14949 + Interview Questions in Maths in Class 11 Page 99 InterviewSolution

4901.	Find the orthocentre of the triangle formed by x+y+10=0,x-y-2=0, 2x+y-7=0.
Answer» ANSWER :(-4,-6)

Discussion

4902.	Prove that the product of first n terms of a G.P. whose first term is a and last term is I, is (al)^(n//2).
Answer» ANSWER :`(AL)^(n//2)`,

Discussion

4903.	A beam of light is sent along the line x-y=1, which after refracting from the x-axis enters the oppositi side by turining through 30^@ towards the normal at the point of incidence on the x-axis. Then the equation of the refracrted ray is
Answer» `(2-sqrt3)x-y=2+sqrt3` `(2+sqrt3)x-y=2+sqrt3` `(2-sqrt3)x-y=2+sqrt3` `y=(2-sqrt3)(x-1)` ANSWER :D

Discussion

4904.	If a(bar(alpha) xx bar(beta)) + b(bar(beta) xx bar(gamma)) +c(bar(gamma) xx bar(alpha)) = 0 and atleast one of the scalars a, b, c is non-zero, then the vectors bar(alpha), bar(beta), bar(gamma) are
Answer» 0 1 `-1` can not be determined Answer :A

Discussion

4905.	( b^(2) -c^(2))/( a^(2)) =
Answer» ` ( SIN (B-C))/( sin (B+ C) ) ` ` ( COS(B-C))/( cos(B+ C) ) ` ` (sin(B+C))/( sin(B- C) ) ` ` (cos(B+C))/( cos(B- C) ) ` ANSWER :A

Discussion

4906.	In a bag there are three balls , one red , one blue and one yellow. A ball is selected ,the colour is recorded and the ball is replaced. A second ball is then selected and the colour is recorded. Show in a tree diagam all the possible combined outcomes .
Answer» ANSWER :`(##SCH_OPM_ISC_MAT_XI_C22_E01_012_A01##)`

Discussion

4907.	Let OAB be a quadrant of a circle with boundary radii OA = 1, OB = 1and bunding arc AB. Then The area of equilateral triangle inscribed in it such that two vertices on OA and OB and one vertex on AB
Answer» `(2 SQRT3 - 3)/2` `(3 sqrt3)/4` `(3 + sqrt3)/4` `(2 sqrt3 + 3)/2` ANSWER :A

Discussion

4908.	Find tan 20^(@) + tan40^(@) + sqrt(3)tan20^(@)tan40^(@).
Answer» ANSWER :`SQRT(3)`

Discussion

4909.	Let OAB be a quadrant of a circle with boundary radii OA = 1, OB = 1and bunding arc AB. Then The area of the square inscribed in it with two vertices on OA and OB and two vertices on are AB is
Answer» `1/5` `2/5` `3/5` `4/5` ANSWER :B

Discussion

4910.	In a triangle ABC, if cot""A/2 cot""B/2=c, cot""B/2 cot""C/2=a and cot""C/2 cot""A/2=b, then 1/(s-a)+1/(s-b)+1/(s-c)=
Answer» ` 1 ` ` 2` ` abc ` ` DELTA ` ANSWER :B

Discussion

4911.	Evaluate the limits : lim_(x to a) (sqrt(x-b)-sqrt(a-b))/(x^2-a^2) ( agt b)
Answer» ANSWER :`1/(4asqrt(a-b))`

Discussion

4912.	The possible percentage error in computing the parallel resistance R of three resistances R_(1),R_(2),R_(3) from the formula 1/R=1/R_(1)+1/R_(2)+1/R_(3), if R_(1),R_(2),R_(3)are each in error by 1.2%
Answer» 1.2 1.3 1.3 1.7 Answer :A

Discussion

4913.	If the circle x^(2) + y^(2) + 2gx + 2fy + c = 0 does not intersects the X - axis then ……..
Answer» `g^(2) lt C` `g^(2) gt c` `g^(2) gt 2C` NONE of these Answer :A

