14949 + Interview Questions in Maths in Class 11 Page 188 InterviewSolution

9351.	Let A = {1, 2, 3,--------n} and B = {a, b, c], the number of functions from A to B that are onto is
Answer» `3^(N)-2^(n)` `3^(n)-2^(n)-1` `3(2^(n)-1)` `3^(n)-3(2^(n)-1)` ANSWER :D

Discussion

9352.	Polar form of sqrt(3) + i is
Answer» `-2(cos""(PI)/( 6)+isin""(pi)/(6))` `2(cos""(pi)/( 6)+isin""(pi)/(6))` `-2(cos""(2pi)/( 3)+isin""(pi)/(6))` `2(cos""(2pi)/( 3)+isin""(pi)/(6))` Solution :Let `sqrt(3)+ i=R(COSTHETA+ isintheta)` `therefore""rcostheta= sqrt(3)` `""rsintheta=1` Squaring and ADDING the above two equations, we get `r^(2)cos^(2)theta+ r^(2)sin ^(2)theta=(sqrt(3))^(2) +(1)^(2)` ` rArr" " r^(2)(cos^(2)theta+sin^(2)theta) =3+1=4` `rArr""r^(2) =4""rArrr=2` Put `r`= 2 in the above two equations, `{:(,"",costheta=(sqrt(3))/(2)rArr costheta=30^(@)),(,and, sintheta=(1)/(2)rArrsintheta=sin30^(@)or sin150^(@)):}}` `rArr""theta=30^(@)=(pi)/(6)` then ` " "sqrt(3)+ i=2(cos""(pi)/( 6)+isin""(pi)/(6))`

Discussion

9353.	Let A = {0, {0, 1}}. The cardinal number of P(A) is :(i) 8(ii) 2(iii) 4(iv) 16
Answer» 8 2 4 16 Answer :C

Discussion

9354.	If the hypotenuse of a right angled triangle is four times the lengthof the perpendicular drawn from the opposite vertex to it, then one of the acute angles is
Answer» `(pi)/(12) ` `(pi)/(6)` `( pi)/(6) ` ` (3pi)/(8)` ANSWER :A

Discussion

9355.	If cos theta=(cosalpha-cos beta)/(1-cosalpha cos beta), then one of the vlaues of tan((theta)/(2)) is
Answer» `COT""(BETA)/2TAN""(alpha)/2` `tanalphatan""(beta)/2` `TAN""beta/2cot""alpha/2` `tan^2""alpha/2tan""beta/2` Answer :A

Discussion

9356.	Which of the following are defined for all x ?
Answer» `SIN [x]+ cos [x]` ( `[x]` denotes greatest integer `le x` ) `SEC^(-1) (1 + sin^(2)x)` `tan(LOG x)` `sqrt(9/8 + cos x + cos 2 x)` Answer :A::B::D

Discussion

9357.	The sum of first three terms of a G.P. is and their product is 1. Find the common ratio and the terms.
Answer» ANSWER :`r=5/2 " or " 2/5; ` TERMS are `2/5,1,5/2` or `5/2 ,1,2/5`

Discussion

9358.	cos100^@.cos40^@+sin100^@.sin40^@=……..
Answer» ANSWER :`(1)/(2)`

Discussion

9359.	Let f(x) = ( x-4) (x -5) ( x-6 ) ( x- 7 ) then
Answer» f (x) = 0 has four roots three roots of f(x) = 0lie in (4,5) U ( 5,6) U ( 6,7) the EQUATION f(x) = 0 has only one root. three roots of f(x) = 0 LIE in (3,4) U ( 4,5) U ( 5,6) ANSWER :B

Discussion

9360.	LetA = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why? {3, 4} ∈ A
Answer» ANSWER :1

Discussion

9361.	Find the slope and inclination of the line through each pair of the following points: (-1, -8) and (5, 7)
Answer» ANSWER : `5/(2), 68^(@)12'`

Discussion

9362.	How many 4 - digit numbers are there with no digit repeated ?
Answer» ANSWER :4536

Discussion

9363.	Find the sum of an infinite number of terms of a G.P. where a is the first term and r(lt1) is the common ratio.
Answer» SOLUTION :

