14949 + Interview Questions in Maths in Class 11 Page 179 InterviewSolution

8901.	Write the contrapositive and converse of the following statements: You cannot comprehend geometry if you do no know hot to reason deductively.
Answer» ANSWER :Contrapositive If you can comprehend geometry then you KNOW how to reason DEDUCTIVELY. Converse:If you don't know to gove proof by deductively then you can't comprehend geometry.

Discussion

8902.	Find the derivative of the following functions: sinxcosx
Answer» ANSWER :`COS2X`

Discussion

8903.	The period of the function f(x)=c^(sin^(2)x +sin^(2)(x+ pi/3) + cos x cos(x + pi/3)) is( where c is constant)
Answer» 1 `PI/2` `pi` Cannot be determined Answer :D

Discussion

8904.	Find the derivate of 2x-(3)/(4)
Answer» ANSWER :2

Discussion

8905.	Theperiodof 3x - [3x]is(where [.]denote greatestintegerfunction le x )
Answer» `(1)/(2)` `1` `2` `(1)/(3)` ANSWER :4

Discussion

8906.	Point (-3,1,-2) is in ........... octant.
Answer» ANSWER :SIXTH

Discussion

8907.	Find the value of sec 510^(@)
Answer» ANSWER :`(-2)/(SQRT(3))`

Discussion

8908.	Express the following in the form a+bi (1-i)^(4)
Answer» ANSWER :`-4`

Discussion

8909.	For all sets A, B and C, if A sub B, then A cap C sub B cap C.
Answer» ANSWER :1

Discussion

8910.	What is meant by superposition of gravitational field?
Answer» Solution :Consider 'n' particles of masses `m_1, m_2, .........m_n ,` distributed in SPACE at positions `vecr_1, vecr_2, vecr_3........,` etc, with RESPECT to POINT P. The total gravitational FIELD at a point P due to all the masses is given by the vector SUM of the gravitational field due to the individual masses. This principle is known as superposition of gravitational fields. `vecE_("total") = vecE_1 + vecE_2 + .......vecE_n` ` =- (Gm_1)/(r_1^2) harr_1 - (Gm_2)/(r_2^2) hatr_2 - ......(Gm_n)/(r_n^2)hatr_n = - sum_(i=1)^(n) (Gm_i)/(r_i^2) hatr_i`

Discussion

8911.	Write the following intervals in set-builder form : [–23, 5)
Answer» Answer :`{ XR : – 23 ≤ X < 5 }`

Discussion

8912.	A point on the line bar(r)=(1-t)(2bar(i)+3bar(j)+4bar(k))+t(3bar(i)-2bar(j)+2bar(k)) is
Answer» `-bar(i)+5bar(J)+2BAR(k)` `bar(i)+6bar(j)+8bar(k)` `bar(i)+8bar(j)+6bar(k)` `bar(i)-8bar(j)+6bar(k)` Answer :C

Discussion

8913.	Find the number of discontinuous functions =f(x) on [-2,2] satisfying x^(2)+y^(2)=4
Answer» ANSWER :THUS there are INFINITE discontinous fucntions

Discussion

8914.	If bara=(1,-1,-6),barb=(1,-3,4) and barc(-2,-5,3) then compute baraxx(barbxxbarc).
Answer» ANSWER :`29i-67barj+16bark,-40bari+62barj+130bark,0`

Discussion

8915.	f(x) = (1 -cos (7(x-pi)))/(x - pi)is continous at x =pi " then " f (pi) =
Answer» 0 1 2 3 Answer :A

Discussion

8916.	Length of latus rectum ofellipse 5x^(2) + 9y^(2) = 45 is …….
Answer» `(5sqrt(5))/(3)` `(5)/(3)` `(2sqrt(5))/(3)` `(10)/(3)` ANSWER :D

Discussion

8917.	The mean and standard deviation of agroup of 100 observations were found to be 20 and 3 respectively .Later , it was found that three observations were incorrect , which were recorded as 21 , 21and 18. Find the mean and standard deviation if the correct observations are omitted.
Answer» ANSWER :20,3.03

