 15^(@).

Find delta and dy for y = log x when x = 3, delta x = 0.003.

Evaluate lim_(xto0)(sinax+bx)/(ax+sinbx)a,b,a+bne0.

Given , cos2^(m)thetacos2^(m+1)theta......cos2^ntheta=(sin2^(n+1)theta)/(2^(n-m+1)sin2^(m) theta)where 2^mtheta ne kpi,n,m,k in l solve the following cos""(pi)/11cos""(2pi)/11cos""(3pi)/11.....cos""(10pi)/11 is equal to

In Delta ABC, if cos A cos B+ sin A sin B sin C=1, then the triangle is

Let f(x)= sin^(2)""x/2+cos^(2)""x/2 and g(x)=sec^(2)x-tan^(2)x. The two functions are equal over the set

Determine whether p,q and "If p, then q " are true or false in each case given below :p : 5

OACB is a parallelogram with bar(OC)=bar(a), bar(AB)=bar(b)" then "bar(OA)=

Find the square root of the complex number 5+12i

Match the statements/ expressions in Column I with the statements/ expressions in Column II.

If f(x)= sgn(x^(2) -2x+ 3)then the value of f(x) is

Two cards are selected randomly from four cards denoted as A, B, C, D without replacement. Describle the sample space for this experiment.

If Tan^(-1)("tan"(5pi)/4)=alpha and Tan^(-1)(-"tan"(2pi)/3)=beta then

Let p be " Ananya is beautiful, " and let q be " Ananya is 165 centimetres tall. " Under what conditions is the statement, "Ananya is beautiful and 165 centimetress tall." true ?

Let p be " Ananya is beautiful, " and let q be " Ananya is 165 centimetres tall. " Under what conditions is the statement, " " Ananya is beautiful and 165 centimetres tall, " false ?

Let p be " Ananya is beautiful, " and let q be " Ananya is 165 centimetres tall. " Under what conditions is the statement," Ananya is beautiful or 165 centimetres tall," false ?

The negation of the following statement is ………..The green plants takes CO_(2) in and gives out O_(2)

A straight line (x)/(a)+(y)/(b)=1 meets the axes in A, B.Aline perpendicular to AB meets the axes in P and Q. The locus of point intersection of AQ and BP is

In.^(2n)C_(3) :.^(n)C_(3) = 11 : 1then n is