14949 + Interview Questions in Maths in Class 11 Page 97 InterviewSolution

4801.	Find the ratios in which the join of (12,-4,8) and (27,-9,18) is intersected by the sphere x^(2)+y^(2)+z^(2)=504.
Answer» ANSWER :`2:3,2:3`

Discussion

4802.	Use p : I like this school , q : I like Mr. Sexena. Express each of the following statements in words . (~p)^^(~q)
Answer» ANSWER :I do not LIKE this SCHOOL and I do not like MR. SAXENA .

Discussion

4803.	Use p : I like this school , q : I like Mr. Sexena. Express each of the following statements in words . (~p)^^q
Answer» ANSWER :I do not LIKE this SCHOOL and I like MR. SAXENA.

Discussion

4804.	Differentiate the following functions: (ax)^(m) + b^(m)
Answer» ANSWER :`"ma"^(m)"X"^(m-1)`

Discussion

4805.	A code word is to consist of two distinct English alphabets followed by two distinct numbers from 1 to 9. For example, PA 31 is one such code word.How many different words are possible ?How many end in an odd number ?
Answer» ANSWER :(i)46800(II)26000

Discussion

4806.	Find perpendicular distance from the origin to the line joining the points ( cos theta , sin theta ) and ( cos phi, sin phi).
Answer» <P> ANSWER :`p= \| ( sin ""(PHI- theta ))/( 2 sin"" ( (phi - theta)/(2) ))\|`

Discussion

4807.	The maximum value of f(x)=(x-2)^(2)(x-3)is
Answer» 2 4 `-4` 0 Answer :D

Discussion

4808.	If 0 lt theta lt (pi)/2 and 5 tan theta = 4 then (5 sin theta - 3 cos theta) / (sintheta +2 cos theta ) = 5/14
Answer» ANSWER :TRUE STATEMENT

Discussion

4809.	If point P divided line segment joining points A(x_1,y_1,z_1) and B(x_2,y_2,z_2) in ratio k : 1 then co - ordinates on P.
Answer» ANSWER :FALSE STATEMENT

Discussion

4810.	If G =(7, 8) and H=(5,4,2), find G xx H and H xx G.
Answer» ANSWER :`G XX H={(7,5),(7,4),(7,2),(8,5),(8,4),(8,2)}` `H xx G={(5,7),(5,8),(4,7),(4,8),(2,7),(2,8)}`

Discussion

4811.	No. of solutions of 16^(sin^(2)x)+16^(cos^(2)x)=10,0lexle2pi is
Answer» 8 6 4 2 Answer :A

Discussion

4812.	Find the domains of the following functions f(x) = x^(2) + x+1
Answer» ANSWER :R

Discussion

4813.	Evaluate : (2-omega^(100))(2-omega^(101))(2-omega^(10))(2-omega^(11))
Answer» ANSWER :49

Discussion

4814.	Write out the expansions of the following: (3x-y)^(4)
Answer» Answer :`81x^(4) - 108x^(3) y + 53x^(2) y- 12 XY^(3) + y^(4)`

Discussion

4815.	For real numbers x and y define x\ R\ y if x - y + sqrt(2) is an irrational number. Then the relation R is
Answer» REFLEXIVE SYMMETRIC TRANSITIVE NONE of these.

Discussion

4816.	If 2x-3y-5=0 is the perpendicular bisector of the line segment joining (3,-4) and (alpha, beta) then find alpha+beta.
Answer» ANSWER :1

Discussion

4817.	If 2R+r=r_(1) then
Answer» `A=90^(@)` `B=90^(@)` `C=90^(@)` `A=60^(@)` ANSWER :A

Discussion

4818.	Name the octants in which the following points lie : (1, 2, 3), (4, -2, 3), (4, -2, -5), (4, 2, -5), (-4, 2, -5), (-4, 2, 5), (-3, -1, 6), (2, -4, -7)
Answer» ANSWER :I,IV,VIII,V,VI,II,III,VII

Discussion

4819.	if 6,10,4 are the sides of a triangle then its obtus angle is
Answer» `110^(@)` `120^(@)` `135^(@)` `115^(@)` Answer :B

Discussion

4820.	Five students secured marks as, 8, 10, 15, 30, 22. Find the standard deviation.
Answer» ANSWER :5.44 MARKS

Discussion

4821.	Diagonals of a parallelogram PQRS must be a
Answer» RECTANGLE SQUARE cyclic QUADRILATERAL rhombus ANSWER :D

Discussion

4822.	A coin is tossed and a die is rolled. The probability that the coin shows head and the die shows 3 is
Answer» `(1)/(6)` `(1)/(12)` `(1)/(9)` `(11)/(12)` Answer :B

