14949 + Interview Questions in Maths in Class 11 Page 35 InterviewSolution

1701.	If z_(1)=2 + 7i and z_(2)=1- 5i, then verify that \|z_(1)z_(2)\|= \|z_(1)\|\|z_(2)\|
Answer» ANSWER :`sqrt1378`

Discussion

1702.	Eight chairs are numbered 1 to 8. Two women and 3 man wish to occupy one chair each. First the women choose the chair each. First the women choose the chairs from amongst the chairs 1 to 4 and then men select from the remaining chairs. Find the total number of possible arrangments.
Answer» ANSWER :1440

Discussion

1703.	Two points A and B with co-ordinates (5, 3), (3, -2) are given. A point P moves so that the area of DeltaPAB is constant and equal to 9 square units. Find the equation to the locus of the point P.
Answer» ANSWER : `5x-2y-37=0,5x-2y-1=0`

Discussion

1704.	Consider the expansion of ((4x)/5-5/(4x))^8 Find the fourth term from the end in the expansion.
Answer» SOLUTION :`-175/(2x^2`]]

Discussion

1705.	If A, B are symmetric matrices of the same order then show that AB-BA is skew symmetric matrix.
Answer» SYMMETRIC matrix Skew symmetric matrix Diagonal matrix identity matrix Answer :B

Discussion

1706.	Compute the following limits. Lt_(xto2)(7x)/(6x+2)
Answer» ANSWER :1

Discussion

1707.	Find the slope of the tangent line to the graph f(x) =x^(2)-x+1 at (1,1)
Answer» ANSWER :SLOPE of TANGENT LINE =1.

Discussion

1708.	If f(x)=sqrtx,x=4,deltax=0.08 then df=
Answer» 0.02 0.0201 0.2 0.021 Answer :A

Discussion

1709.	Let U = {1,2,3,4,5,6,7}, A = {1,5,6} and B = {1,2,6,7}FindA cup B
Answer» SOLUTION :{1,2,5,6,7}

Discussion

1710.	Complete solution set of [cot^(-1)x]+2[tan^(-1)x]=0, where [.] denotes the greatest integer function, is equal to
Answer» (0,cot1) (0,TAN1) `(tan 1, OO)` `(cot1,tan1)` Answer :D

Discussion

1711.	a( r r _1 +r_2r_3)=
Answer» `( CA - r_3r_1) /( r_2)` ` ( r_3r- r_1r_2)/( AB ) ` ` ( r_3^(2))/( 4R-r_1-r_2)` ABC ANSWER :D

Discussion

1712.	Find the number of arrangemements of the letters of the word INDEPEDENCE. In how many of these arrangments , (i) DO the words start with P. (ii) DO all the vowels always occur together . (iii) Do the vowels never occur togather (Iv) do the words begin with I and end in P?
Answer» ANSWER :(i) 138600, (II) 16800, (III) 1646400, (IV) 12600

Discussion

1713.	Simplify : i^(-6)
Answer» ANSWER :`-1`

Discussion

1714.	3 - Circles with radii a, b, c touch one another externally tangents at contact points meet in a point P then the distance of P to the contact point of any 2-circles is
Answer» `(ABC)/(a + B + C)` `SQRT((abc)/(a+b+c))` `sqrt((a+b+c)/(abc))` `(a+b+ c)/(abc)` ANSWER :B

Discussion

1715.	If sin x + "cosec"x + tan y + cot y = 4 where x and y in (0,(pi)/2) tan"" (y)/2 is a root of the equation
Answer» `alpha^2+2alpha+1=0` `alpha^2+2alpha-1=0` `2alpha^2-2alpha-1=0` `alpha^2-alpha-1=0` ANSWER :B

Discussion

1716.	One value of theta which satisfies the equation sin^(4)theta-2sin^(2)theta-1 lies between 0and2pi.
Answer» ANSWER :FALSE

Discussion

1717.	StatementI : Rank of a matrix is defined for only square matrices StatementII : Trace of a matrix is defined for square matrices only Which of the above Statement(s) is true ?
Answer» only I is TRUE only II is true Both I, II are true NEITHER I nor II are true ANSWER :B

