14949 + Interview Questions in Maths in Class 11 Page 195 InterviewSolution

9701.	If R_(1)is the circumradius of the pedal triangle of a given triangle ABC, and R_(2)is the circumradius of the pedal triangle of the pedal triangle formed, and so on R_(3), R_(4)……then the value of sum_(i=1)^(infty) R_(i), where R (circumradius) of Delta ABC is 5 is
Answer» 8 10 12 15 Answer :B

Discussion

9702.	Let f(x) = {{:("sin"("cos"^(-1) x) + "cos"("sin"^(-1)x),x le 0),("sin"("cos"^(-1)x) -"cos"("sin"^(-1)x),x gt 0):} and g(x) = f(\|x\|) + \|f(x)\| f'(1/2) =
Answer» `0` `2` `3` `1` ANSWER :A

Discussion

9703.	If f: R rarr R is a polynomal function satisfying the functional equation f(f(x))=6x-f(x), then f(17) is equal to
Answer» 17 -51 34 -34 Answer :B::C

Discussion

9704.	Which of the following is true for z = (3 + 2 i sin theta)//(1 - 2 i sin theta), where i = sqrt(-1)
Answer» z is purely IMAGINARY for `THETA = N PI pm pi//3, n in Z` z is purely imaginary for `theta = n pi pm pi//2, n in Z` z is purely imaginary for `theta = n pi, n in Z` z is purely imaginary for `theta = 2 n pi, n in Z` ANSWER :A

Discussion

9705.	Equation having n degree has n solution.
Answer» ANSWER :TRUE STATEMENT

Discussion

9706.	A= {1, 2, 3, 4, 5}, B= {1, 3, 5, 6}, C= {1, 2, 3}, then find the following sets. A - B
Answer» ANSWER :`={2, 4}`

Discussion

9707.	If the point (a,a) falls between the lines abs(x+y)=2, then :
Answer» `absa=2` `absa=1` `absalt1` `absalt1/2` ANSWER :C

Discussion

9708.	If A=2 sin^(2) theta - cos 2 theta, then
Answer» `-1leAle3` `1leAle2` `-2leAle4` `-3leAle-2` ANSWER :A

Discussion

9709.	Evaluate the following limits : Lt_(xto1)(log_(e)^(x))/(x-1)
Answer» ANSWER :1

Discussion

9710.	A-=(-4,0) ,B-=(4,0). M and N are the variable point of the y-axis such that M lies below N and MN=4. Lines AM and BN intersect at P. The locus of P is
Answer» `2xy-16-x^2=0` `2xy+16-x^2=0` `2xy+16+x^2=0` `2xy-16+x^2=0` ANSWER :D

Discussion

9711.	If (x)/(tan (theta+ alpha))=(y)/(tan (theta+ beta))=(z)/(tan (theta+ gamma) then sum (x+y)/(x-y) sin^(2)(alpha- beta)=
Answer» 1 `-1` 0 None Answer :C

Discussion

9712.	sin(2tan^(-1)(8/15))=
Answer» `230/289` `240/289` `120/249` `120/289` ANSWER :B

Discussion

9713.	Three are 12 points in a plane, no of three of which are in the same straight line, except 5 points whoich are collinear. Find (i) the numbers of lines obtained from the pairs of these points. (ii) the numbers of triangles that can be formed with vertices as these points.
Answer» Solution :(i) No. of lines FORMED by joining the 12 points, taking 2 at a TIME `=.^(12)C_(2)` No of lines formed by joining the 5 points taking 2 at a time `= .^(5)C_(2)` But 5 collinear points when joined pairwise, give only one line `:.` The required NUMBER of lines `= .^(12)C_(2) - .^(5)C_(2) +1` `= 66 - 10 +1` `= 57` (ii) No of triangles formed by joining 12 points by taking 3 points at a time `= .^(12)C_(3)` No. of triangles formed by joining 5 points by taking 3 points at a time `= .^(5)C_(3)` But there is no triangle formed by joining 3 points out of 5 collinear points `:.` The required number of triangles formed `=.^(12)C_(3)-.^(5)C_(3)` `= 220 - 10 = 210`