Discussion

8918.	Solve tan^(2) theta = 1, theta in [-pi, pi]
Answer» ANSWER :`{-(3PI)/(4), (-PI)/(4), (pi)/(4), (3pi)/(4)}`

Discussion

8919.	Find the roots of x^(2) + 3x +9=0
Answer» ANSWER :`(-3 +-3sqrt(3)i)/2`

Discussion

8920.	The sum of all odd numbers between 1 and 100 which are divisible by 3, is
Answer» 83667 90000 83660 None of these Answer :A

Discussion

8921.	If y = tan^(-1)((1+x^(2))/(1-x^(2))) Find dy/dx.
Answer» ANSWER :`-2X^(3)/(1+x^(4))`

Discussion

8922.	a^(2) cot A+ b^(2) cot B+ c ^(2) cot C =
Answer» ` (abc)/ ( R ) ` ` (2abc)/( R ) ` `( 3AB) /( R ) ` ` S+ ( DELTA )/ ( R ) ` ANSWER :A

Discussion

8923.	P and Q are (3,1,2)and(1,-2,-4). Equation of the plane through 'Q' and perpendicular to PQ is :
Answer» `2x+3y+6z+28=0` `2x-3y+6z-28=0` `2x-3y-6z+28=0` `2x-2y-6z+12=0` ANSWER :A

Discussion

8924.	Evaluate the following limits. Lt_(t to8)(root(3)(t)-2)/(t^(2)-64)
Answer» ANSWER :`1/192`

Discussion

8925.	Solve 5x+1> (-24) , 5x-1
Answer» ANSWER :` THEREFORE X INN(4,5,5)`

Discussion

8926.	Eccentricity of hypewrbola (x ^(2))/(k ) + ( y ^(2))/(k)) =1 ( k lt 0) is
Answer» `SQRT(1+K )` ` sqrt(1-k )` `sqrt(1+ (1)/(k))` ` sqrt(1- (1)/(k))` ANSWER :D

Discussion

8927.	If x,y,z are in A.P and Tan^(-1) x, Tan^(-1) y and Tan^(-1) zare also in A.P., then
Answer» `x=y=z` `2x=3y=6z` `6x=3y=2z` `6x=4y=3z` ANSWER :A

Discussion

8928.	How many seven -digits phone numbers are possible if 0 and 1 cannot be used as the first digit and the first three digits cannot be 555, 411 or 936?
Answer» ANSWER :` [ 8 XX 10 xx 10 -3] xx 10 xx 10 xx 10 xx 10 = 7970000`

Discussion

8929.	Evaluate the following limits : Lt_(ntooo)(q^(n)+p^(n))^(1/n),0ltpltq
Answer» ANSWER :Q

Discussion

8930.	For arithmetic sequence a = 2 and a_5 = 14 then d = ........
Answer» ANSWER :`2a_(m)`

Discussion

8931.	3(sinx-cosx)^(4)+6(sinx+cosx)^(2) + 4(sin^(6) x+cos^(6)x) is equal to
Answer» ANSWER :13

Discussion

8932.	Using binomial theorem , Prove that a^(n)-b^(n) is divisible by (a-b)
Answer» ANSWER :EXPAND USING `a^(N) =(a-b+b)^(n)`

Discussion

8933.	Evaluate the following limits : Lt_(xto0)(e^(sinx)-1)/x
Answer» ANSWER :1

Discussion

8934.	Period of cos "" (3x)/(5) + 2 sin"" (2x)/( 7) - 5 cot 14 x is
Answer» `7pi` `14 PI` `28 pi` `70 pi` ANSWER :D

Discussion

8935.	Of the parabola, 4(y-1)^(2)= -7(x-3) find The length of the latus rectum.
Answer» ANSWER :`(7)/(4)`

Discussion

8936.	If f(x) = (x+1)/(x-1) (x ne -1) then find (fofof)(x) and (fofofof)(x).
Answer» ANSWER :`F(X),x`

Discussion

8937.	Write the negation of the following statements: sqrt(2) is not a complex number.
Answer» ANSWER :`SQRT(2)` is a COMPLEX NUMBER.