Discussion

4823.	If (bar(a), bar(b))=60^(@)" then "(-bar(a), -bar(b))=
Answer» `60^(@)` `30^(@)` `45^(@)` `90^(@)` ANSWER :A

Discussion

4824.	Consider the function f(x) satisfying the identityf(x) + f((x-1)/( x))= 1+ x AA x in R - {0,1}, and g(x)=2f ( x)- x+1 The range of y = g(x) is
Answer» `(-OO, 5]` `[1, oo)` `(-oo, 1] uu [5, oo)` `[5]` ANSWER :C

Discussion

4825.	Evaluate: (i) "sin""(3pi)/(8) (ii) "sin""(5pi)/(24) (iii) "tan""(pi)/(8).
Answer» ANSWER :(i) `(sqrt(2+sqrt2))/(2)` (II) `(sqrt(6+3sqrt2)-sqrt(2-sqrt2))/(4)` (III) `sqrt2-1`

Discussion

4826.	Iftan^(2) (pi ( x + y) ) + cot^(2) ( pi( x + y)) = 1 + sqrt((2 x )/( 1 + x^(2))where x, y are real, then theleast positivevalueof y is
Answer» 1 `(1)/(4)` `(1)/(4)` `(3)/(5)` ANSWER :A

Discussion

4827.	A car starts from a point P at time t = 0 seconds and stops at point Q. The distance x, in metres, covered by it, in t seconds is given by x = t^(2)(2-(t)/(3)) Find the time taken by it to reach Q and also find distance between P and Q.
Answer» Answer :`x]_(t=4) = 4^(2)(2-(4)/(3)) = 16((2)/(3)) = (32)/(3)m`

Discussion

4828.	If S_1, S_2, S_3are the sum of first n natural numbers, their squares and their cubes, respectively , show that 9 S_(2)^(2) = S_(3) (1+ 8S_1)
Answer» ANSWER :`9S_(2)^(2)`

Discussion

4829.	Probabilities of A, B and C becoming managers are 4/9, 2/9 and 1/3 respectively. Probabilities that the Bonus Scheme will be introduced if A, B and C become managers are 3/10, 1/2 and 4/5 respectively. If the bonus scheme has been introduced, then probability that the manager appointed was A is
Answer» `4/23` `5/23` `6/23` `7/23` ANSWER :C

Discussion

4830.	If 8 sin x=(sqrt(3))/(cosx)+1/(sinx) then x=
Answer» <P>`n p +(pi)/6, n in Z` `npi+(pi)/3, NIN Z` `(npi)/2-(pi)/12, n in Z` `(npi)/2-(pi)/6, n in Z` ANSWER :A::B

Discussion

4831.	If vec(a)= (1)/(7) (2vec(i) + 3vec(j) -6vec(k)), vec(b)= (1)/(7) (3vec(i) - 6vec(j) + 2vec(k)) and vec(c )= (1)/(7) (6vec(i) + 2vec(j)- 3vec(k)) are such that vec(a) xx vec(b)= lamda vec(c ) then find lamda.
Answer» ANSWER :1

Discussion

4832.	If A and B be the points (3,4,5) and (-1,3,-7) respectively, find the locus of P such that PA ^(2) + PB ^(2) = k ^(2).
Answer» ANSWER :`K ^(2) =0`

Discussion

4833.	If cos(theta+phi)=mcos(theta-phi), then prove that tantheta=(1-m)/(1+m)cotphi.
Answer» ANSWER :`THEREFORE TANTHETA=((1-m)/(1+m))cotphi`

Discussion

4834.	If sin theta = cos phi , then the possible values of (1)/(pi) (theta pm phi - (pi)/(2)) are
Answer» 0 1 2 3 Answer :A::C

Discussion

4835.	Solve the following equations : x^(2)+2x+2=0
Answer» ANSWER :`-1+-i`

Discussion

4836.	Find the derivative of the w.r.t.x ax ^(2n) log x + b x ^(n) e ^(-x)
Answer» Answer :`AX ^(2N-1) + 2a n ^(2n -1) `

Discussion

4837.	If alpha,beta are acute angles, sin alpha = (4)/(5), tan beta = (5)/(12) then the descending order of A= sin (alpha+beta), B cos(alpha+beta),C= tan(alpha+beta) is
Answer» A,B,C B,C,A B,A,C C,A,B Answer :D

Discussion

4838.	Solve sin 5 theta = cos 2 theta,0 < theta < pi.
Answer» ANSWER :`{((2N+(-1)^(n))pi//2)/(5+(-1)^(n)2):n in Z}`

Discussion

4839.	If sinx+cosx=sqrt(y+1/y)for x in [0,pi] then
Answer» `x=pi//4` `y=0` `y=1` `x=3pi//4` ANSWER :A::C

Discussion

4840.	Find a negative value of m if the Co-effcient ofx^(2) in the expanion of(1 + x)^(m) , \|x\| lt 1is 6 .
Answer» ANSWER :` THEREFORE ` NEGATIVE VALUE of m is - 3