Discussion

1718.	If vec(a) = vec(i) + 2vec(j) - 3vec(k), vec(b)= 2vec(i) + vec(j) - vec(k) and vec(u) is a vector satisfying vec(a) xx vec(u) = vec(a) xx vec(b) and vec(a).vec(u)= 0, then 2\|vec(u)\|^(2)=
Answer» 5 4 7 9 Answer :A

Discussion

1719.	d/(dx){cos^(-1)((4x^3)/27-x)}=
Answer» `4/(SQRT(9-x^2))` `1/(sqrt(9-x^2))` `(-3)/(sqrt(9-x^2))` `(-1)/(sqrt(9-x^2))` Answer :C

Discussion

1720.	If y=tan^(-1)(e^(x)) find dy/dx at x=0:
Answer» 1 0 `-1/2` `1/2` ANSWER :D

Discussion

1721.	How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated?
Answer» ANSWER :120

Discussion

1722.	The maximum of f(x)=2x^(3)-9x^(2)+12x+4 occurs at x=
Answer» 1 2 `-1` `-2` ANSWER :A

Discussion

1723.	A point P is inside an equilateral triangle. If the distances of P from sides 8, 10, 12 then length of the side of the triangle is
Answer» 10 `10sqrt(3)` `20sqrt(3)` `30sqrt(3)` ANSWER :C

Discussion

1724.	Find the derivative of (x+cosx)/(tanx)
Answer» ANSWER :`((1-sin X)TANX-(x+cos x)SEC^(2)x)/((tanx)^(2))`

Discussion

1725.	Evaluate the following limits : Lim_(xto 0^(-)) {(\|x\|)/x + x^(2) +3}
Answer» ANSWER :2

Discussion

1726.	A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 60^(@). When he retires 40m from the bank, he finds the angle to be 30^(@). The breadth of the river is
Answer» ` 20 SQRT3 MT` ` 25 mt` ` 20 mt` ` 30 mt` ANSWER :C

Discussion

1727.	Let A (1,2,-1) ,B(2,1,3) and if the length of projection of segment vec (AB) on the plane x - 2y - 2z =1 is d then the value of [d] (where [] is G.I.F)
Answer» ANSWER :3

Discussion

1728.	State true of false for the following: The locus represented by \|z-1\|=\|z-i\|. Is a line perpendicular to the join the points (1,0) and (0,1)
Answer» ANSWER :1

Discussion

1729.	Find the derivate of (5x^(3)+3x-1)(x-1)
Answer» ANSWER :`20X^(3)-15X^(2)+6x-4`

Discussion

1730.	The locus of the point z is the Argand plane for which \|z +1\|^(2) + \|z-1\|^(2)= 4 is a
Answer» STRAIGHT line Pair of straight lines Parabola Circle Answer :D

Discussion

1731.	Find the degree measure of the angle subtended at the centre of circle of radius 100 cm by an are of length 22 cm.
Answer» ANSWER :` 12 ^(@) 36'`

Discussion

1732.	Construct the consumer price index number for 1990 taking 1989 as the base year and usingsimple average of price relative method for the following data:
Answer» ANSWER :95

Discussion

1733.	Construct the consumer price index number for 1990, taking 1989 as the base year and using simple average of price relative method for the following data:
Answer» ANSWER :95

Discussion

1734.	Show that 4x^(2) + 16y^(2) - 24y - 32y - 12 = 0is the equatin of an ellipse ,and find its foci, vertices, eccentricity and directrices.
Answer» ANSWER :`X = 3 + (3)/(SQRT(3))`

Discussion

1735.	Using the expansion in simplify (a+b)^6+(a-b)^6
Answer» SOLUTION :`2[a^6+15a^4b^2+15a^2b^4+b^6]`

Discussion

1736.	A tank with rectangular base and rectangular side, open at the top is to be constructed so that its depth is 2m and volume is 8m^(3). If building of tank costs Rs. 70 per sq metres for the base and Rs. 45 per square metre for sides. What is the cost of least expensive tank ?
Answer» ANSWER :1000

Discussion

1737.	………..of the following is statement.
Answer» X is a REAL number SWITCH off the fan. 6 is a natural number Let me go Answer :A::C::D