Discussion

9714.	8 boys and 2 girls sit in a row randomly. The probability that two girls do not sit together is …………..
Answer» `(1)/(5)` `(4)/(5)` `(3)/(5)` `(2)/(5)` ANSWER :B

Discussion

9715.	If x = (2sintheta)/(1+costheta+sintheta), then (1-costheta+sintheta)/(1+sintheta) is equal to
Answer» 1+x 1-x x 1/x Answer :C

Discussion

9716.	If tantheta=(1)/(2)andtanphi=(1)/(3), then the value of theta+phi is
Answer» ANSWER :TRUE STATEMENT

Discussion

9717.	(b) Find the sum to n terms of the series 1 xx 2 xx 3 + 2 xx 3 xx 4 + 3 xx 4 xx 5 + ...
Answer» ANSWER :`(N(n+1)(n+2)(n+3))/4`

Discussion

9718.	LetP(sintheta,costheta),(0lethetale2pi), " be a point in a triangle with vertices "(0,0) (sqrt3//2,0) and (0,sqrt3//2). Then
Answer» `0ltthetaltpi//12` `5pi//2ltthetaltpi//2` `0ltthetalt5pi//2` `5pi//2ltthetaltpi` ANSWER :A::B

Discussion

9719.	The arithmetic mean of the non-zero solutions of the equation "Tan"^(-1)1/(2x+1)+"Tan"^(-1)1/(4x+1)="Tan"^(-1)2/x^(2) is
Answer» 2 3 4 5 Answer :B

Discussion

9720.	Two sides of a triangle are given by the roots of the equationx^(2)-5x+6=0 and the angle between the sides is 60 ° Then the perimeter of the triangle is a
Answer» `5+sqrt(2)` `5+sqrt(3)` `5+sqrt(5)` `5+sqrt(7)` ANSWER :D

Discussion

9721.	Let P(2, 0), Q(-2, 0) and R(4, 0) then the locus of S such that SQ^(2)+SR^(2)=2SP^(2) is
Answer» a STRAIGHT LINE PARALLEL to x-axis a straight line parallel to y-axis x + y = 4 xy=0 Answer :2

Discussion

9722.	If cos 2 x gt \|sin x\| , x in (- (pi)/( 2), pi) " then "x in
Answer» `( - (pi)/(6), (pi)/(6)) CUP ((5 pi)/(6), pi)` `(- (pi)/(6), (pi)/(6))cup (pi, (pi)/(2))` `(- pi, (pi)/(2))cup ((5 pi)/(6), pi)` `(-pi , (pi)/(2)) cup ((5PI)/(6), 2 pi)` ANSWER :A

Discussion

9723.	The mean life of a sample of 60 bulbs was 650 hours and the standard deviation was 8 hours. A second sample of 80 bulbs has mean life of 660 hours standard deviation 7 hours . Find the overall standard deviation.
Answer» ANSWER :8.9

Discussion

9724.	If x ^(y) = log x then (dy)/(dx) at x =e is
Answer» `y/x((In x^(oo x - 1)) + 2ln(ln("log " x))` `y/x(log x)^(log(logx))(2LOG(logx)+1)` `y/(x In x) [(In x)^2 + 2ln(log x)]` `(y log y)/(x log x) [2 log(logx) + 1]` ANSWER :B::D

Discussion

9725.	Let g(x) = log (f(x)) where f(x) is twice differentiable positive function on (0,oo)such that f(x+1)=xf(x) then for N = 1,2,3 and g''(N+1/2)-g''(1/2) = k (1+(1)/(9)+1/25+......+1/((2N-1)^2)) then 'k' is
Answer» ANSWER :-4

Discussion

9726.	For non null sets A and B (AcapB)cup(A-B) = …. .
Answer» ANSWER :A

Discussion

9727.	If bara,barb, barc are vectors such that [barabarbbarc]=4 then [baraxxbarbbarbxxbarcbarcxxbara] is equal to
Answer» 16 64 4 8 Answer :A

Discussion

9728.	A straight line moves so that the sum of the reciprocals of its intercepts made on axes is constant. Show that the line passes through a fixed point. Thinking Process : For line which makes intercepts on axis (x)/(a) + (y)/( b) = 1 If (1)/( a) + (1)/( b) =constant ( (1)/(k) ) then ( k)/( a) + (k)/( b) =1and we say if passes from point (k,k).
Answer» ANSWER :FIXED POINT will be `(X,y) = (K,k)`