Discussion

4841.	If 0 le x le (pi)/(3) then range of f(x) = sec ((pi)/(6) - x) + sec((pi)/(6)+x) is
Answer» `((4)/(sqrt(3)),OO)` `[(4)/(sqrt(3)),oo)` `(0, (4)/(sqrt(3))]` `(0, (4)/(sqrt(3)))` Answer :B

Discussion

4842.	If alpha + beta- gamma= pi, prove thatsin^(2)alpha + sin^(2)beta - sin^(2)gamma = 2sin alpha sin beta cos gamma.
Answer» ` 2 sin alpha sin BETA cos GAMMA` ` 2 cos alpha cos beta cos gamma ` `2 sin alpha sin beta sin gamma` NONE of these ANSWER :A

Discussion

4843.	Vertex A of the triangle ABC is at origin. The equation of median through B and C are 15x-4y-240=0 and 15x-52y+240=0 respectively
Answer» ANSWER :A-q; B-p; C-s; D-t

Discussion

4844.	Assertion (A) : The slopes of one line represented by 2x^(2)–5xy+2y^(2) = 0 is 4 times the slope of the second line. Reason (R): If the slopes of lines represented by ax^(2)+2hxy+by^(2)=0 are in m:n then ((m+n)^(2))/(mn)=(4h^(2))/(ab)
Answer» A is TRUE, R is true and R `RARR A` A is true, R is true and `R CANCEL rArr A` A is true, R is false A is false, R is true ANSWER :A

Discussion

4845.	If A is non Singular and (A-2I)(A-4I)=0 then 1/6A+4/3A^(-1)=
Answer» I 0 2I 6I Answer :A

Discussion

4846.	There are 6 different noavls and 3 different dictionary we have to select 4 nocvals and I dictionary from them and arrange them on a shelf such that the doctionary remain in the maddle always, How many way this arrangement will be done ?
Answer» ANSWER :A

Discussion

4847.	If n in N ,and the period of (cos nx)/(sin(x//n)) is 4pi , then n=
Answer» 1 2 3 4 Answer :2

Discussion

4848.	If the three planes x + y + z, x + 2y + 3z =14 and 2x + 5y + lamda z = mu,- oo lt lamda lt 00, mu in R - [ 36]from a triangular prism then the value of lamda equals
Answer» ANSWER :8

Discussion

4849.	The minimum value of 3cosx+4sinx+8 is
Answer» 5 9 7 3 Answer :D

Discussion

4850.	Using binomial theorem, indicate which of the following two number is larger : (1.01)^(1000000), 10000.
Answer» ANSWER :`(1.01)^(1000000)GT 10000 (i.e.)(1.01)^(1000000)`is LARGER.

Discussion

Explore topic-wise InterviewSolutions in .

Find the ratios in which the join of (12,-4,8) and (27,-9,18) is intersected by the sphere x^(2)+y^(2)+z^(2)=504.

Use p : I like this school , q : I like Mr. Sexena. Express each of the following statements in words . (~p)^^(~q)

Use p : I like this school , q : I like Mr. Sexena. Express each of the following statements in words . (~p)^^q

Differentiate the following functions: (ax)^(m) + b^(m)

A code word is to consist of two distinct English alphabets followed by two distinct numbers from 1 to 9. For example, PA 31 is one such code word.How many different words are possible ?How many end in an odd number ?

Find perpendicular distance from the origin to the line joining the points ( cos theta , sin theta ) and ( cos phi, sin phi).

The maximum value of f(x)=(x-2)^(2)(x-3)is

If 0 lt theta lt (pi)/2 and 5 tan theta = 4 then (5 sin theta - 3 cos theta) / (sintheta +2 cos theta ) = 5/14

If point P divided line segment joining points A(x_1,y_1,z_1) and B(x_2,y_2,z_2) in ratio k : 1 then co - ordinates on P.

If G =(7, 8) and H=(5,4,2), find G xx H and H xx G.

No. of solutions of 16^(sin^(2)x)+16^(cos^(2)x)=10,0lexle2pi is

Find the domains of the following functions f(x) = x^(2) + x+1

Evaluate : (2-omega^(100))(2-omega^(101))(2-omega^(10))(2-omega^(11))

Write out the expansions of the following: (3x-y)^(4)

For real numbers x and y define x\ R\ y if x - y + sqrt(2) is an irrational number. Then the relation R is

If 2x-3y-5=0 is the perpendicular bisector of the line segment joining (3,-4) and (alpha, beta) then find alpha+beta.