Discussion

8938.	Solve the equation for0 le x le 2pi. tan theta + sqrt3 =0
Answer» ANSWER :`(2PI )/(3), (5PI)/(3)`

Discussion

8939.	If z= x + yi and omega = ((1- zi))/(z-i), then \|omega\|=1 implies that in the complex plane
Answer» z LIES on the IMAGINARY axis z lies on the real axis z lies on the UNIT circle None of these Answer :B

Discussion

8940.	Prove that (-1/2,2,0) is thecircumcenter of the triangle with vertices (1,1,0),(1,2,1) and (-2,2,-1).
Answer» ANSWER :`=((-1)/(2),2,0)`

Discussion

8941.	Find the approximations of the following root(4)(17)
Answer» ANSWER :2.03125

Discussion

8942.	If the vertices of a triangle are (1,4,2),(-2,1,2),(2,3,-4) then the angles are
Answer» Answer :`lfloorA=(PI)/(2),lfloorB=cos^(-1)((3)/(2sqrt(7))),lfloorC=cos^(-1)sqrt((19)/(28))`

Discussion

8943.	If the extremities of a diagonal of square are (1,-2,3),(2,-3,5) then the length of its side is
Answer» ANSWER :`SQRT(3)`

Discussion

8944.	Consider the planes 3x - 6y + 2z + 5=0 and 4x - 12 y + 3z = 3. The plne 67 x - 162 y + 47 z + 44 =0 bisects the angle between the given planes which
Answer» contains origin is acute is OBTUSE RIGHT ANGLE ANSWER :A::B

Discussion

8945.	Evaluate the following limits in Exercises lim_(xto1)(ax^(2)+bx+c)/(cx^(2)+bx+a),a+b+cne0
Answer» ANSWER :1

Discussion

8946.	If x+ y = 3e^2then d/(dx)(x^y)=0 for x =
Answer» E `e^2` `e^e` `2e^2` ANSWER :B

Discussion

8947.	There are four events E_(1),E_(2),E_(3),andE_(4) one of which must and onlyone can happen The odds are 2:5 in favour ofE_(1),3:4 in favour of E_(2) and 1:3 in favour of E_(3) . Find the odds against E_(4).
Answer» ANSWER :`27:1`

Discussion

8948.	Find the 13^(th) term in the expansion of (9x-(1)/(3sqrtx))^(18) :xne0 ?
Answer» ANSWER :18564

Discussion

8949.	A,B and C are three mutually exclusiveevents associated with a random experiment . Find P(A) given that P(B)=(3)/(2)P(A)andP(C )=(1)/(2)P(B).
Answer» <P> ANSWER :`P(A)=(4)/(13)`

Discussion

8950.	Express the following in the form a+bi, where a and b are rea numbers ((1-i)/(1+ i))^(2)
Answer» ANSWER :`-1 + 0I`

Discussion

Explore topic-wise InterviewSolutions in .

Write the contrapositive and converse of the following statements: You cannot comprehend geometry if you do no know hot to reason deductively.

Find the derivative of the following functions: sinxcosx

The period of the function f(x)=c^(sin^(2)x +sin^(2)(x+ pi/3) + cos x cos(x + pi/3)) is( where c is constant)

Find the derivate of 2x-(3)/(4)

Theperiodof 3x - [3x]is(where [.]denote greatestintegerfunction le x )

Point (-3,1,-2) is in ........... octant.

Find the value of sec 510^(@)

Express the following in the form a+bi (1-i)^(4)

For all sets A, B and C, if A sub B, then A cap C sub B cap C.

What is meant by superposition of gravitational field?

Write the following intervals in set-builder form : [–23, 5)

A point on the line bar(r)=(1-t)(2bar(i)+3bar(j)+4bar(k))+t(3bar(i)-2bar(j)+2bar(k)) is

Find the number of discontinuous functions =f(x) on [-2,2] satisfying x^(2)+y^(2)=4

If bara=(1,-1,-6),barb=(1,-3,4) and barc(-2,-5,3) then compute baraxx(barbxxbarc).

f(x) = (1 -cos (7(x-pi)))/(x - pi)is continous at x =pi " then " f (pi) =

Length of latus rectum ofellipse 5x^(2) + 9y^(2) = 45 is …….

The mean and standard deviation of agroup of 100 observations were found to be 20 and 3 respectively .Later , it was found that three observations were incorrect , which were recorded as 21 , 21and 18. Find the mean and standard deviation if the correct observations are omitted.

Solve tan^(2) theta = 1, theta in [-pi, pi]

Find the roots of x^(2) + 3x +9=0

The sum of all odd numbers between 1 and 100 which are divisible by 3, is

If y = tan^(-1)((1+x^(2))/(1-x^(2))) Find dy/dx.

a^(2) cot A+ b^(2) cot B+ c ^(2) cot C =

P and Q are (3,1,2)and(1,-2,-4). Equation of the plane through 'Q' and perpendicular to PQ is :

Evaluate the following limits. Lt_(t to8)(root(3)(t)-2)/(t^(2)-64)

Solve 5x+1> (-24) , 5x-1

Eccentricity of hypewrbola (x ^(2))/(k ) + ( y ^(2))/(k)) =1 ( k lt 0) is

If x,y,z are in A.P and Tan^(-1) x, Tan^(-1) y and Tan^(-1) zare also in A.P., then

How many seven -digits phone numbers are possible if 0 and 1 cannot be used as the first digit and the first three digits cannot be 555, 411 or 936?

Evaluate the following limits : Lt_(ntooo)(q^(n)+p^(n))^(1/n),0ltpltq

For arithmetic sequence a = 2 and a_5 = 14 then d = ........

3(sinx-cosx)^(4)+6(sinx+cosx)^(2) + 4(sin^(6) x+cos^(6)x) is equal to

Using binomial theorem , Prove that a^(n)-b^(n) is divisible by (a-b)

Evaluate the following limits : Lt_(xto0)(e^(sinx)-1)/x

Period of cos "" (3x)/(5) + 2 sin"" (2x)/( 7) - 5 cot 14 x is

Of the parabola, 4(y-1)^(2)= -7(x-3) find The length of the latus rectum.

If f(x) = (x+1)/(x-1) (x ne -1) then find (fofof)(x) and (fofofof)(x).

Write the negation of the following statements: sqrt(2) is not a complex number.

Solve the equation for0 le x le 2pi. tan theta + sqrt3 =0

If z= x + yi and omega = ((1- zi))/(z-i), then |omega|=1 implies that in the complex plane

Prove that (-1/2,2,0) is thecircumcenter of the triangle with vertices (1,1,0),(1,2,1) and (-2,2,-1).

Find the approximations of the following root(4)(17)

If the vertices of a triangle are (1,4,2),(-2,1,2),(2,3,-4) then the angles are

If the extremities of a diagonal of square are (1,-2,3),(2,-3,5) then the length of its side is

Consider the planes 3x - 6y + 2z + 5=0 and 4x - 12 y + 3z = 3. The plne 67 x - 162 y + 47 z + 44 =0 bisects the angle between the given planes which

Evaluate the following limits in Exercises lim_(xto1)(ax^(2)+bx+c)/(cx^(2)+bx+a),a+b+cne0

If x+ y = 3e^2then d/(dx)(x^y)=0 for x =

There are four events E_(1),E_(2),E_(3),andE_(4) one of which must and onlyone can happen The odds are 2:5 in favour ofE_(1),3:4 in favour of E_(2) and 1:3 in favour of E_(3) . Find the odds against E_(4).

Find the 13^(th) term in the expansion of (9x-(1)/(3sqrtx))^(18) :xne0 ?

A,B and C are three mutually exclusiveevents associated with a random experiment . Find P(A) given that P(B)=(3)/(2)P(A)andP(C )=(1)/(2)P(B).

Express the following in the form a+bi, where a and b are rea numbers ((1-i)/(1+ i))^(2)