14949 + Interview Questions in Maths in Class 11 Page 62 InterviewSolution

3051.	A conical vesel of height 10 mts and radius 5 units.is being filled water at uniform rate of 3/2 cu.mts/min. The rate at which the level of water rises when the depth of water in the vessle is 4mts is
Answer» `3pi` MTS/MIN `(3)/(4pi)` mts /min `(3)/(8pi)` mts/min `(7)/(2pi)` mts/min Answer :C

Discussion

3052.	For the quadratic equation (k-1)x^(2)=kx-1, k!=1 the roots are numerically equal but opposite sign, then k is greater than
Answer» `-1` `1` 0 2 Answer :C

Discussion

3053.	Write a brief description of the meaning of the notation lim_(xrarr8)f(x)=25
Answer» ANSWER :25

Discussion

3054.	Find the approximate value of (x-1)^(3)(x-2)^(2)(x-3) at x = 0.001
Answer» ANSWER :11.948

Discussion

3055.	If the sides of a triangle are ax^2+2hxy+by^2=0 and y=x+c, then its area is
Answer» `(c^2sqrt(h^2-ab))/ABS(a+b+2h)` `abs((csqrt(h^2-ab))/(a+b+2h))` `(csqrt(h^2-ab))/abs(a+b+2h)` `(csqrt(h^2-ab))/abs(a+b+2h)` ANSWER :A

Discussion

3056.	If y=cosx,y_(n)=(d^(n)(cosx))/(dx^(n)) then \|{:(y_(4),y_(5),y_(6)),(y_(7),y_(8),y_(9)),(y_(10),y_(11),y_(12)):}\|=
Answer» `-COSX` `cosx` 0 1 Answer :C

Discussion

3057.	(i) Prove that the line y = 2x touches the circle x^(2) + y^(2) + 16x + 12y 4-80 = 0 and find the co-ordinates of the point of contact. (ii) The circle x^(2) + y^(2) -6 x - 10y + y = 0 does not intersect or touch either axis and the point (1,4) is inside the circle. Calculate the range of possible values of p .
Answer» ANSWER :29

Discussion

3058.	Elements of [(1,-1,0),(0,4,2),(3,-4,6)] with their cofactors and choose the correct answer {:("Element ","Co factor"),("(I) "-1,"(a) "-2),("(II)"1,"(b)32"),("(III)3","(c)4"),("(IV)6","(d)6"),(,"(e) "-6):}
Answer» B,d,a,c b, d, c,a d,b,a,c d,a,b,c Answer :C

Discussion

3059.	If aN= {ax : x in N}" then "3N cap 7N="………."
Answer» `21 N` `10N` `4 N` NONE of these Answer :A

Discussion

3060.	The values of x satisfying sin^(-1)x+sin^(-1)(1-x)=cos^(-1)x is/are
Answer» 0 `1/2` 1 2 Answer :A::B

Discussion

3061.	The maximum valueof sin^(2)xcos^(3)xis
Answer» `(6sqrt(3))/(25sqrt(5))` `(9sqrt(3))/(25sqrt(5))` `(9sqrt(2))/(6sqrt(5))` `(SQRT(2))/(sqrt(5))` ANSWER :A

Discussion

3062.	If sin^(3) x sin 3x = sum_(m = 0)^(6) c_(m) cos (m) x,"where" c_(0), c_(1),….,c_(6) are constants, then
Answer» `c_(0) + c_(2) + c_(4) + c_(6) = 0` `c_(1) + c_(3) + c_(5) = 6` `2 c_(2) + 3 c_(6) = 0` `c_(4) + 2 c_(6) = 0` ANSWER :A

Discussion

3063.	When the axes are rotated through an anglepi/2, find the new coordinates of the point (alpha,0)
Answer» ANSWER :`(0,-ALPHA)`