If 2R+r=r_(1) then

Name the octants in which the following points lie : (1, 2, 3), (4, -2, 3), (4, -2, -5), (4, 2, -5), (-4, 2, -5), (-4, 2, 5), (-3, -1, 6), (2, -4, -7)

if 6,10,4 are the sides of a triangle then its obtus angle is

Five students secured marks as, 8, 10, 15, 30, 22. Find the standard deviation.

Diagonals of a parallelogram PQRS must be a

A coin is tossed and a die is rolled. The probability that the coin shows head and the die shows 3 is

If (bar(a), bar(b))=60^(@)" then "(-bar(a), -bar(b))=

Consider the function f(x) satisfying the identityf(x) + f((x-1)/( x))= 1+ x AA x in R - {0,1}, and g(x)=2f ( x)- x+1 The range of y = g(x) is

Evaluate: (i) "sin""(3pi)/(8) (ii) "sin""(5pi)/(24) (iii) "tan""(pi)/(8).

Iftan^(2) (pi ( x + y) ) + cot^(2) ( pi( x + y)) = 1 + sqrt((2 x )/( 1 + x^(2))where x, y are real, then theleast positivevalueof y is

A car starts from a point P at time t = 0 seconds and stops at point Q. The distance x, in metres, covered by it, in t seconds is given by x = t^(2)(2-(t)/(3)) Find the time taken by it to reach Q and also find distance between P and Q.

If S_1, S_2, S_3are the sum of first n natural numbers, their squares and their cubes, respectively , show that 9 S_(2)^(2) = S_(3) (1+ 8S_1)

Probabilities of A, B and C becoming managers are 4/9, 2/9 and 1/3 respectively. Probabilities that the Bonus Scheme will be introduced if A, B and C become managers are 3/10, 1/2 and 4/5 respectively. If the bonus scheme has been introduced, then probability that the manager appointed was A is

If 8 sin x=(sqrt(3))/(cosx)+1/(sinx) then x=

If vec(a)= (1)/(7) (2vec(i) + 3vec(j) -6vec(k)), vec(b)= (1)/(7) (3vec(i) - 6vec(j) + 2vec(k)) and vec(c )= (1)/(7) (6vec(i) + 2vec(j)- 3vec(k)) are such that vec(a) xx vec(b)= lamda vec(c ) then find lamda.

If A and B be the points (3,4,5) and (-1,3,-7) respectively, find the locus of P such that PA ^(2) + PB ^(2) = k ^(2).

If cos(theta+phi)=mcos(theta-phi), then prove that tantheta=(1-m)/(1+m)cotphi.

If sin theta = cos phi , then the possible values of (1)/(pi) (theta pm phi - (pi)/(2)) are

Solve the following equations : x^(2)+2x+2=0

Find the derivative of the w.r.t.x ax ^(2n) log x + b x ^(n) e ^(-x)

If alpha,beta are acute angles, sin alpha = (4)/(5), tan beta = (5)/(12) then the descending order of A= sin (alpha+beta), B cos(alpha+beta),C= tan(alpha+beta) is

Solve sin 5 theta = cos 2 theta,0 < theta < pi.

If sinx+cosx=sqrt(y+1/y)for x in [0,pi] then

Find a negative value of m if the Co-effcient ofx^(2) in the expanion of(1 + x)^(m) , |x| lt 1is 6 .

If 0 le x le (pi)/(3) then range of f(x) = sec ((pi)/(6) - x) + sec((pi)/(6)+x) is

If alpha + beta- gamma= pi, prove thatsin^(2)alpha + sin^(2)beta - sin^(2)gamma = 2sin alpha sin beta cos gamma.

Vertex A of the triangle ABC is at origin. The equation of median through B and C are 15x-4y-240=0 and 15x-52y+240=0 respectively

Assertion (A) : The slopes of one line represented by 2x^(2)–5xy+2y^(2) = 0 is 4 times the slope of the second line. Reason (R): If the slopes of lines represented by ax^(2)+2hxy+by^(2)=0 are in m:n then ((m+n)^(2))/(mn)=(4h^(2))/(ab)

If A is non Singular and (A-2I)(A-4I)=0 then 1/6A+4/3A^(-1)=

There are 6 different noavls and 3 different dictionary we have to select 4 nocvals and I dictionary from them and arrange them on a shelf such that the doctionary remain in the maddle always, How many way this arrangement will be done ?

If n in N ,and the period of (cos nx)/(sin(x//n)) is 4pi , then n=

If the three planes x + y + z, x + 2y + 3z =14 and 2x + 5y + lamda z = mu,- oo lt lamda lt 00, mu in R - [ 36]from a triangular prism then the value of lamda equals

The minimum value of 3cosx+4sinx+8 is

Using binomial theorem, indicate which of the following two number is larger : (1.01)^(1000000), 10000.