Discussion

1738.	If= 60 ^(@), B= 30 ^(@)" then "a: b: c
Answer» ` 1: 2: 3` ` 1: 2: SQRT3` ` sqrt3: 1: 2` ` sqrt3:2: 1` ANSWER :C

Discussion

1739.	Prove that cos^(4)A-sin^(4)A=cos^(2)A-sin^(2)A.
Answer» ANSWER :RIGHT SIDE

Discussion

1740.	If Y = "tan"^(-1)((1)/(1 + x + x^2)) + "tan"^(-1) (1/(x^2 + 3x + 3)) + "tan"^(-1)(1/(x^2 + 5x + 7)) + ….+ upto n term then y^1(0) =
Answer» `(-1)/(1 + N^2)` `(-n^2)/(1 + n^2)` `(n^2)/(1 + n^2)` `n` ANSWER :B

Discussion

1741.	Find the term independent of x in the expansion of the following binomials: (2x^(2) - (1)/(x) )^12 What is its value?
Answer» ANSWER :`T_9 = 7920`

Discussion

1742.	Using the words ''necessary and sufficient'' rewrite the statement ''The integer n is odd if and only if n^(2) is odd''. Also check whether the statement is true.
Answer» Answer :If integer n is ODD then its necessary and SUFFICIENT CONDITION is `n^(2)` is also odd. FALSE statement

Discussion

1743.	Find the value of ""^6P_5
Answer»

Discussion

1744.	Find the numbers of intergral values of a for which the equation cos2x+asinx=2a-7 has a solution.
Answer» ANSWER :5

Discussion

1745.	What is the number of terms in the expansion of each of the following? (vi) (5+7x)^(15) + (5-7x)^(15)
Answer» ANSWER :8

Discussion

1746.	Eliminating theta from the following(i) x = a cos^(3) theta " " y = b sin^(3) theta
Answer» ANSWER :1

Discussion

1747.	Compute the derivative of 6x^(100)-x^(55)+x.
Answer» Answer :`600 x^(99)-55 x^(54)+1`

Discussion

1748.	Which of the following statements are true and which are false? s: If x and y are odd then xy is odd.
Answer» ANSWER :1

Discussion

1749.	Find the modulus and amplitude of the following complex numbers and hence express them into polar form -1- sqrt3i
Answer» Answer :Modulus= 2, AMPLITUDE= `-(2PI)/(3); z= 2 [COS (-(2pi)/(3)) + "i sin" (-(2pi)/(3))]`

Discussion

1750.	Find the modulus and amplitude of the following complex numbers and hence express them into polar form sqrt3+i
Answer» Answer :MODULUS= 2, AMPLITUDE= `(pi)/(6); z= 2 ("cos"(pi)/(6) + "ISIN"(pi)/(6))`

Discussion

Explore topic-wise InterviewSolutions in .

If z_(1)=2 + 7i and z_(2)=1- 5i, then verify that |z_(1)z_(2)|= |z_(1)||z_(2)|

Eight chairs are numbered 1 to 8. Two women and 3 man wish to occupy one chair each. First the women choose the chair each. First the women choose the chairs from amongst the chairs 1 to 4 and then men select from the remaining chairs. Find the total number of possible arrangments.

Two points A and B with co-ordinates (5, 3), (3, -2) are given. A point P moves so that the area of DeltaPAB is constant and equal to 9 square units. Find the equation to the locus of the point P.

Consider the expansion of ((4x)/5-5/(4x))^8 Find the fourth term from the end in the expansion.

If A, B are symmetric matrices of the same order then show that AB-BA is skew symmetric matrix.

Compute the following limits. Lt_(xto2)(7x)/(6x+2)

Find the slope of the tangent line to the graph f(x) =x^(2)-x+1 at (1,1)

If f(x)=sqrtx,x=4,deltax=0.08 then df=

Let U = {1,2,3,4,5,6,7}, A = {1,5,6} and B = {1,2,6,7}FindA cup B

Complete solution set of [cot^(-1)x]+2[tan^(-1)x]=0, where [.] denotes the greatest integer function, is equal to

a( r r _1 +r_2r_3)=

Find the number of arrangemements of the letters of the word INDEPEDENCE. In how many of these arrangments , (i) DO the words start with P. (ii) DO all the vowels always occur together . (iii) Do the vowels never occur togather (Iv) do the words begin with I and end in P?

Simplify : i^(-6)

3 - Circles with radii a, b, c touch one another externally tangents at contact points meet in a point P then the distance of P to the contact point of any 2-circles is

If sin x + "cosec"x + tan y + cot y = 4 where x and y in (0,(pi)/2) tan"" (y)/2 is a root of the equation

One value of theta which satisfies the equation sin^(4)theta-2sin^(2)theta-1 lies between 0and2pi.

StatementI : Rank of a matrix is defined for only square matrices StatementII : Trace of a matrix is defined for square matrices only Which of the above Statement(s) is true ?

If vec(a) = vec(i) + 2vec(j) - 3vec(k), vec(b)= 2vec(i) + vec(j) - vec(k) and vec(u) is a vector satisfying vec(a) xx vec(u) = vec(a) xx vec(b) and vec(a).vec(u)= 0, then 2|vec(u)|^(2)=

d/(dx){cos^(-1)((4x^3)/27-x)}=

If y=tan^(-1)(e^(x)) find dy/dx at x=0:

How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated?

The maximum of f(x)=2x^(3)-9x^(2)+12x+4 occurs at x=

A point P is inside an equilateral triangle. If the distances of P from sides 8, 10, 12 then length of the side of the triangle is

Find the derivative of (x+cosx)/(tanx)

Evaluate the following limits : Lim_(xto 0^(-)) {(|x|)/x + x^(2) +3}

A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 60^(@). When he retires 40m from the bank, he finds the angle to be 30^(@). The breadth of the river is

Let A (1,2,-1) ,B(2,1,3) and if the length of projection of segment vec (AB) on the plane x - 2y - 2z =1 is d then the value of [d] (where [] is G.I.F)

State true of false for the following: The locus represented by |z-1|=|z-i|. Is a line perpendicular to the join the points (1,0) and (0,1)

Find the derivate of (5x^(3)+3x-1)(x-1)

The locus of the point z is the Argand plane for which |z +1|^(2) + |z-1|^(2)= 4 is a

Find the degree measure of the angle subtended at the centre of circle of radius 100 cm by an are of length 22 cm.

Construct the consumer price index number for 1990 taking 1989 as the base year and usingsimple average of price relative method for the following data:

Construct the consumer price index number for 1990, taking 1989 as the base year and using simple average of price relative method for the following data:

Show that 4x^(2) + 16y^(2) - 24y - 32y - 12 = 0is the equatin of an ellipse ,and find its foci, vertices, eccentricity and directrices.

Using the expansion in simplify (a+b)^6+(a-b)^6

A tank with rectangular base and rectangular side, open at the top is to be constructed so that its depth is 2m and volume is 8m^(3). If building of tank costs Rs. 70 per sq metres for the base and Rs. 45 per square metre for sides. What is the cost of least expensive tank ?

………..of the following is statement.

If= 60 ^(@), B= 30 ^(@)" then "a: b: c

Prove that cos^(4)A-sin^(4)A=cos^(2)A-sin^(2)A.

If Y = "tan"^(-1)((1)/(1 + x + x^2)) + "tan"^(-1) (1/(x^2 + 3x + 3)) + "tan"^(-1)(1/(x^2 + 5x + 7)) + ….+ upto n term then y^1(0) =

Find the term independent of x in the expansion of the following binomials: (2x^(2) - (1)/(x) )^12 What is its value?

Using the words ''necessary and sufficient'' rewrite the statement ''The integer n is odd if and only if n^(2) is odd''. Also check whether the statement is true.

Find the value of ""^6P_5

Find the numbers of intergral values of a for which the equation cos2x+asinx=2a-7 has a solution.

What is the number of terms in the expansion of each of the following? (vi) (5+7x)^(15) + (5-7x)^(15)

Eliminating theta from the following(i) x = a cos^(3) theta " " y = b sin^(3) theta

Compute the derivative of 6x^(100)-x^(55)+x.

Which of the following statements are true and which are false? s: If x and y are odd then xy is odd.

Find the modulus and amplitude of the following complex numbers and hence express them into polar form -1- sqrt3i

Find the modulus and amplitude of the following complex numbers and hence express them into polar form sqrt3+i