Discussion

3064.	Find the equation of locus of a point such that the sum of whose distances from (0,2) and (0,-2) is 6.
Answer» ANSWER :`(x^(2))/(5)+(y^(2))/(9)=1`

Discussion

3065.	The minute hand of a big clock in 36cms long what is the angle (in radians ) described by the minute hand in 20 minutes.
Answer» SOLUTION :`(2PI)/3` RADIANS

Discussion

3066.	If f(x)=(3x-7)/(5x-3) then (fof)(x)=
Answer» `X` `-x` `3X` `F(x)` ANSWER :A

Discussion

3067.	Evaluate(41)/( 2!2!)
Answer» ANSWER :` 6`

Discussion

3068.	construct truthtable forp vv(~q)
Answer» ANSWER :`(##SCH_OPM_ISC_MAT_XI_C27_E04_021_A01##)`

Discussion

3069.	Write the conjugate of i^(7)
Answer» ANSWER :i

Discussion

3070.	Find the standard deviation of the first n natural numbers.
Answer» ANSWER :`SQRT( (n^2 - 1)/(12))`

Discussion

3071.	Solve: (x^2-2x+5)/(3x^2-2x-5)>1/2.
Answer» ANSWER :`[-5,-1]UU((5)/(3),3]`

Discussion

3072.	Evaluate the following limits : Lt_(xtooo)((x^(2)+4x-3)/(x^(2)-2x+5))^(x)
Answer» ANSWER :`E^(6)`

Discussion

3073.	If tan^(2)alpha tan^(2)beta+tan^2betatan^(2)lamda+tan^(2)lambdatan^(2)alpha+2tan^(2)alpha tan^(2) beta tan^(2)lamda = 1then sin^2alpha+sin^2beta+sin^2lamda=
Answer» 0 -1 1 2 Answer :C

Discussion

3074.	cos x =- 1/2, x lies in third quadrant. find trignometry ratio
Answer» Answer :`sin x = - (sqrt3)/(2), COSEC x =- (2)/( sqrt3), SEC x =-2 , tan x = sqrt3 ,cot x = (1)/(sqrt3)`

Discussion

3075.	Find the multiplicative inverse of the following complex number. -1+i sqrt(3)
Answer» ANSWER :`-(1)/(4)-(SQRT(3))/(4)i`

Discussion

3076.	Find the coefficient of x inthe expansion of(1-3x+7x^(2))(1-x)^(16)
Answer» ANSWER :`= - 19`

Discussion

3077.	If f(x)=f(2a-x) then the graph of f(x) is symmetric about the line
Answer» `y=a` `X=2a` `x=a` `x = -a` ANSWER :C

Discussion

3078.	Match the statements/expressions given in Column I with the values given in Column II
Answer» ANSWER :A::B::C::D

Discussion

3079.	Find the vector equation of the plane passing through the point (1, -2, 5) and parallel to the vectors (6, -5, -1), (-3, 5, 0).
Answer» ANSWER :`BAR(R)=(bar(i)-2bar(J)+5bar(k))+s(6bar(i)-5bar(j)-bar(k))+t(-3bar(i)+5bar(j)), s, t in R`

Discussion

3080.	Check whether the function f (x) = {{:(3 + x if x ge 0), ( 3-x if x lt 0):} is differentiable at x =0.
Answer» ANSWER :`x=0`

Discussion

3081.	In triangle ABC,(r_(3)+r_(1))sqrt([(rr_(1))/(r_(3)r_(1))])=
Answer» a B c 0 Answer :B

Discussion

3082.	If the distance S travelled by a particle in time t is given by s = t^(2) - 2t + 5 then its acceleration is
Answer» 0 0 2 3 Answer :C

Discussion

3083.	Solve the equation 4costheta+5sintheta=5 if tan51^(@)21^(')=5/4
Answer» Solution :Let `theta=51^(@)21^(')` `THEREFORE tantheta=5/4` `rArr sintheta=5/sqrt(41)` and `cosphi=4/sqrt(41)` Now `4costheta+5sintheta=5` Divide both sides by `sqrt(4^(2)+5^(2))=sqrt(41)` `4/sqrt(41) costheta+5/sqrt(41)sintheta=5/(sqrt(41))` `rArr COS(theta-phi)=cos(pi/2-phi)` `rArr (theta-phi)=2NPI+-(pi/2-phi)` Taking positive SIGN `(theta-phi)=2npi+(pi/2-phi)` `rArr theta=2npi+pi/2` Ans. Taking negative sign `(theta-phi)=2npi-(pi/2-phi)` `rArr theta=2npi-(pi/2-theta)` `rArr theta=2npi-pi/2+2theta` `rArr theta=2npi-90^(@)+2 xx 51^(@)21^(')` `=2npi-90^(@)+102^(@)42^(')` `=2npi+12^(2)42^(')` Ans.

Discussion

3084.	A= {0, 2, 4, 6, 8, 10}. Insert the appropriate symbol in" or "notin in the blank space. -2"………"A
Answer» ANSWER :`NOTIN`

Discussion

3085.	Simplify: [i^(18) + ((1)/(i))^(25)]^(3)
Answer» ANSWER :`2(1-i)`

Discussion

3086.	If the origin is the centroid of a triangle ABC having vertices A(a, 1, 3), B(-2, b, -5) and C(4, 7, c), Find the values of a, b, c.
Answer» ANSWER :a = -2, B = -8 and C = 2.

Discussion

3087.	Find the derivative with respect to x of the following: (ii) sqrt ( x) + (1)/( sqrt x)
Answer» ANSWER :`(1)/(2 SQRTX)- (1)/( 2 SQRT(x^3) )`

Discussion

3088.	Orthocentre of triangle formed by the lines x^(2)-xy-x+y=0 and 2x-y+4=0 is
Answer» (11, 4) (11, -4) (-11, -4) (-11, 4) ANSWER :B

Discussion

3089.	cos^(2)25^(@)+cos^(2)35^(@)-cos25^(@) cos35^(@)=
Answer» `1/4` `3/4` `5/4` `1/2` ANSWER :B

Discussion

3090.	Statement -1: For each natural number n, (n+1)^(7) - n^(7) -1 is divisible by 7. Statement - 2 : For each natural number n, n^(7) - n is divisible by 7.
Answer» Statement-1 is TRUE, Statement-2 is true, Statement-1 is true, Statement-2 is true & Statement -2 is CORRECT EXPLANATION of Statement-1 Statement-1 is true, Statement -2 is true & Statement -2 is not a correct explanation of Statement-1 Statement-1 is true, Statement-2 is false. Answer :B

Discussion

3091.	Letf(x) = [ 2x^(3) - 6]when [x] is greatest integer less than or equal to x then the number of points in (1,2) where f is discontionuous is
Answer» 5 13 7 12 Answer :B

Discussion

3092.	Evaluate the following limits : Lim_(x to a) (sqrt(x)-sqrt(a))/(x-a)
Answer» ANSWER :`1/(2sqrt(a))`

Discussion

3093.	Let a function y = y (x) be defined parametrically by x = 2t - \|t\|, y =t^2 +t\|t\|. Then y^(1) (x), x gt 0
Answer» 0 4x 2x x Answer :B

Discussion

3094.	Verify the following : (0, 7, 10), (-1, 6, 6) and (-4, 9, 6) are the vertices of a right angled triangle.
Answer» ANSWER :36

Discussion

3095.	If a_(1), a_(2), a_(3).,,,,,,,,a_(n) are in A.P and their common difference is d. The value of the series sin d_(1) [sec a_(1).sec a_(2) + sec a_(2).sec a_(3)+ ….+ sec a_(n-1).sec a_(n)] is……..
Answer» `sec a_(1).sec a_(N)` `COSEC a_(1)- cosec a_(n)` `cot a_(1)- cot a_(n)` `tan a_(n)- tan a_(1)` ANSWER :D

Discussion

3096.	S_(1),S_(2), S_(3),...,S_(n) are sums of n infinite geometric progressions. The first terms of these progressions are 1, 2^(2)-1, 2^(3)-1, ..., 2^(n) – 1 and the common ratios are (1)/(2),(1)/(2^(2)),(1)/(2^(3)), ...., (1)/(2^(n)). Calculate the value of S_(1), +S_(2),+ ... + S_(n).
Answer» ANSWER :`2(2^(N)-1)`

Discussion

3097.	The number of words which can be formed out of the Letters of the word 'ARTICLE, so that vowels occupy the even place in
Answer» 1440 144 7! `""^4C_4xx""^3C_3` ANSWER :A::D

Discussion

3098.	If f(x)=sin^(2)((pi)/8 + (x)/2) -sin^2((pi)/8-(x)/(2)), then the period of f is
Answer» `pi` `(pi)/(2)` `(pi)/(3 )` `2PI` Answer :4

Discussion

3099.	Statement-I : In DeltaABC, if sinA- cos B= cos C then B=(pi)/(2) Statement-II : \|sinx+cosx\| ge sqrt(2) Which of the above statements is correct ?
Answer» Only I Only II Both I & II NEITHER I nor II Answer :A

Discussion

3100.	Find the sum of n terms of the following series : (i) 3+7+13+21+31+… (ii) 1+5+12+22+35+… (iii) 5+7+13+31+85+… (iv) 2+4+7+11+16+…
Answer» SOLUTION :N/a

Discussion

Explore topic-wise InterviewSolutions in .

A conical vesel of height 10 mts and radius 5 units.is being filled water at uniform rate of 3/2 cu.mts/min. The rate at which the level of water rises when the depth of water in the vessle is 4mts is

For the quadratic equation (k-1)x^(2)=kx-1, k!=1 the roots are numerically equal but opposite sign, then k is greater than

Write a brief description of the meaning of the notation lim_(xrarr8)f(x)=25

Find the approximate value of (x-1)^(3)(x-2)^(2)(x-3) at x = 0.001

If the sides of a triangle are ax^2+2hxy+by^2=0 and y=x+c, then its area is

If y=cosx,y_(n)=(d^(n)(cosx))/(dx^(n)) then |{:(y_(4),y_(5),y_(6)),(y_(7),y_(8),y_(9)),(y_(10),y_(11),y_(12)):}|=

Elements of [(1,-1,0),(0,4,2),(3,-4,6)] with their cofactors and choose the correct answer {:("Element ","Co factor"),("(I) "-1,"(a) "-2),("(II)"1,"(b)32"),("(III)3","(c)4"),("(IV)6","(d)6"),(,"(e) "-6):}

If aN= {ax : x in N}" then "3N cap 7N="………."

The values of x satisfying sin^(-1)x+sin^(-1)(1-x)=cos^(-1)x is/are

The maximum valueof sin^(2)xcos^(3)xis

If sin^(3) x sin 3x = sum_(m = 0)^(6) c_(m) cos (m) x,"where" c_(0), c_(1),….,c_(6) are constants, then

When the axes are rotated through an anglepi/2, find the new coordinates of the point (alpha,0)

Find the equation of locus of a point such that the sum of whose distances from (0,2) and (0,-2) is 6.

The minute hand of a big clock in 36cms long what is the angle (in radians ) described by the minute hand in 20 minutes.

If f(x)=(3x-7)/(5x-3) then (fof)(x)=

Evaluate(41)/( 2!2!)

construct truthtable forp vv(~q)

Write the conjugate of i^(7)

Find the standard deviation of the first n natural numbers.

Solve: (x^2-2x+5)/(3x^2-2x-5)>1/2.

