14949 + Interview Questions in Maths in Class 11 Page 14 InterviewSolution

651.	If log_(3)(x^(2)-6x+11) le 1, then the exhausitive range of values of x is
Answer» `(-OO, 2) uu (4, oo)` `(2, 4)` `(-oo, 1) uu (1, 3) uu (4, oo) ` `[2, 4]` Answer :D

Discussion

652.	Prove that the semi-latus rectum of a parabola is the harmonic mean of two parts of focal chord .
Answer»

Discussion

653.	Differentiate the following w.r.t. x : 3x(2x-1) (x+2)
Answer» ANSWER :`X (2X -1) + 2x (x+2) + (2x -1) (x+2)`

Discussion

654.	Write the converse and contrapositive of the following statement: A positive integer is prime only if it has no divisors other than 1 and itself.
Answer» ANSWER :not PRIME

Discussion

655.	If f : R rarr R and g: R rarr R are given by f(x)=\|x\| and g(x)={x} for each x in R, then \|x in R : g(f(x))le f(g(x))}=
Answer» `Z UU (-OO, 0)` `(-oo, 0)` Z R Answer :D

Discussion

656.	The parabola y^(2)=4ax passes through the point (2,-6). Find the length of its latus rectum.
Answer» ANSWER :18 UNITS

Discussion

657.	(i) The sum of three numbers in G.P. is 21 and sum of their squares is 189. Find the numbers. (ii) The sum of 3 numbers in a G.P. is 19 and the sum of their squares is 133. Find the numbers.
Answer» SOLUTION :N/a

Discussion

658.	Evaluate (ii) sin^(2). (2pi)/(3) + cos^(2). (5pi)/(6) - tan^(2). (3 pi)/(4)
Answer» ANSWER :`1/2`

Discussion

659.	If sqrt((1+cos alpha)/(1-cos alpha))=cosec alpha + cot alpha, then the quadrants in which alpha lies are
Answer» I, IV II, III I, II III, IV Answer :C

Discussion

660.	Use p : Ramesh is rich , q : Pradeep is poor. Think of " poor " as " not rich " , and write eachof these statements in symbolic form. It is not true that Ramesh and Pradeep both are rich.
Answer» <P> ANSWER :`~[p ^^(~Q)]`

Discussion

661.	Use p : Ramesh is rich , q : Pradeep is poor. Think of " poor " as " not rich " , and write eachof these statements in symbolic form. Either Ramesh is poor or Pradeep is poor.
Answer» <P> ANSWER :`(~p) VV Q`

Discussion

662.	Use p : Ramesh is rich , q : Pradeep is poor. Think of " poor " as " not rich " , and write eachof these statements in symbolic form. Either Ramesh is rich or Pradeep is rich .
Answer» <P> ANSWER :`p VV (~Q)`

Discussion

663.	Use p : Ramesh is rich , q : Pradeep is poor. Think of " poor " as " not rich " , and write eachof these statements in symbolic form. Ramesh is poor and pradeep is rich.
Answer» <P> ANSWER :`(~p)^^ (~Q)`

Discussion

664.	Use p : Ramesh is rich , q : Pradeep is poor. Think of " poor " as " not rich " , and write eachof these statements in symbolic form. Pradeep and Ramesh are both rich.
Answer» <P> ANSWER :`(~p)^^ p`

Discussion

665.	Use p : Ramesh is rich , q : Pradeep is poor. Think of " poor " as " not rich " , and write eachof these statements in symbolic form. Neither Ramesh nor Pradeep is rich.
Answer» <P> ANSWER :`(~p)^^ Q`.

Discussion

666.	Use p : Ramesh is rich , q : Pradeep is poor. Think of " poor " as " not rich " , and write eachof these statements in symbolic form. Ramesh is not rich and Pradeep is poor.
Answer» <P> ANSWER :`(~p)^^ Q`

Discussion

667.	The sum of the squares of first n natural numbers is :
Answer» `(1)/(6)N(n+1)(2n+1)` `(1)/(2)n(n+1)` `(1)/(4)n^(2)(n+1)^(2)` NONE of these Solution :N/a

Discussion

668.	ABCDEF is a regular hexagon. If bar(AB)+bar(AE)+bar(BC)+bar(DC)+bar(ED)+bar(AC)=lambdabar(AC)" then "lambda=
Answer» 1 2 3 4 Answer :C

Discussion

669.	Find the point to which the axes are to be translatedto eliminate x and y terms (remove first degree terms) in the equation 2x^(2) + 4xy + 5y^(2) - 4x - 22y + 7 = 0
Answer» ANSWER :(-2, 3)

Discussion

670.	If e^((1+sin^(2)x+sin^(4)x+...oo)log2)=16, then tan^(2)x =
Answer» 1 2 3 4 Answer :C

Discussion

671.	If bar(r)=3bar(i)+2bar(j)-5bar(k), bar(a)=2bar(i)-bar(j)+bar(k), bar(b)=bar(i)+3bar(j)-2bar(k) and bar(c)=-2bar(i)+bar(j)-3bar(k) such that bar(r)=lambdabar(a)+mubar(b)+deltabar(c)" then "mu, lambda/2, delta are in
Answer» A.P G.P H.P A.G.P Answer :A

Discussion

672.	r^(2) cot ""(A)/(2)cot ""(B)/(2) cot ""(C)/(2)
Answer» ` DELTA ` ` 2 Delta ` ` 3 DELA ` ` 4 Delta ` ANSWER :A

Discussion

673.	S_(n) = 1^(3) + 2^(3) + 3^(3) + …... + n^(3)and T_(n) = 1+ 2 + 3+ 4…...n
Answer» `S_(N) = T_(n)^(3)` `S_(n) = T_(n^2) ` `S_(n) = T_(n)^(2)` `S_(n) = T_(n)^(3)` ANSWER :C

Discussion

674.	sin ( 240^(@) + theta) + cos (330^(@) + theta ) = 0
Answer» ANSWER :`(204)/(325), (-253)/(325), (-204)/(253)`

Discussion

675.	Delta^("le") ABC is an Isoscels with AC = CB angle ABD = 60^(@) , angle BAE = 50^(@), angle C = 20^(@) " then " angle EDB =
Answer» `30^(@)` `45^(@)` `60^(@)` `90^(@)` ANSWER :A

Discussion

676.	The value of (sinx+cosx)^(2)+cos^(2)((pi)/(4)+x) lies in
Answer» [0,1] [0,2] [1,2] [0,3] ANSWER :C

Discussion

677.	Write the 5th and 8th terms of an AP whose 10th term is 43 and the common difference is 4.
Answer» ANSWER :23,35

Discussion

678.	If the radius of a sphere is increased from 7cm to 7.02cm. The find the approximate increase in the volume of the sphere
Answer» ANSWER :12.32

Discussion

679.	If the line lx+my+n=0 meets the pair of lines 3x^(2)+7xy-5y^(2)=0 at A and B such that OA=OB then locus of midpoint of AB is
Answer» `5X^(2)-7xy+3y^(2)=0` `3x^(2)-14xy-3y^(2)=0` `7x^(2)-16xy-7y^(2)=0` `5x^(2)+7xy-3y^(2)=0` ANSWER :C

Discussion

680.	Let U= {1, 2, 3, 4, 5, 6, 7, 8, 9}, A= {1, 2, 3, 4}, B= {2, 4, 6, 8}"and "C= {3, 4, 5, 6}.Find the following sets.A cup C, (A cup C)'= U- (A cup C)
Answer» Answer :`={1, 2, 3, 4, 5, 6}`

Discussion

681.	Find the shortest distance from (-6,0) to (a) 2x+y=3 (b) x^2-y^2+16=0
Answer» ANSWER :`3SQRT5`

Discussion

682.	Transform the equation 2x^(2)y-4+4y=0 to parallel axes when the origin is shifted to the point (1,-2)
Answer» ANSWER :`2X^(2)+y^(2)-6=0`

Discussion

683.	Solve the equationsqrt2x^(2)+x+sqrt2=0 ?
Answer» ANSWER :`(-1+-sqrt7t)/(2SQRT2)`

Discussion

684.	If bara, barb are two non-zero vectors and c is nonzero scalar, and bara. barr = c, bara xx barr = barb then barr =
Answer» `bara-BARAXXBARB` `(cbara)/(abs(bara)^(2))-(baraxxbarb)/(abs(bara)^(2))` `(bara)/(abs(bara)^(2))-c(baraxxbarb)/(abs(bara)^(2))` `cbara-(baraxxbarb)` ANSWER :B

Discussion

685.	If 2 vertices of a triangle are (-2,3) and (5-1), orthocenter lies at the origin and centered on the line x+y=7 then the 3rd vertx lies at
Answer» (7,4) (8,14) (12,21) `(64/11,102/11)` ANSWER :A

Discussion

686.	In three dimensions there may be more than one point, which are equidistant from three given noncolliner points A,B,C. One of these points will be circumcentre of the triangle ABC The circumcentre of the triangle ABC where A,B,C are (a,0,0), (0,1,0) and (0,0,c) will lie in the plane
Answer» `(X)/(a)+(y)/(B)+(z)/( c)=1` `(x)/(a)+(y)/(b) +(z)/( c)=2` `(x)/(a)+(y)/(b)+(z)/(c )=3` `(x)/(b)+(y)/(b)+(z)/(c )=4` Answer :a

Discussion

687.	In three dimensions there may be more than one point, which are equidistant from three given noncolliner points A,B,C. One of these points will be circumcentre of the triangle ABC y coordinate of the circumcentre of triangle ABC must be ac
Answer» `(AC)/(a+b+c)` `(a^(2)c^(2)-b^(4))/(a^(3)+b^(3)+c^(3))` `((b^(2)c^(2)+a^(2)b^(2)-a^(2)c^(2))/(a^(2)b^(2)+b^(2)c^(2)+c^(2)a^(2)))` `(b^(3)(a^(2)+c^(2)))/(2(b^(2)c^(2)+a^(2)c^(2)+a^(2)b^(2)))` Answer :c

Discussion

688.	Find the number of permutations of 8 things, taken 3 at a time, in which 2 particular things are always :(i)included(ii) excluded.
Answer» ANSWER :(i)36(II)120

Discussion

689.	Differentiate the following functions w.r.t. x: sec mx
Answer» ANSWER :`m SEC MX TAN mx`

Discussion

690.	If a^(2) + b^(2) + c^(2) = 8 R^(2), then the triangle is
Answer» RIGHT ANGLED ISOSCELES EQUILATERAL Scalcnc Answer :A

Discussion

691.	If (2+sqrt(3))cosx=1-sinx then x =
Answer» `2npi+(PI)/(2),2npi-(pi)/(3)` `npipm(pi)/(2),npipm(pi)/(3)` `npipm(pi)/(2),npi-(pi)/(3)` `npi-(pi)/(2),npipm(pi)/(3)` ANSWER :A

Discussion

692.	Let alpha, beta be such that pi lt alpha- beta lt 3pi. If sin alpha+ Sin beta=(-21)/(65) and cos alpha+ Cos beta=(-27)/(65) then the value of "cos" (alpha- beta)/(2) is
Answer» `(-3)/(SQRT(130))` `(-6)/(65)` `(6)/(65)` `(3)/(sqrt(130))` Answer :A

Discussion

693.	If f_(k) (x) = (1)/(k)(sin^(k) x + cos^(k)x) where x in R,k le 1 the f_(4)(x)-f_(6)(x)=
Answer» `(1)/(6)` `(1)/(3)` `(1)/(9)` `(1)/(12)` ANSWER :D

Discussion

694.	If e^(x) + e^(f(x)) =e, then domain of f(x) is:
Answer» `(-OO, 1)` `(-oo, 0)` `(1, oo)` `(2, oo)` ANSWER :A

Discussion

695.	Find the component statements of the following compound statements: It is raining and it is cold.
Answer» <P> ANSWER :p: It is rainign Q: It is COLD

Discussion

696.	Write the converse of the inverse of p implies q.
Answer» <P> ANSWER :~Q =>~p

Discussion

697.	If A= phi then how many elements are in n[P[P(phi)]]?
Answer» ANSWER :`= 4`

Discussion

698.	Let f:(-oo,oo)to(-oo,oo)be defined by f(x)=x^(3)+1Statement - I : The function f has a local exremum at x=0Statement 2 :The function f is continuous and differentiable on (-oo,oo)andf(0)=0
Answer» STATEMENT - I is TRUE , Statement - 2 is True , Statement -2 is a CORRECT EXPLANATION for Statement - I Statement - I is True , Statement -2 is True , Statement -2 NOT a correct explanation for Statement -1. Statement - I is True , Statement -2 is False Statement- 1 is False , Statement -2 is True Answer :D

Discussion

699.	Prove that sqrt((1-x)/(1+x)) is approximately equal to 1-x+(x^(2))/(2) when x is very small.
Answer» ANSWER :`=1-X+(x^(2))/(2)=RHS`

Discussion

700.	Evaluate the following limits. Lt_(xto0)1/(x^(2)-3x+2)
Answer» ANSWER :`1//2`

Discussion

Explore topic-wise InterviewSolutions in .

If log_(3)(x^(2)-6x+11) le 1, then the exhausitive range of values of x is

Prove that the semi-latus rectum of a parabola is the harmonic mean of two parts of focal chord .

Differentiate the following w.r.t. x : 3x(2x-1) (x+2)

Write the converse and contrapositive of the following statement: A positive integer is prime only if it has no divisors other than 1 and itself.

If f : R rarr R and g: R rarr R are given by f(x)=|x| and g(x)={x} for each x in R, then |x in R : g(f(x))le f(g(x))}=

The parabola y^(2)=4ax passes through the point (2,-6). Find the length of its latus rectum.

(i) The sum of three numbers in G.P. is 21 and sum of their squares is 189. Find the numbers. (ii) The sum of 3 numbers in a G.P. is 19 and the sum of their squares is 133. Find the numbers.

Evaluate (ii) sin^(2). (2pi)/(3) + cos^(2). (5pi)/(6) - tan^(2). (3 pi)/(4)

If sqrt((1+cos alpha)/(1-cos alpha))=cosec alpha + cot alpha, then the quadrants in which alpha lies are

Use p : Ramesh is rich , q : Pradeep is poor. Think of " poor " as " not rich " , and write eachof these statements in symbolic form. It is not true that Ramesh and Pradeep both are rich.

Use p : Ramesh is rich , q : Pradeep is poor. Think of " poor " as " not rich " , and write eachof these statements in symbolic form. Either Ramesh is poor or Pradeep is poor.

Use p : Ramesh is rich , q : Pradeep is poor. Think of " poor " as " not rich " , and write eachof these statements in symbolic form. Either Ramesh is rich or Pradeep is rich .

Use p : Ramesh is rich , q : Pradeep is poor. Think of " poor " as " not rich " , and write eachof these statements in symbolic form. Ramesh is poor and pradeep is rich.

Use p : Ramesh is rich , q : Pradeep is poor. Think of " poor " as " not rich " , and write eachof these statements in symbolic form. Pradeep and Ramesh are both rich.

Use p : Ramesh is rich , q : Pradeep is poor. Think of " poor " as " not rich " , and write eachof these statements in symbolic form. Neither Ramesh nor Pradeep is rich.

Use p : Ramesh is rich , q : Pradeep is poor. Think of " poor " as " not rich " , and write eachof these statements in symbolic form. Ramesh is not rich and Pradeep is poor.