Discussion

9364.	A_1,A_2….A_n " are points on the line y=x lying in th positive quadrant such that " OA_n =Noa_(n-1)O " being the origin . If " OA_1=1 " and the coordinates of "A_n are (2520sqrt2,2520sqrt2), then n =
Answer» 5 6 7 8 Answer :C

Discussion

9365.	If the straight lines x=1 +s,y=-3-lambdas,z=1+lambdas and x=(t)/(2),y=t ,z=2-t with parameters s and t respectively are co planar then lambda =
Answer» `-2` `-1` `-1/2` `0` ANSWER :A

Discussion

9366.	If (1+x)/(1 -x)=cos2theta +isin2theta, prove that that x=itantheta.
Answer» ANSWER :N/a

Discussion

9367.	Insert the n A.M's between 7 and 71 in such a way that the 5^(th) A.M. is 27. Find the numbers of A.M's.
Answer» ANSWER :n=15

Discussion

9368.	Find the sum to n terms of the series(1)/(1xx2) +(1)/(2xx3)+(1)/(3xx4) + . . . . . .
Answer» ANSWER :`N/(n+1)`

Discussion

9369.	State whether each of the following statements are true or false. If the statement is false, rewrite the given statement correctly. (i) If P= {m, n} and Q = {n, m}, then P xx Q= {(m, n),(n, m)}. (ii) If A and B are non-empty sets, then A xx B is a non-empty set of ordered pairs (x, y) such that x in A and y in B. (iii) If A={1,2}, B={3,4} then A xx (B cap phi)=phi
Answer» ANSWER :1

Discussion

9370.	State whether each of the following statements are true or false. If the statement is false, rewrite the given statement correctly If A and B are non-empty sets, then A xx B is a non-empty set of ordered pairs (x,y) such that x in A and y in B
Answer» ANSWER :1

Discussion

9371.	cos^(-1)(8/17)-cos^(-1)(5/13)=
Answer» `"COS"^(-1)140/221` `"Cos"^(-1)220/221` `"Cos"^(-1)7/11` `"Cos"^(-1)221/220` ANSWER :B

Discussion

9372.	(i) Let y=((2+5x)^(2))/(x^(3) -1)then find dy/dx
Answer» Answer :`= (-(2+5x) (5x^(3) +6x^(2) +10))/( (x^3 - 1)^2)`

Discussion

9373.	If A= {1, 3, 5, {2, 4}}" and "B= {2, 4} then,
Answer» `4 in A` `{4} SUB A` `B sub A` NONE of these Answer :D

Discussion

9374.	The two planes represented by 12 x ^(2) - 2y ^(2) - 6z^(2) - 7 yz + 6zx - 2 xy =0 are
Answer» `2x + y + 2Z = 0,6 x-2y + 3Z =0` `2x -y + 2z =0,6 x + 2y - 3z =0` `2x - y + 2z + 4=0,6x + 2y - 3z =0` `2x -y + 2z = 0,6 x + 2y - 3z + 1=0` ANSWER :B

Discussion

9375.	If3 tan 2 x - 4 tan 3 x = tan ^(2) 3 x tan 2 x then x =
Answer» `n pi , n in Z` `(2 n + 1) (pi)/(2), n in Z` `n pi PM tan ^(-1) sqrt((3)/(5)), n in Z` `2 n pi pm sin^(-1) ((1)/(2)), n in Z` Answer :A::C

Discussion

9376.	Let OA, OB, OC be the co-terminal edges of a rectangular parallelopiped of volume V and let P be the vertex opposite to 0. Then
Answer» 2V 12V `3sqrt3V` 0 Answer :A

Discussion

9377.	When A= phi, then number of elements in P(A) is………..
Answer» ANSWER :`1`

Discussion

9378.	Statement-Iunderset(x to 0)(Lt)(sqrt((1 -cos 2x)/(2)))/(x)does not exist . Statement-II :f(x) = \|x\|is continuous on R Which of the above statement is correct
Answer» only I only II Both I and II NEITHER I or II ANSWER :C

