14949 + Interview Questions in Maths in Class 11 Page 73 InterviewSolution

3601.	Mean and standard deviation of 100 observations were found to be 40 and 10, respectively . If at the time of calculation two observation were wrongly taken as 30 and 70 in place of 3 and 27 respectively, find the correct standard deviation.
Answer» ANSWER :10.24

Discussion

3602.	If barmu =bara-barb, barv=bara+barb and absbara=absbarb, " then " barmu.barv is
Answer» `LT 0` `GT0` `2absbara^(2)` 0 Answer :D

Discussion

3603.	If y = sqrt((secx-1)/(sec x +1) ) then (dy)/(dx)=
Answer» `1/(2)sec^2""x/2` `sec^2""x/2` `1/2 TAN""x/2` `tan""x/2` ANSWER :A

Discussion

3604.	Let ABCD be a quadrilateral with area 18. with side AB parallel to the side CD and CD = 2 AB. Let AD be perpendicular to AB and CD. If a circle is drawn inside the quadrilateral ABCD touching all the sides, then its radius is
Answer» 3 2 `3//2` 1 Answer :B

Discussion

3605.	If there is an error of 0.05 cm in the side of a cube 10cm then the error in its surface area is
Answer» `6 c.m^(2)` `12 c.m^(2)` `5 c.m^(2)` `3 c.m^(2)` ANSWER :A

Discussion

3606.	If y = (sinx)^(x)then (dy)/(dx) =
Answer» `y(LOG(SINX)+xcotx)` `y(log(sinx)-xcotx)` `-y(log(sinx)-xcotx)` `-y(log(sinx)+xcotx)` ANSWER :A

Discussion

3607.	Check whether the given sentence is a statement or not: "May you live long !"
Answer» ANSWER :Not a STATEMENT

Discussion

3608.	If a,b,c are in A.P. b,c,d are in G.P,c,d,e are in H. P. then show that a,c,e are in G. P.
Answer» ANSWER :` RARR C^(2) +cancelce = ae + cancelce rArr c^(2) = ae rArr a ,c,E ` are in G.P.

Discussion

3609.	The total number of solutions of sin[x]=cos{x} (where {.} denotes the fractional part) in [0,2pi] is equal
Answer» 5 6 8 7 Answer :B

Discussion

3610.	Find the roots of the equations:sqrt(3)x^(2)-sqrt(2)x+3sqrt(3)=0.
Answer» ANSWER :`(SQRT(2)pmisqrt(34))/(2sqrt(3))`.

Discussion

3611.	If log_(2)(sinx)-log_(2)(cosx)-log_(2)(1-tanx)-log_(2)(1+tanx)=-1 then tan2x=
Answer» 0 1 `-1` 2 Answer :B

Discussion

3612.	……………of the following is converse of the contrapositive statement of the conditional statement p implies~q
Answer» `pimpliesq` `~pimplies~p` `~qimpliesp` `~pimpliesq` ANSWER :D

Discussion

3613.	(a^(2)-b^(2))/(c^(2)-a^(2))=c/b . (sin(A-B))/(sin(C-A))
Answer» SOLUTION :NA

Discussion

3614.	Translate the following statements into symbolic form: Either x=2 or x=3 is a root of 3x^(2)-x-10=0.
Answer» ANSWER :`3X^(2)-x-10=0`

Discussion

3615.	The value of cos ^(2) 10^(@) - cos 10^(@) cos 50^(@) + cos ^(2) 50^(@) is equal to
Answer» `4//3` `1//3` `3//4` `3` ANSWER :C

Discussion

3616.	Write the contrapositive of the following statement: If you are born in India, then you are a citizen of India.
Answer» ANSWER :not BORN in INDIA.

Discussion

3617.	The minimum area of a triangle formed by any tangent to the ellipse (x^(2))/(16)+(y^(2))/(81)=1 and the cordinate axes is
Answer» 12 18 26 36 Answer :D

Discussion

3618.	Write the set {x : x is a positive integer and x^(2) < 40} in the roster form.
Answer» Answer :`{1, 2, 3, 4, 5, 6}`

Discussion

3619.	Find the angle between the lines whose direction cosines are given by the equation 3l + m + 5n = 0 and 6mn - 2nl + 5lm = 0
Answer» ANSWER :`COS^(-1)((1)/(6))`

Discussion

3620.	Write Negation of the following statements: 11 is a prime number.
Answer» ANSWER :11 is not a PRIME NUMBER.

Discussion

3621.	Iff(x) = (cos 3x - cos 4x)/( xsin2x), x in 0, f (0) = (7)/(4)then f(x) at x = 0 is
Answer» CONTINUOUS DISCONTINUOUS not DETERMINED NONE ANSWER :A

Discussion

3622.	If tan x/2 "coth"x/2 =1, then cos x cosh x =
Answer» 1 2 0 `-1` ANSWER :A

Discussion

3623.	The variance of 15 observations is 6. If each observation is increased by 8, find the variance of the resulting observations.
Answer» ANSWER :6

Discussion

3624.	What is the number of all possible matrices with each entry as 0 or 1 ? (i) If the order of matrices is 2xx2 If the order of matrices is 2xx3 (iii)If the order of matrices is 3xx3
Answer» ANSWER :(i) 16 (ii) 64 (iii) 512

Discussion

3625.	The negation of p^^q is the disjunction of. . . . . . . . . . . . .
Answer» <P> ANSWER :`~p` and `~Q`

Discussion

3626.	A point C = (5a + 4b - 5c)/(3) divides the line joining A = a - 2b + 3c and B in the ratio 2 : 1, then the poistion vector of B is
Answer» `BAR(a)+3BAR(B)-4bar(c)` `2bar(a)-3bar(b)+4bar(c)` `2bar(a)+3bar(b)+4bar(c)` `2bar(a)+3bar(b)-4bar(c)` Answer :D

Discussion

3627.	If the probabilities for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fails is
Answer» `gt0.5` 0.5 `le0.5` 0 Answer :C

Discussion

3628.	A plane passes through (2,3,-1) and is perpendicular to the line having d.c's ((3)/(sqrt(74)),(-4)/(sqrt(74)),(7)/(sqrt(74))). The perpendicular distance from origin to this plane is
Answer» `(3)/(sqrt(74))` `(5)/(sqrt(74))` `(6)/(sqrt(74))` `(13)/(sqrt(74))` Answer :D

Discussion

3629.	Find the union of each of the following pairs of sets. A= {1, 2, 3, 4, 5}, B= {2, 3, 5, 7}
Answer» ANSWER :`A cup B = {1, 2, 3, 4, 5, 7}`

Discussion

3630.	Which term of the following sequences: (a) 2,2sqrt4,4.......... is 128 ?(b) sqrt3,3,3sqrt3 ,............. is 729 ? (c) 1/3,1/9,1/(27),......." is " 1/19683 ?
Answer» Answer :(a) `13^(th)` , (B) `12^(th)` , (c) `9^(th)`

Discussion

3631.	Given that P(n, r)=n(n-1)(n-2)….to r factors What are the values of P(n, 4) and P(n, 2)?
Answer» SOLUTION :`N(n-l)(n-2)(n-3),n(n-l)`

Discussion

3632.	Two sides of a rhombus ABCD are parallel to lines y=x+2 and y=7x+3. If the diagonals of the rhombus intersect at point (1,2) and the vertex A is on the y -axis is , then possible coordinates of A are
Answer» `(0,5/2)` (0,0) (0,5) (0,3) ANSWER :A::C

Discussion

3633.	Find the transformed equation of x cos alpha + y sin alpha = pif the axes are rotated through an angle alpha
Answer» <P> ANSWER :X = P

Discussion

3634.	Twocards are drawn from a pack of 52 cards . What is the probabilitythat either both are red or both are kings ?
Answer» ANSWER :`=(55)/(221)`

Discussion

3635.	From the top of a tree, a man observes the angle of deppression of a point which is at distance of 40 metres from the foot is 75^(@). The height of the tree is
Answer» `40sqrt3mts` `21sqrt3mts` `40(2+sqrt3)MTS` `3sqrt21mts` ANSWER :A

Discussion

3636.	If a^(2)+b^(2)+c^(2)=1 then the range of ab+bc+ca is
Answer» `[1, OO)` `[ (-1)/(2), oo]` `(- 1/2, 1)` `[ (-1)/(2), 1]` ANSWER :D

Discussion

3637.	The points A(2, 9, 12), B(1, 8, 8), C(-2, 11, 8) D(-1, 12, 12) form
Answer» A parallelogram A RHOMBUS A SQUARE A RECTANGLE ANSWER :C

Discussion

3638.	If cosalpha=-0.6andpiltalphalt(3pi)/(2) then tan((alpha)/(4)) = ………..
Answer» `(1-SQRT(5))/(2)` `(sqrt(5)-1)/(2)` `(sqrt(5))/(2)` `(sqrt(5)+1)/(2)` ANSWER :D

Discussion

3639.	If A=sin^(2)theta+cos^(4)theta, then for all real values of theta:
Answer» `3/4 LE A le 13/16` `3/4 le A le 1` `1 leAle2` `13/16 le Ale1` SOLUTION :N//A

Discussion

3640.	If (x_(1),y_1,z_1) and (x_2,y_2,z_2) are two vertices and (alpha, beta, gamma) is the centroid of a triangle, find the third vertex of the triangle.
Answer» ANSWER :`(3alpha-x_(1)-x_(2),3beta-y_(1)-y_(2),3gamma-z_(1)-z_(2))`

Discussion

3641.	The sum of three decreasing numbers in A.P. is 27. If-1,-1, 3 are added to them respectively, the resulting series is in G.P. The numbers are
Answer» 5,9,13 15,9,3 13,9,5 17,9,1 Answer :D

Discussion

3642.	Simplify: sqrt(-20) + sqrt(-12)
Answer» ANSWER :`2(SQRT5 + SQRT3)i`

Discussion

3643.	A= {2, 4, 6, 9} B= {4, 6, 18, 27, 54} R= {(a,b): a in A, b in B, a lt b, a is a factor of b} Find domain and range of R
Answer» ANSWER :Domain of R = {2, 6, 9} RANGE of R = {4, 6, 18, 27 , 54}

Discussion

3644.	Prove that (1+tanA)^(2)+(1-tanA)^(2)=2sec^(2)A.
Answer» ANSWER :RIGHT SIDE

Discussion

3645.	Value of 'c' of Lagrange's mean value theorem for f(x) = 2x - x^(2)in [0,1]
Answer» 1 0 `1//2` `-1` ANSWER :C

Discussion

3646.	Find the number of terms in the following expansions. ( sqrt(3) + sqrt(5) )^(7) ( sqrt(3) - sqrt(5) )^(7)
Answer» ANSWER :`=4`

Discussion

3647.	Answer the equation: int(sinx+sin2x)/(cos2x+cosx)dx
Answer» ANSWER :`(2)/(3)LOG\|"sec"(3X)/(2)\|+C`

Discussion

3648.	Find the number ofpermutations of the letter of the words ' COMMISIONS.'
Answer» ANSWER :` 226800`

Discussion

3649.	Using 2105 as base year, the index number for the price of a commodity in 2016 is 118.Then the indexnumber for 2015 taking 2016 as base year is :
Answer» (a)`84 . 74` (b)`87 . 45` (C)` 8 . 475` (d)`847 . 5 ` Answer :A

Discussion

3650.	One number is selected from first 120 natural number .then probability of an event that selected number is multiple of 5 or 15 is …. .
Answer» ANSWER :`1/5`

Discussion

Explore topic-wise InterviewSolutions in .

Mean and standard deviation of 100 observations were found to be 40 and 10, respectively . If at the time of calculation two observation were wrongly taken as 30 and 70 in place of 3 and 27 respectively, find the correct standard deviation.

If barmu =bara-barb, barv=bara+barb and absbara=absbarb, " then " barmu.barv is

If y = sqrt((secx-1)/(sec x +1) ) then (dy)/(dx)=

Let ABCD be a quadrilateral with area 18. with side AB parallel to the side CD and CD = 2 AB. Let AD be perpendicular to AB and CD. If a circle is drawn inside the quadrilateral ABCD touching all the sides, then its radius is

If there is an error of 0.05 cm in the side of a cube 10cm then the error in its surface area is

If y = (sinx)^(x)then (dy)/(dx) =

Check whether the given sentence is a statement or not: "May you live long !"

If a,b,c are in A.P. b,c,d are in G.P,c,d,e are in H. P. then show that a,c,e are in G. P.

The total number of solutions of sin[x]=cos{x} (where {.} denotes the fractional part) in [0,2pi] is equal

Find the roots of the equations:sqrt(3)x^(2)-sqrt(2)x+3sqrt(3)=0.

If log_(2)(sinx)-log_(2)(cosx)-log_(2)(1-tanx)-log_(2)(1+tanx)=-1 then tan2x=

……………of the following is converse of the contrapositive statement of the conditional statement p implies~q

(a^(2)-b^(2))/(c^(2)-a^(2))=c/b . (sin(A-B))/(sin(C-A))

Translate the following statements into symbolic form: Either x=2 or x=3 is a root of 3x^(2)-x-10=0.

The value of cos ^(2) 10^(@) - cos 10^(@) cos 50^(@) + cos ^(2) 50^(@) is equal to

Write the contrapositive of the following statement: If you are born in India, then you are a citizen of India.

The minimum area of a triangle formed by any tangent to the ellipse (x^(2))/(16)+(y^(2))/(81)=1 and the cordinate axes is

Write the set {x : x is a positive integer and x^(2) < 40} in the roster form.

Find the angle between the lines whose direction cosines are given by the equation 3l + m + 5n = 0 and 6mn - 2nl + 5lm = 0

Write Negation of the following statements: 11 is a prime number.

Iff(x) = (cos 3x - cos 4x)/( xsin2x), x in 0, f (0) = (7)/(4)then f(x) at x = 0 is

If tan x/2 "coth"x/2 =1, then cos x cosh x =

The variance of 15 observations is 6. If each observation is increased by 8, find the variance of the resulting observations.

What is the number of all possible matrices with each entry as 0 or 1 ? (i) If the order of matrices is 2xx2 If the order of matrices is 2xx3 (iii)If the order of matrices is 3xx3

The negation of p^^q is the disjunction of. . . . . . . . . . . . .

A point C = (5a + 4b - 5c)/(3) divides the line joining A = a - 2b + 3c and B in the ratio 2 : 1, then the poistion vector of B is

If the probabilities for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fails is

A plane passes through (2,3,-1) and is perpendicular to the line having d.c's ((3)/(sqrt(74)),(-4)/(sqrt(74)),(7)/(sqrt(74))). The perpendicular distance from origin to this plane is

Find the union of each of the following pairs of sets. A= {1, 2, 3, 4, 5}, B= {2, 3, 5, 7}

Which term of the following sequences: (a) 2,2sqrt4,4.......... is 128 ?(b) sqrt3,3,3sqrt3 ,............. is 729 ? (c) 1/3,1/9,1/(27),......." is " 1/19683 ?

Given that P(n, r)=n(n-1)(n-2)….to r factors What are the values of P(n, 4) and P(n, 2)?

Two sides of a rhombus ABCD are parallel to lines y=x+2 and y=7x+3. If the diagonals of the rhombus intersect at point (1,2) and the vertex A is on the y -axis is , then possible coordinates of A are

Find the transformed equation of x cos alpha + y sin alpha = pif the axes are rotated through an angle alpha

Twocards are drawn from a pack of 52 cards . What is the probabilitythat either both are red or both are kings ?

From the top of a tree, a man observes the angle of deppression of a point which is at distance of 40 metres from the foot is 75^(@). The height of the tree is

If a^(2)+b^(2)+c^(2)=1 then the range of ab+bc+ca is

The points A(2, 9, 12), B(1, 8, 8), C(-2, 11, 8) D(-1, 12, 12) form

If cosalpha=-0.6andpiltalphalt(3pi)/(2) then tan((alpha)/(4)) = ………..

If A=sin^(2)theta+cos^(4)theta, then for all real values of theta:

If (x_(1),y_1,z_1) and (x_2,y_2,z_2) are two vertices and (alpha, beta, gamma) is the centroid of a triangle, find the third vertex of the triangle.

The sum of three decreasing numbers in A.P. is 27. If-1,-1, 3 are added to them respectively, the resulting series is in G.P. The numbers are

Simplify: sqrt(-20) + sqrt(-12)

A= {2, 4, 6, 9} B= {4, 6, 18, 27, 54} R= {(a,b): a in A, b in B, a lt b, a is a factor of b} Find domain and range of R

Prove that (1+tanA)^(2)+(1-tanA)^(2)=2sec^(2)A.

Value of 'c' of Lagrange's mean value theorem for f(x) = 2x - x^(2)in [0,1]

Find the number of terms in the following expansions. ( sqrt(3) + sqrt(5) )^(7) ( sqrt(3) - sqrt(5) )^(7)

Answer the equation: int(sinx+sin2x)/(cos2x+cosx)dx

Find the number ofpermutations of the letter of the words ' COMMISIONS.'

Using 2105 as base year, the index number for the price of a commodity in 2016 is 118.Then the indexnumber for 2015 taking 2016 as base year is :

One number is selected from first 120 natural number .then probability of an event that selected number is multiple of 5 or 15 is …. .