The sum of the squares of first n natural numbers is :

ABCDEF is a regular hexagon. If bar(AB)+bar(AE)+bar(BC)+bar(DC)+bar(ED)+bar(AC)=lambdabar(AC)" then "lambda=

Find the point to which the axes are to be translatedto eliminate x and y terms (remove first degree terms) in the equation 2x^(2) + 4xy + 5y^(2) - 4x - 22y + 7 = 0

If e^((1+sin^(2)x+sin^(4)x+...oo)log2)=16, then tan^(2)x =

If bar(r)=3bar(i)+2bar(j)-5bar(k), bar(a)=2bar(i)-bar(j)+bar(k), bar(b)=bar(i)+3bar(j)-2bar(k) and bar(c)=-2bar(i)+bar(j)-3bar(k) such that bar(r)=lambdabar(a)+mubar(b)+deltabar(c)" then "mu, lambda/2, delta are in

r^(2) cot ""(A)/(2)cot ""(B)/(2) cot ""(C)/(2)

S_(n) = 1^(3) + 2^(3) + 3^(3) + …... + n^(3)and T_(n) = 1+ 2 + 3+ 4…...n

sin ( 240^(@) + theta) + cos (330^(@) + theta ) = 0

Delta^("le") ABC is an Isoscels with AC = CB angle ABD = 60^(@) , angle BAE = 50^(@), angle C = 20^(@) " then " angle EDB =

The value of (sinx+cosx)^(2)+cos^(2)((pi)/(4)+x) lies in

Write the 5th and 8th terms of an AP whose 10th term is 43 and the common difference is 4.

If the radius of a sphere is increased from 7cm to 7.02cm. The find the approximate increase in the volume of the sphere

If the line lx+my+n=0 meets the pair of lines 3x^(2)+7xy-5y^(2)=0 at A and B such that OA=OB then locus of midpoint of AB is

Let U= {1, 2, 3, 4, 5, 6, 7, 8, 9}, A= {1, 2, 3, 4}, B= {2, 4, 6, 8}"and "C= {3, 4, 5, 6}.Find the following sets.A cup C, (A cup C)'= U- (A cup C)

Find the shortest distance from (-6,0) to (a) 2x+y=3 (b) x^2-y^2+16=0

Transform the equation 2x^(2)y-4+4y=0 to parallel axes when the origin is shifted to the point (1,-2)

Solve the equationsqrt2x^(2)+x+sqrt2=0 ?

If bara, barb are two non-zero vectors and c is nonzero scalar, and bara. barr = c, bara xx barr = barb then barr =

If 2 vertices of a triangle are (-2,3) and (5-1), orthocenter lies at the origin and centered on the line x+y=7 then the 3rd vertx lies at

In three dimensions there may be more than one point, which are equidistant from three given noncolliner points A,B,C. One of these points will be circumcentre of the triangle ABC The circumcentre of the triangle ABC where A,B,C are (a,0,0), (0,1,0) and (0,0,c) will lie in the plane

In three dimensions there may be more than one point, which are equidistant from three given noncolliner points A,B,C. One of these points will be circumcentre of the triangle ABC y coordinate of the circumcentre of triangle ABC must be ac

Find the number of permutations of 8 things, taken 3 at a time, in which 2 particular things are always :(i)included(ii) excluded.

Differentiate the following functions w.r.t. x: sec mx

If a^(2) + b^(2) + c^(2) = 8 R^(2), then the triangle is

If (2+sqrt(3))cosx=1-sinx then x =

Let alpha, beta be such that pi lt alpha- beta lt 3pi. If sin alpha+ Sin beta=(-21)/(65) and cos alpha+ Cos beta=(-27)/(65) then the value of "cos" (alpha- beta)/(2) is

If f_(k) (x) = (1)/(k)(sin^(k) x + cos^(k)x) where x in R,k le 1 the f_(4)(x)-f_(6)(x)=

If e^(x) + e^(f(x)) =e, then domain of f(x) is:

Find the component statements of the following compound statements: It is raining and it is cold.

Write the converse of the inverse of p implies q.

If A= phi then how many elements are in n[P[P(phi)]]?

Let f:(-oo,oo)to(-oo,oo)be defined by f(x)=x^(3)+1Statement - I : The function f has a local exremum at x=0Statement 2 :The function f is continuous and differentiable on (-oo,oo)andf(0)=0

Prove that sqrt((1-x)/(1+x)) is approximately equal to 1-x+(x^(2))/(2) when x is very small.

Evaluate the following limits. Lt_(xto0)1/(x^(2)-3x+2)