Discussion

9379.	If the points (1,1,-3) and (1,0, -3) lie on opposite sides of the plane x + y + 3z + d=0then
Answer» `d LT 7` ` d gt 8` `7 lt d lt 8` ` d lt 7 or d gt 8` ANSWER :C

Discussion

9380.	Cartesian equation of the line passing through the points bar(a)=2bar(i)+bar(j)-2bar(k) and bar(b)=2bar(i)+2bar(j)-bar(k) is
Answer» `x-2=(y-1)/1=(z+2)/1` `x+2=y+1=z+2` `y-1=z+2, x-2=0` `(y-1)/2=(z-2)/1, x-2=0` ANSWER :C

Discussion

9381.	If (1,-2,-2) and (0,2,1) are direction ratios of two lines, then direction cosines of a line perpendicular to both the lines are
Answer» `((1)/(3),-(1)/(3),(2)/(3))` `c((2)/(3),-(1)/(3),(2)/(3))` `(-(2)/(3),(1)/(3),(2)/(3))` `((2)/(sqrt(14)),-(1)/(sqrt(14)),(3)/(sqrt(14)))` Answer :B

Discussion

9382.	Construct truth tables for each of the following : [(~p)^^ q]implies(p vv q)
Answer» ANSWER :`(##SCH_OPM_ISC_MAT_XI_C27_E06_019_A01##)` [RECALL that p => q is false only when p is true and q is false ]

Discussion

9383.	The value of "tan"^(-1)4/7+"tan"^(-1)4/19+"tan"^(-1)4/39+"tan"^(-1)4/67……..oo equals
Answer» `(pi)/2-tan^(-1)""1/2` `tan^(-1)1+COT^(-1)3` `cot^(-1)1+cot^(-1)""1/2+cot^(-1)""1/3` `cot^(-1)1+tan^(-1)3` ANSWER :B

Discussion

9384.	Consider a pyramid OPQRS located in the first octan (x ge 0, y ge 0z ge 0) with O as origin, and OP and OR along the x-axis and the y-axis, respectively. The base OPQR of the pyramid is a square with OP =3. The point S is directly above the midpoint T of diagonal OQ such that TS = 3. Then
Answer» the ACUTE angle between OQ and OS is `pi//3` the EQUATION of the plane containing the triangle `OQS is x-y =0` the length of the perpendicular from P to the plane containing the triangle OQS is `(3)/(SQRT3)` the perpendicular distance from O to the straight line containing RS is `sqrt ((15)/(2))` Answer :B::C::D

Discussion

9385.	Solve (\|x_2\|-1)/(\|x-2\|-2)le0
Answer» ANSWER :HENCE the REQUIRED SOLUTION is `(0,1)UU (3,4)`

Discussion

9386.	If 2sin^(2)theta=3costheta,"where "0lethetale2pi, then find the value of theta.
Answer» ANSWER :`(5PI)/(3)`

Discussion

9387.	L_1 and L_2" are two intersecting lines. If the image of " L_1 " w.r.t. " L_2 " and that of " L_2 " w.r.t. " L_1 " concide, then the angle between " L_1 and L_2is
Answer» `20^@` `15^@` `45^@` `60^@` ANSWER :B

Discussion

9388.	Which of the following sentences are statements? Give reasons for your answer: The product of (-1) and 8 is 8.
Answer» ANSWER :This sentence is FALSE as the product is `(-8)`. THEREFORE, it is a STATEMENT.

Discussion

9389.	The sum of first three terms of a G.P is 7 and the sum of their squares is 21. Determine the first five terms of the G.P.
Answer» ANSWER :4,2,1,`1/2,1/4` or 1,2,4,8,16

Discussion

9390.	If (2+sqrt(3))costheta=1-sintheta, then one general value is:
Answer» `2npi+pi/2` `npi+pi/2` `npi+pi/3` NONE of these Solution :N//A

Discussion

9391.	The point to which (0,0) is to be shifted to eliminate x and y terms of the equation 4x^(2) + 9y^(2) - 8x + 36y + 4 = 0 is
Answer» (1, 3) (-4, 3) (-1, 2) (1, 2)