Evaluate the following limits : Lt_(xtooo)((x^(2)+4x-3)/(x^(2)-2x+5))^(x)

If tan^(2)alpha tan^(2)beta+tan^2betatan^(2)lamda+tan^(2)lambdatan^(2)alpha+2tan^(2)alpha tan^(2) beta tan^(2)lamda = 1then sin^2alpha+sin^2beta+sin^2lamda=

cos x =- 1/2, x lies in third quadrant. find trignometry ratio

Find the multiplicative inverse of the following complex number. -1+i sqrt(3)

Find the coefficient of x inthe expansion of(1-3x+7x^(2))(1-x)^(16)

If f(x)=f(2a-x) then the graph of f(x) is symmetric about the line

Match the statements/expressions given in Column I with the values given in Column II

Find the vector equation of the plane passing through the point (1, -2, 5) and parallel to the vectors (6, -5, -1), (-3, 5, 0).

Check whether the function f (x) = {{:(3 + x if x ge 0), ( 3-x if x lt 0):} is differentiable at x =0.

In triangle ABC,(r_(3)+r_(1))sqrt([(rr_(1))/(r_(3)r_(1))])=

If the distance S travelled by a particle in time t is given by s = t^(2) - 2t + 5 then its acceleration is

Solve the equation 4costheta+5sintheta=5 if tan51^(@)21^(')=5/4

A= {0, 2, 4, 6, 8, 10}. Insert the appropriate symbol in" or "notin in the blank space. -2"………"A

Simplify: [i^(18) + ((1)/(i))^(25)]^(3)

If the origin is the centroid of a triangle ABC having vertices A(a, 1, 3), B(-2, b, -5) and C(4, 7, c), Find the values of a, b, c.

Find the derivative with respect to x of the following: (ii) sqrt ( x) + (1)/( sqrt x)

Orthocentre of triangle formed by the lines x^(2)-xy-x+y=0 and 2x-y+4=0 is

cos^(2)25^(@)+cos^(2)35^(@)-cos25^(@) cos35^(@)=

Statement -1: For each natural number n, (n+1)^(7) - n^(7) -1 is divisible by 7. Statement - 2 : For each natural number n, n^(7) - n is divisible by 7.

Letf(x) = [ 2x^(3) - 6]when [x] is greatest integer less than or equal to x then the number of points in (1,2) where f is discontionuous is

Evaluate the following limits : Lim_(x to a) (sqrt(x)-sqrt(a))/(x-a)

Let a function y = y (x) be defined parametrically by x = 2t - |t|, y =t^2 +t|t|. Then y^(1) (x), x gt 0

Verify the following : (0, 7, 10), (-1, 6, 6) and (-4, 9, 6) are the vertices of a right angled triangle.

If a_(1), a_(2), a_(3).,,,,,,,,a_(n) are in A.P and their common difference is d. The value of the series sin d_(1) [sec a_(1).sec a_(2) + sec a_(2).sec a_(3)+ ….+ sec a_(n-1).sec a_(n)] is……..

S_(1),S_(2), S_(3),...,S_(n) are sums of n infinite geometric progressions. The first terms of these progressions are 1, 2^(2)-1, 2^(3)-1, ..., 2^(n) – 1 and the common ratios are (1)/(2),(1)/(2^(2)),(1)/(2^(3)), ...., (1)/(2^(n)). Calculate the value of S_(1), +S_(2),+ ... + S_(n).

The number of words which can be formed out of the Letters of the word 'ARTICLE, so that vowels occupy the even place in

If f(x)=sin^(2)((pi)/8 + (x)/2) -sin^2((pi)/8-(x)/(2)), then the period of f is

Statement-I : In DeltaABC, if sinA- cos B= cos C then B=(pi)/(2) Statement-II : |sinx+cosx| ge sqrt(2) Which of the above statements is correct ?

Find the sum of n terms of the following series : (i) 3+7+13+21+31+… (ii) 1+5+12+22+35+… (iii) 5+7+13+31+85+… (iv) 2+4+7+11+16+…