Discussion

9729.	150 workers were engaged to finish a job in a certain number of days. 4 workers dropped out on second day, 4 more workers dropped out on third day and so on.
Answer» ANSWER :25

Discussion

9730.	A coin is tossed . If it results in a head , a coin is tossed , otherwise a die is thrown . Describe the following events :A : getting at least one head ,
Answer» ANSWER :`A={HH,HT}`

Discussion

9731.	A coin is tossed . If it results in a head , a coin is tossed , otherwise a die is thrown . Describe the following event :Getting a tail
Answer» Answer :`C=[T1,T2,T3,T4,T5,T6,HT}`

Discussion

9732.	A coin is tossed . If it results in a head , a coin is tossed , otherwise a die is thrown . Describe the following events : B : getting even number ,
Answer» ANSWER :`B={T2,T4,T6}`

Discussion

9733.	A coin is tossed . If it results in a head , a coin is tossed , otherwise a die is thrown . Describe the following events : D : getting a tail and an odd number .
Answer» ANSWER :`D={T1,T3,T5}`

Discussion

9734.	Write the negation of the statement " The number 2 is greater then 7"
Answer» ANSWER :The NUMBER 2 is not GREATER than 7.

Discussion

9735.	Ifsin 3 theta - sin theta = 4 cos ^(2) theta - 2" then " theta =
Answer» `{(2n+1)(PI)/4, N in Z}uu{(2+1)(pi)/2, n in Z}` `{(2n+1)(pi)/2, n in Z}uu{(4n+1)(pi)/2, n in Z}` `{(2n+1)(pi)/4, n in Z}uu{(4n+1)(pi)/2, n in Z}` `{(4n+1) , n in Z}uu{(4n+1)(pi)/2, n inZ}` Answer :C

Discussion

9736.	if nC_12 = nC_8, then n is equal to
Answer» 20 12 6 30 Answer :20

Discussion

9737.	The period of f(x)=sin x+ tan (x/2) + sin (x/2^(2))+tan (x/2^(3))+ ------- + sin ((x)/(2^(n-1)))+tan((x)/(2^(n)))
Answer» `2PI` `2^(N)pi` `2^(n) pi/3` `3^(n) pi` Answer :B

Discussion

9738.	Find the middle term in expansion of : (2ax -b/(x^(2)))^(12)
Answer» ANSWER :`(59136 a^(6)B^(6))/(X^(6))`

Discussion

9739.	If theta=3alpha and sin theta =(a)/(sqrt(a^(2)+beta^(2))),, the value of the expression a cosec alpha - b sec alpha is
Answer» `(a)/(SQRT(a^(2)+B^(2)))` `2sqrt(a^(2)+b^(2))` `a+b` `(sqrt(a^(2)+b^(2)))/(2)` ANSWER :B

Discussion

9740.	Ifcos 2B=(cos (A+C))/(cos(A-C)) , then tan A , tan B , tan Care in
Answer» A.P. G.P. H.P. A.G.P. Answer :B

Discussion

9741.	Find the derivatives of the function cot ^(-1) (cosec 3x )
Answer» ANSWER :`(3 cosec 3 x COT 3X)/( 1 + cosec ^(2) 3x)`

Discussion

9742.	If y= ( sin^(4) x - cos^(4) x + sin^(2) x cos^(2) x )/( sin^(4) x + cos^(4) x + sin^(2) x cos^(2) x) , x in ( 0, (pi)/(2) ), then
Answer» `- (3)/(2) le y le (1)/(2)` `1 le y le (1)/(2)` `- (5)/(3) le y le 1` none of these Answer :C

Discussion

9743.	Value of 'c' of Rolle's theorem for f(x) = \|x\|in [-1,1] is
Answer» 0 1 `-1` does not exists Answer :D

Discussion

9744.	When two complex numbers are equal? Find the real values of x and y for which 3x+2iy-ix+5y=7+5i
Answer» Answer :TWO COMPLEX NUMBERS `z_1` and `z_2` =` IM(z_2),x = -1, y = 2`

Discussion

9745.	If 0 lt A lt pi/4, then prove that tan^(-1)(1/2tan2A)+tan^(-1)(cotA)+tan^(-1)(cot^(3)A)=
Answer» `PI` `2PI` `3PI` `4PI` ANSWER :A

Discussion

9746.	Find the number of ways in which fiveidentical balls can be distributed among ten identical boxes, if not more than one can go into a box.
Answer» ANSWER :` (10!)/( 515!)`

Discussion

9747.	A straight line through the point (2, 2) intersects the lines sqrt(3)x+y=0 and sqrt(3)x-y=0 at the points A and B. The equation to the line AB so that the triangle OAB is equilateral is
Answer» x-2 =0 y-2=0 x+y-4=0 x+y+4=0 Answer :B

Discussion

9748.	Write contrapositive and converse of the following statements: If square ABCD is a square then its diagonals are congruent.
Answer» ANSWER :CONTRAPOSITIVE: If DIAGONALS of `SQUAREABCD` are not congruent it is not square. CONVERSE: If diagonals of `squareABCD` are congruent, then it is square.

Discussion

9749.	The centroid of the triangle formed by the points (1,2,3),(2,3,1),(3,1,2) is
Answer» ANSWER :(2,2,2)

Discussion

9750.	The mean and standard deviation of marks obtained by 50 students of a class in three subjects, Mathematics, Physics and Chemistry are given below: Which of the three subjects shows the highest variability in marks and which shows the lowest?
Answer» Solution :Coefficient of variation in maths `=(SIGMA)/x XX 100=12/42xx100=28.57` Coefficient of variation in physics `=(sigma)/x xx 100=15/32xx100=46.875` Coefficient of variation in CHEMISTRY `=(sigma)/x xx 100=20/40.9xx 100=48.89` Therefore, chemistry shows highest VARIABILITY and maths shows lowest variability.

Discussion

Explore topic-wise InterviewSolutions in .

If R_(1)is the circumradius of the pedal triangle of a given triangle ABC, and R_(2)is the circumradius of the pedal triangle of the pedal triangle formed, and so on R_(3), R_(4)……then the value of sum_(i=1)^(infty) R_(i), where R (circumradius) of Delta ABC is 5 is

Let f(x) = {{:("sin"("cos"^(-1) x) + "cos"("sin"^(-1)x),x le 0),("sin"("cos"^(-1)x) -"cos"("sin"^(-1)x),x gt 0):} and g(x) = f(|x|) + |f(x)| f'(1/2) =

If f: R rarr R is a polynomal function satisfying the functional equation f(f(x))=6x-f(x), then f(17) is equal to

Which of the following is true for z = (3 + 2 i sin theta)//(1 - 2 i sin theta), where i = sqrt(-1)

Equation having n degree has n solution.

A= {1, 2, 3, 4, 5}, B= {1, 3, 5, 6}, C= {1, 2, 3}, then find the following sets. A - B

If the point (a,a) falls between the lines abs(x+y)=2, then :

If A=2 sin^(2) theta - cos 2 theta, then

Evaluate the following limits : Lt_(xto1)(log_(e)^(x))/(x-1)

A-=(-4,0) ,B-=(4,0). M and N are the variable point of the y-axis such that M lies below N and MN=4. Lines AM and BN intersect at P. The locus of P is

If (x)/(tan (theta+ alpha))=(y)/(tan (theta+ beta))=(z)/(tan (theta+ gamma) then sum (x+y)/(x-y) sin^(2)(alpha- beta)=

sin(2tan^(-1)(8/15))=

Three are 12 points in a plane, no of three of which are in the same straight line, except 5 points whoich are collinear. Find (i) the numbers of lines obtained from the pairs of these points. (ii) the numbers of triangles that can be formed with vertices as these points.

8 boys and 2 girls sit in a row randomly. The probability that two girls do not sit together is …………..

If x = (2sintheta)/(1+costheta+sintheta), then (1-costheta+sintheta)/(1+sintheta) is equal to

If tantheta=(1)/(2)andtanphi=(1)/(3), then the value of theta+phi is

(b) Find the sum to n terms of the series 1 xx 2 xx 3 + 2 xx 3 xx 4 + 3 xx 4 xx 5 + ...

LetP(sintheta,costheta),(0lethetale2pi), " be a point in a triangle with vertices "(0,0) (sqrt3//2,0) and (0,sqrt3//2). Then

The arithmetic mean of the non-zero solutions of the equation "Tan"^(-1)1/(2x+1)+"Tan"^(-1)1/(4x+1)="Tan"^(-1)2/x^(2) is

Two sides of a triangle are given by the roots of the equationx^(2)-5x+6=0 and the angle between the sides is 60 ° Then the perimeter of the triangle is a

Let P(2, 0), Q(-2, 0) and R(4, 0) then the locus of S such that SQ^(2)+SR^(2)=2SP^(2) is

If cos 2 x gt |sin x| , x in (- (pi)/( 2), pi) " then "x in

The mean life of a sample of 60 bulbs was 650 hours and the standard deviation was 8 hours. A second sample of 80 bulbs has mean life of 660 hours standard deviation 7 hours . Find the overall standard deviation.

If x ^(y) = log x then (dy)/(dx) at x =e is

Let g(x) = log (f(x)) where f(x) is twice differentiable positive function on (0,oo)such that f(x+1)=xf(x) then for N = 1,2,3 and g''(N+1/2)-g''(1/2) = k (1+(1)/(9)+1/25+......+1/((2N-1)^2)) then 'k' is

For non null sets A and B (AcapB)cup(A-B) = …. .

If bara,barb, barc are vectors such that [barabarbbarc]=4 then [baraxxbarbbarbxxbarcbarcxxbara] is equal to

150 workers were engaged to finish a job in a certain number of days. 4 workers dropped out on second day, 4 more workers dropped out on third day and so on.

A coin is tossed . If it results in a head , a coin is tossed , otherwise a die is thrown . Describe the following events :A : getting at least one head ,

A coin is tossed . If it results in a head , a coin is tossed , otherwise a die is thrown . Describe the following event :Getting a tail

A coin is tossed . If it results in a head , a coin is tossed , otherwise a die is thrown . Describe the following events : B : getting even number ,

A coin is tossed . If it results in a head , a coin is tossed , otherwise a die is thrown . Describe the following events : D : getting a tail and an odd number .

Write the negation of the statement " The number 2 is greater then 7"

Ifsin 3 theta - sin theta = 4 cos ^(2) theta - 2" then " theta =

if nC_12 = nC_8, then n is equal to

The period of f(x)=sin x+ tan (x/2) + sin (x/2^(2))+tan (x/2^(3))+ ------- + sin ((x)/(2^(n-1)))+tan((x)/(2^(n)))

Find the middle term in expansion of : (2ax -b/(x^(2)))^(12)

If theta=3alpha and sin theta =(a)/(sqrt(a^(2)+beta^(2))),, the value of the expression a cosec alpha - b sec alpha is

Ifcos 2B=(cos (A+C))/(cos(A-C)) , then tan A , tan B , tan Care in

Find the derivatives of the function cot ^(-1) (cosec 3x )

If y= ( sin^(4) x - cos^(4) x + sin^(2) x cos^(2) x )/( sin^(4) x + cos^(4) x + sin^(2) x cos^(2) x) , x in ( 0, (pi)/(2) ), then

Value of 'c' of Rolle's theorem for f(x) = |x|in [-1,1] is

When two complex numbers are equal? Find the real values of x and y for which 3x+2iy-ix+5y=7+5i

If 0 lt A lt pi/4, then prove that tan^(-1)(1/2tan2A)+tan^(-1)(cotA)+tan^(-1)(cot^(3)A)=

Find the number of ways in which fiveidentical balls can be distributed among ten identical boxes, if not more than one can go into a box.

A straight line through the point (2, 2) intersects the lines sqrt(3)x+y=0 and sqrt(3)x-y=0 at the points A and B. The equation to the line AB so that the triangle OAB is equilateral is

Write contrapositive and converse of the following statements: If square ABCD is a square then its diagonals are congruent.

The centroid of the triangle formed by the points (1,2,3),(2,3,1),(3,1,2) is

The mean and standard deviation of marks obtained by 50 students of a class in three subjects, Mathematics, Physics and Chemistry are given below: Which of the three subjects shows the highest variability in marks and which shows the lowest?