Discussion

9392.	The vector equation of the plane passing through the origin and the point 4bar(j) and 2bar(j)+bar(k) is
Answer» `BAR(r)=s(4bar(j))+t(2BAR(j)+bar(K))` `bar(r)=s(-2bar(j)-bar(k))+t(4bar(j))` `bar(r)=s(4bar(i))+t(2bar(j)+bar(k))` `bar(r)=s(2bar(j))+t(bar(t)+bar(k))` ANSWER :A

Discussion

9393.	Resolve the following rational expression into partial fractions. (3x + 1)/((x - 2)(x + 1))
Answer» ANSWER :`(7)/(3(x - 2)) + (2)/(3(x + 1))`

Discussion

9394.	The range of the function f(x)=(e^(x)-e^(\|x\|))/(e^(x)+e^(\|x\|)) is
Answer» `(-OO,oo)` `[0,1)` `(-1, 0]` `(-1,1)` ANSWER :C

Discussion

9395.	Solve for x , sin x = ( -sqrt3)/(2), (0 lt x lt 2pi).
Answer» ANSWER :`300^(@)`

Discussion

9396.	If a in {-1, 2, 3, 4, 5} and b in {0, 3, 6}. Write the set of all ordered pairs (a,b) such that a + b= 5. How many subset has it?
Answer» ANSWER :8

Discussion

9397.	A student was asked to prove a statement by induction. He proved (i) P(5) is true and (ii) truth of P(n) rArr truth of P(n+1), n in N. On the basis of this, he could conclude that P(n) is true
Answer» for no `N in N` for all `n ge 5, n in N` for all `n in N` for all `n ge 1, n in N` Answer :B

Discussion

9398.	The sum of (2n+1) terms of the series a-(a+d)+a(a+ad)-(a+3d)+… is :
Answer» a+3nd 3a+nd 2a+3nd a+nd Solution :N/a

Discussion

9399.	Let f(x)= int e^(x)(x-1)(x-2)dx. Then f decreases in the interveal
Answer» `(-OO,-2)` `(-2,-1)` `(1,2)` `(2,oo)` ANSWER :C

Discussion

9400.	Using simple average of price relatives method, the price index for 2001, taking 1991 as base year, was found to be 127. If sum p_0 = 263, find x and y from the following data:
Answer» ANSWER :`y=27`

Discussion

Explore topic-wise InterviewSolutions in .

Let A = {1, 2, 3,--------n} and B = {a, b, c], the number of functions from A to B that are onto is

Polar form of sqrt(3) + i is

Let A = {0, {0, 1}}. The cardinal number of P(A) is :(i) 8(ii) 2(iii) 4(iv) 16

If the hypotenuse of a right angled triangle is four times the lengthof the perpendicular drawn from the opposite vertex to it, then one of the acute angles is

If cos theta=(cosalpha-cos beta)/(1-cosalpha cos beta), then one of the vlaues of tan((theta)/(2)) is

Which of the following are defined for all x ?

The sum of first three terms of a G.P. is and their product is 1. Find the common ratio and the terms.

cos100^@.cos40^@+sin100^@.sin40^@=……..

Let f(x) = ( x-4) (x -5) ( x-6 ) ( x- 7 ) then

LetA = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why? {3, 4} ∈ A

Find the slope and inclination of the line through each pair of the following points: (-1, -8) and (5, 7)

How many 4 - digit numbers are there with no digit repeated ?

Find the sum of an infinite number of terms of a G.P. where a is the first term and r(lt1) is the common ratio.

A_1,A_2….A_n " are points on the line y=x lying in th positive quadrant such that " OA_n =Noa_(n-1)O " being the origin . If " OA_1=1 " and the coordinates of "A_n are (2520sqrt2,2520sqrt2), then n =

If the straight lines x=1 +s,y=-3-lambdas,z=1+lambdas and x=(t)/(2),y=t ,z=2-t with parameters s and t respectively are co planar then lambda =

If (1+x)/(1 -x)=cos2theta +isin2theta, prove that that x=itantheta.