Discussion

4914.	x intercept of line 4x + 3y - 12 is 3.
Answer» ANSWER :TRUE STATEMENT

Discussion

4915.	32 sin^(6) 15^(0) - 48 sin^(4) 15^(0) + 18 sin^(2) 15^(0) =
Answer» 1 2 3 -1 Answer :A

Discussion

4916.	Without repetition of the number, two digit numbers are formed with the numbers 1, 2, 3, 4, 5. The probability that such a number is divisible by 4 is ......
Answer» `(1)/(30)` `(1)/(20)` `(1)/(40)` NONE of these ANSWER :D

Discussion

4917.	If alpha, beta are the roots of x^(2)-(a-2)x-(a+1)=0 where 'a' is a variable then the minimum value of alpha^(2)+beta^(2) is
Answer» 1 3 5 7 Answer :C

Discussion

4918.	Find the equation of a straight on which length of perpendicular from the origin is four units and the line makes an angles 120^@ with the positive direction of x - axis.
Answer» ANSWER :8

Discussion

4919.	Sine function whose period is 6 is
Answer» `SIN""(2pi X)/(3)` `sin""(pi x)/(3)` `sin""(pi x)/(6)` `sin""(3pi x)/(2)` Answer :B

Discussion

4920.	Solve the equations: Q. sqrt((x^(2)+2)/(x^(2)-2))+6sqrt((x^(2)-2)/(x^(2)+2))=5.
Answer» ANSWER :`pmsqrt((5)/(2)),pmsqrt((10)/(3))`.

Discussion

4921.	Resolve the rational expressions into partial fractionsx/((x-1)^(3)
Answer» ANSWER :`(1)/((X - 1)^(2)) + (1)/((x - 1)^(3))`

Discussion

4922.	From a point (2, 0) the feet of perpendiculars to the lines of the pair 2y^2 - 3xy + x^2 = 0 are P and Q then find the equation of the line PQ.
Answer» ANSWER :X + 3Y - 4 = 0

Discussion

4923.	Let ABC be a triangle with integer sides a,b,c and angle C = 90^(@) The greatest area of the triangle of r = 3is
Answer» 54 60 84 96 Answer :C

Discussion

4924.	R= {(x, x^(2)): x is a prime number less then 15} Express R in roster form.
Answer» Answer :R= {(2, 4) (3,9)(5, 25) (7, 49) (11, 121) (13, 169)}

Discussion

4925.	Using section formula, prove that the three points A (-2,3,5), B (1,2,3) and C (7,0,-1) are collinear.
Answer» ANSWER :`LAMDA = -3/2`

Discussion

4926.	If f(x) = \|sin x - \|cos x\|\|, then the value f'(x) at x = 7 pi//6 is
Answer» positive `(1 - SQRT(3))/(2)` `0` negative Answer :A

Discussion

4927.	The sum of first three terms of a G.P is (39)/(10) and their product is 1. Find the common ratio and the terms.
Answer» ANSWER :`r=5/2 " or " 2/5; ` TERMS are `2/5,1,5/2` or `5/2 ,1,2/5`

Discussion

4928.	Find a, b such that 7.2, a, b, 3 are in A.P.
Answer» ANSWER :a=5.8 ,b=4.4

Discussion

4929.	f:(-1,1) to B defined byf(x)=tan^(-1)((2x)/(1-x^(2))) is bijection then B =
Answer» `[-pi/4, pi/4]` `(-pi/2, pi/2)` `(-pi/2,pi/4]` `[pi/4, pi/2]` ANSWER :A

Discussion

4930.	If the pairs of lines3x^(2)-5xy+py^(2)=0 and 6x^(2)-xy-5y^(2)=0 have one line in common, then P=
Answer» `2,(25)/(4)` `-2,(25)/(4)` `-2,(-25)/(4)` `2,(-25)/(4)` ANSWER :D

Discussion

4931.	Let 0 le a,b,c,d le piwhere b,c are not complementary such that 2cosa + 6cos b + 7cosc + 9cosd = 0 and 2sina-6sinb + 7 sinc-9sind=0 .Then the value of (cos(a+d))/(cos(b+c)) =
Answer» `1//3` `3//4` `5//4` `7//3` ANSWER :D

Discussion

4932.	A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point 'O' on the ground is 45^(@). It flies off horizontally straight away from the point 'O'. After one second, the elevation of the bird from 'O' is reduced to 30^(@). Then the speed (in m/s) of the bird is
Answer» `40( SQRT(2)-1)` `40( sqrt(3)-sqrt(2))` `20 sqrt(2)` `20(sqrt(3)-1)` Answer :D

Discussion

4933.	If theta=20^(@), then 8cos^(3)theta-6 cos theta is
Answer» `-1` 1 0 2 Answer :B

Discussion

4934.	sin(tan^(-1)(7/24))=
Answer» `24//25` `7//25` `7//24` `25//24` ANSWER :B

Discussion

4935.	Find the coefficient of x^5 in (x+3)^8
Answer» ANSWER :`1512`

Discussion

4936.	ABCDE is a pentagon then bar(AB)+bar(AE)+bar(BC)+bar(DC)+bar(ED)+bar(AC)=
Answer» `3BAR(AC)` `BAR(AC)` `2BAR(AC)` `4bar(AC)` ANSWER :A

Discussion

4937.	Write the value of theta in (0,\ pi/2)for which area of the triangle formed by points O(0,0),\ A(a\ costheta,\ b sintheta)a n d\ B(a\ costheta,\ -b\ sintheta)is maximum.
Answer» `pi/6` `pi/4` `pi/3` NONE of these ANSWER :B

Discussion

4938.	If 0 lt phi lt pi//2 , and x = sum_(n = 0)^(infty) cos^(2n) phi, y = sum_(n=0)^(infty) sin^(2n ) phi and z = sum_(n=0)^(infty) cos^(2n) phi sin^(2n) phi, then
Answer» xy + z XZ + y x + y + z YZ + x Answer :A::C

Discussion

4939.	The side of a given square is 10cm. The mid points of its sides are joined to form a new square. Again the mid poind of the sides of this new square are joined to form another square. This process is continued indefinitely. Find the sum of the area.
Answer» ANSWER :`200CM^(2)`

Discussion

4940.	If k is a negative constant , what is the relation between sigma_u and sigma_x
Answer» SOLUTION :`sigma_u=abs(K)sigma_x` or `sigma_u=-ksigma_x`

Discussion

4941.	Draw the graphs of the following : x^(2) -1 = y
Answer» ANSWER :`(##AKS_ELT_AI_MAT_XI_VIB_P02_C01_E01_026_A01##)`

Discussion

4942.	Let f(x) be defined for all x gt 0 and be continuous . Let f(x) satisfy the relation f(x/y) = f(x)-f(y) for all 'x' and 'y' and f(e)=1 then
Answer» `f(X)` is bounded `f(1/x) RARR 0` `as x rarr 0` `x f (x) rarr 0` as `x rarr 0` `f(x)= LN x` ANSWER :D

Discussion

4943.	If cosh 2x = 199, then coth x =
Answer» `(5)/(3sqrt(11))` `(5)/(6sqrt(11))` `(7)/(3sqrt(11))` `(10)/(3sqrt(11))` ANSWER :D

Discussion

4944.	Evaluate Lim_(x to 0) (log (a+x) - log(a-x))/x , a gt 0
Answer» ANSWER :`2/a`

Discussion

4945.	sin (x+a)
Answer» ANSWER :COS (x+a)

Discussion

4946.	Find the sumof the sequence (2)/(9), -(1)/(3), +(1)/(2), -(3)/(4)……5 - terms.
Answer» ANSWER :`(55)/(72)`

Discussion

4947.	The shortest distance between the skew lines barr=(bari+3barj+3barK)+t(bari+3barj+2bark) and barr=(4bari+5barj+6bark)+t(2bari+3barj+bark) is
Answer» `SQRT6` 3 `2SQRT3` `SQRT3` ANSWER :D

Discussion

4948.	The mean and variance of eight observations are 9 and 9.25, respectively. If six of the observations are 6, 7, 10, 12, 12 and 13, find the remaining two observations.
Answer» ANSWER :4, 8

Discussion

4949.	The mean of 100 observations is 40 and their standard deviation respectively is 10. if 5 is added to each observation then the new mean and new standard deviation will be
Answer» 40,10 40,15 50,10 45,10 Answer :D

Discussion

4950.	Find the distance between a focus and an extremity of the minor axis of the ellipse (i) 4x^(2)+5y^(2)=100"(ii) "x^(2)/a^(2)+y^(2)/b^(2)=1.
Answer» ANSWER :(i) 5 (II) a

Discussion

Explore topic-wise InterviewSolutions in .

Find the orthocentre of the triangle formed by x+y+10=0,x-y-2=0, 2x+y-7=0.

Prove that the product of first n terms of a G.P. whose first term is a and last term is I, is (al)^(n//2).

A beam of light is sent along the line x-y=1, which after refracting from the x-axis enters the oppositi side by turining through 30^@ towards the normal at the point of incidence on the x-axis. Then the equation of the refracrted ray is

If a(bar(alpha) xx bar(beta)) + b(bar(beta) xx bar(gamma)) +c(bar(gamma) xx bar(alpha)) = 0 and atleast one of the scalars a, b, c is non-zero, then the vectors bar(alpha), bar(beta), bar(gamma) are

( b^(2) -c^(2))/( a^(2)) =

In a bag there are three balls , one red , one blue and one yellow. A ball is selected ,the colour is recorded and the ball is replaced. A second ball is then selected and the colour is recorded. Show in a tree diagam all the possible combined outcomes .

Let OAB be a quadrant of a circle with boundary radii OA = 1, OB = 1and bunding arc AB. Then The area of equilateral triangle inscribed in it such that two vertices on OA and OB and one vertex on AB

Find tan 20^(@) + tan40^(@) + sqrt(3)tan20^(@)tan40^(@).

Let OAB be a quadrant of a circle with boundary radii OA = 1, OB = 1and bunding arc AB. Then The area of the square inscribed in it with two vertices on OA and OB and two vertices on are AB is

In a triangle ABC, if cot""A/2 cot""B/2=c, cot""B/2 cot""C/2=a and cot""C/2 cot""A/2=b, then 1/(s-a)+1/(s-b)+1/(s-c)=

Evaluate the limits : lim_(x to a) (sqrt(x-b)-sqrt(a-b))/(x^2-a^2) ( agt b)

The possible percentage error in computing the parallel resistance R of three resistances R_(1),R_(2),R_(3) from the formula 1/R=1/R_(1)+1/R_(2)+1/R_(3), if R_(1),R_(2),R_(3)are each in error by 1.2%

If the circle x^(2) + y^(2) + 2gx + 2fy + c = 0 does not intersects the X - axis then ……..

x intercept of line 4x + 3y - 12 is 3.

32 sin^(6) 15^(0) - 48 sin^(4) 15^(0) + 18 sin^(2) 15^(0) =

Without repetition of the number, two digit numbers are formed with the numbers 1, 2, 3, 4, 5. The probability that such a number is divisible by 4 is ......

If alpha, beta are the roots of x^(2)-(a-2)x-(a+1)=0 where 'a' is a variable then the minimum value of alpha^(2)+beta^(2) is

Find the equation of a straight on which length of perpendicular from the origin is four units and the line makes an angles 120^@ with the positive direction of x - axis.

Sine function whose period is 6 is

Solve the equations: Q. sqrt((x^(2)+2)/(x^(2)-2))+6sqrt((x^(2)-2)/(x^(2)+2))=5.

Resolve the rational expressions into partial fractionsx/((x-1)^(3)

From a point (2, 0) the feet of perpendiculars to the lines of the pair 2y^2 - 3xy + x^2 = 0 are P and Q then find the equation of the line PQ.

Let ABC be a triangle with integer sides a,b,c and angle C = 90^(@) The greatest area of the triangle of r = 3is

R= {(x, x^(2)): x is a prime number less then 15} Express R in roster form.

Using section formula, prove that the three points A (-2,3,5), B (1,2,3) and C (7,0,-1) are collinear.

If f(x) = |sin x - |cos x||, then the value f'(x) at x = 7 pi//6 is

The sum of first three terms of a G.P is (39)/(10) and their product is 1. Find the common ratio and the terms.

Find a, b such that 7.2, a, b, 3 are in A.P.

f:(-1,1) to B defined byf(x)=tan^(-1)((2x)/(1-x^(2))) is bijection then B =

If the pairs of lines3x^(2)-5xy+py^(2)=0 and 6x^(2)-xy-5y^(2)=0 have one line in common, then P=

Let 0 le a,b,c,d le piwhere b,c are not complementary such that 2cosa + 6cos b + 7cosc + 9cosd = 0 and 2sina-6sinb + 7 sinc-9sind=0 .Then the value of (cos(a+d))/(cos(b+c)) =

A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point 'O' on the ground is 45^(@). It flies off horizontally straight away from the point 'O'. After one second, the elevation of the bird from 'O' is reduced to 30^(@). Then the speed (in m/s) of the bird is

If theta=20^(@), then 8cos^(3)theta-6 cos theta is

sin(tan^(-1)(7/24))=

Find the coefficient of x^5 in (x+3)^8

ABCDE is a pentagon then bar(AB)+bar(AE)+bar(BC)+bar(DC)+bar(ED)+bar(AC)=

Write the value of theta in (0,\ pi/2)for which area of the triangle formed by points O(0,0),\ A(a\ costheta,\ b sintheta)a n d\ B(a\ costheta,\ -b\ sintheta)is maximum.

If 0 lt phi lt pi//2 , and x = sum_(n = 0)^(infty) cos^(2n) phi, y = sum_(n=0)^(infty) sin^(2n ) phi and z = sum_(n=0)^(infty) cos^(2n) phi sin^(2n) phi, then

The side of a given square is 10cm. The mid points of its sides are joined to form a new square. Again the mid poind of the sides of this new square are joined to form another square. This process is continued indefinitely. Find the sum of the area.

If k is a negative constant , what is the relation between sigma_u and sigma_x

Draw the graphs of the following : x^(2) -1 = y

Let f(x) be defined for all x gt 0 and be continuous . Let f(x) satisfy the relation f(x/y) = f(x)-f(y) for all 'x' and 'y' and f(e)=1 then

If cosh 2x = 199, then coth x =

Evaluate Lim_(x to 0) (log (a+x) - log(a-x))/x , a gt 0

sin (x+a)

Find the sumof the sequence (2)/(9), -(1)/(3), +(1)/(2), -(3)/(4)……5 - terms.

The shortest distance between the skew lines barr=(bari+3barj+3barK)+t(bari+3barj+2bark) and barr=(4bari+5barj+6bark)+t(2bari+3barj+bark) is

The mean and variance of eight observations are 9 and 9.25, respectively. If six of the observations are 6, 7, 10, 12, 12 and 13, find the remaining two observations.

The mean of 100 observations is 40 and their standard deviation respectively is 10. if 5 is added to each observation then the new mean and new standard deviation will be

Find the distance between a focus and an extremity of the minor axis of the ellipse (i) 4x^(2)+5y^(2)=100"(ii) "x^(2)/a^(2)+y^(2)/b^(2)=1.