Insert the n A.M's between 7 and 71 in such a way that the 5^(th) A.M. is 27. Find the numbers of A.M's.

Find the sum to n terms of the series(1)/(1xx2) +(1)/(2xx3)+(1)/(3xx4) + . . . . . .

State whether each of the following statements are true or false. If the statement is false, rewrite the given statement correctly If A and B are non-empty sets, then A xx B is a non-empty set of ordered pairs (x,y) such that x in A and y in B

cos^(-1)(8/17)-cos^(-1)(5/13)=

(i) Let y=((2+5x)^(2))/(x^(3) -1)then find dy/dx

If A= {1, 3, 5, {2, 4}}" and "B= {2, 4} then,

The two planes represented by 12 x ^(2) - 2y ^(2) - 6z^(2) - 7 yz + 6zx - 2 xy =0 are

If3 tan 2 x - 4 tan 3 x = tan ^(2) 3 x tan 2 x then x =

Let OA, OB, OC be the co-terminal edges of a rectangular parallelopiped of volume V and let P be the vertex opposite to 0. Then

When A= phi, then number of elements in P(A) is………..

Statement-Iunderset(x to 0)(Lt)(sqrt((1 -cos 2x)/(2)))/(x)does not exist . Statement-II :f(x) = |x|is continuous on R Which of the above statement is correct

If the points (1,1,-3) and (1,0, -3) lie on opposite sides of the plane x + y + 3z + d=0then

Cartesian equation of the line passing through the points bar(a)=2bar(i)+bar(j)-2bar(k) and bar(b)=2bar(i)+2bar(j)-bar(k) is

If (1,-2,-2) and (0,2,1) are direction ratios of two lines, then direction cosines of a line perpendicular to both the lines are

Construct truth tables for each of the following : [(~p)^^ q]implies(p vv q)

The value of "tan"^(-1)4/7+"tan"^(-1)4/19+"tan"^(-1)4/39+"tan"^(-1)4/67……..oo equals

Consider a pyramid OPQRS located in the first octan (x ge 0, y ge 0z ge 0) with O as origin, and OP and OR along the x-axis and the y-axis, respectively. The base OPQR of the pyramid is a square with OP =3. The point S is directly above the midpoint T of diagonal OQ such that TS = 3. Then

Solve (|x_2|-1)/(|x-2|-2)le0

If 2sin^(2)theta=3costheta,"where "0lethetale2pi, then find the value of theta.

L_1 and L_2" are two intersecting lines. If the image of " L_1 " w.r.t. " L_2 " and that of " L_2 " w.r.t. " L_1 " concide, then the angle between " L_1 and L_2is

Which of the following sentences are statements? Give reasons for your answer: The product of (-1) and 8 is 8.

The sum of first three terms of a G.P is 7 and the sum of their squares is 21. Determine the first five terms of the G.P.

If (2+sqrt(3))costheta=1-sintheta, then one general value is:

The point to which (0,0) is to be shifted to eliminate x and y terms of the equation 4x^(2) + 9y^(2) - 8x + 36y + 4 = 0 is

The vector equation of the plane passing through the origin and the point 4bar(j) and 2bar(j)+bar(k) is

Resolve the following rational expression into partial fractions. (3x + 1)/((x - 2)(x + 1))

The range of the function f(x)=(e^(x)-e^(|x|))/(e^(x)+e^(|x|)) is

Solve for x , sin x = ( -sqrt3)/(2), (0 lt x lt 2pi).

If a in {-1, 2, 3, 4, 5} and b in {0, 3, 6}. Write the set of all ordered pairs (a,b) such that a + b= 5. How many subset has it?

A student was asked to prove a statement by induction. He proved (i) P(5) is true and (ii) truth of P(n) rArr truth of P(n+1), n in N. On the basis of this, he could conclude that P(n) is true

The sum of (2n+1) terms of the series a-(a+d)+a(a+ad)-(a+3d)+… is :

Let f(x)= int e^(x)(x-1)(x-2)dx. Then f decreases in the interveal

Using simple average of price relatives method, the price index for 2001, taking 1991 as base year, was found to be 127. If sum p_0 = 263, find x and y from the following data: