14949 + Interview Questions in Maths in Class 11 Page 202 InterviewSolution

10051.	Find the square roots of the following : 1+i
Answer» ANSWER :`+-( SQRT((sqrt(2)+1)/(2))+i sqrt((sqrt(2)-1)/(2)))`

Discussion

10052.	What is science?
Answer» Solution :The word SCIENCE comes from a Latin word 'scientia' meaning 'to know'. (II) Science is á SYSTEMATIC ATTEMPT to understand natural phenomena in much knowledge GAINED through systematic observation and experiment.

Discussion

10053.	The value of (0.32)^128 is ________
Answer» `(5)/(7)` `(7)/(5)` 4 2 Answer :B

Discussion

10054.	Let z_(1) =2-I, z_(2) =-2 + i, Find (i) (Re(z_(1)z_(2))/barz_(1)), (ii) Im(1/(z_(1)barz_(1)))
Answer» ANSWER :(i) `-2/5`, (II) 0

Discussion

10055.	If sinx + cos x + tanx + cotx + secx + "cosec "x =7, 0 lt x lt pi//2 and sin2x=a-bsqrt(7) then (a,b in Z^(+))
Answer» a=8 b=22 a=22 b=8 Answer :C::D

Discussion

10056.	y=mx is one of the lines represented by ax^2+2hxy+by^2=0 if a+2hm+bm^2=
Answer» -1 1 0 2 Answer :C

Discussion

10057.	Statement 1: If -2h =a+b, then one line of the pair of lines ax^(2)+2hxy+by^(2)=0bisects the angle between coordinate axes in positive quadrant. Statement 2: If ax + y (2h + a) = 0 is a factor ofax^(2)+2hxy+by^(2)=0,then b + 2h +a=0
Answer» Both the statements are true but statement 2 is the correct EXPLANATION of statement Both the statements are true but statement 2 is not the correct explanation of statement 1 Statement 1 is true and statement 2 is false Statement 1 is false and statement 2 is true Answer :B

Discussion

10058.	Show that the line are tangent to the given hyperbolas and determine the points of contact. x - 2y + 1 =0, x ^(2) -6y ^(2) =3
Answer» ANSWER :`(-3, -1)`

Discussion

10059.	Show that the function f:NtoN defined by f(x)=2x-1 is one-one but not onto.
Answer» ANSWER : `(##VVA_ISC_MAT_XI_MTP_03_E01_022_A01##)`

Discussion

10060.	Write down the slopes of the following lines: 2x+3y+1=0
Answer» ANSWER : `(-2)/(3)`

Discussion

10061.	If ((20) ,(r))=((20),(r+2)) then ((r),(2))=........ .
Answer» ANSWER :36

Discussion

10062.	Find the derivative of 99x at x=100.
Answer» ANSWER :99

Discussion

10063.	Find the component statements of the following compound statements: All rational numbers are real and all real numbers are complex.
Answer» <P> ANSWER :p: All rational numbers are REAL. q: All real numbers are complex.

Discussion

10064.	Prove that (sin theta + sin 2 theta )/(1+cos 0 + cos 2 theta )= tan theta
Answer» `"tan"(THETA)/(2)` `"cot"(theta)/(2)` `tan theta` `cot theta` ANSWER :C

Discussion

10065.	Prove that the equation 2x^(2)+3xy-2y^(2)+3x+y+1=0 represents a pair of perpendicular lines and find the lines.
Answer» ANSWER :`2x-y+1=0, x+2y+1=0`

Discussion

10066.	If sin^(-1)(12/13)+sec^(-1)(13/x)=(pi)/2 then x=
Answer» 12 13 11 5 Answer :A

Discussion

10067.	Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces : {x : x is an equilateral triangle in a plane} . . .{x : x is a triangle in the same plane}
Answer» ANSWER :`⊂`

Discussion

10068.	e^(sin h^(-1) (cot theta))
Answer» `SEC THETA` `TAN theta` `sec theta + tan theta` `sec theta - tan theta` ANSWER :C

Discussion

10069.	If 2bar(i)-bar(j)+bar(k), bar(i)-3bar(j)-5bar(k), 3bar(i)-4bar(j)-4bar(k) are the vertices of a triangle then the vector equation of the median passing through 2bar(i)-bar(j)+bar(k) is
Answer» `bar(r)=(2bar(i)-bar(J)+bar(k))+t(2bar(i)-7/2bar(j)-9/2bar(k))` `bar(r)=(2bar(i)-bar(j)+bar(k))+t(5bar(j)+11bar(k))` `bar(r)=(bar(i)-3BAR(j)-5bar(k))+t(2bar(i)-9/2bar(k))` `bar(r)=(2bar(i)-bar(j)+bar(k))+t(5bar(i)+11bar(k))` ANSWER :B

Discussion

10070.	Expand the following Cos(A-B-C)
Answer» ANSWER :`cosAcosBcosC- cosAsinBsinC+sinAsinBcosC+sinAcosBsinC`

Discussion

10071.	Find the derivative of the function (x ^(2) - 3) (4x ^(3) +1)
Answer» ANSWER :`20 X ^(4) - 36 x ^(2) + 2X`

Discussion

10072.	Find the value of(i) sin. (5pi)/(3)
Answer» ANSWER :`(-SQRT(3))/(2)`

Discussion

10073.	Evaluate the following limits : Lim_(x to oo) sqrt(((x+sin x)/(x- cos x))) is equal to
Answer» 0 1 `-1` NONE of these ANSWER :A

Discussion

10074.	A vertical tower stands on a declivity which is inclinde at 15^(@) to the horizon. From the foot of the tower a man ascends the declivity from 80 feet and then finds that the towersubteds an angle of 30^(@). The height of the tower is
Answer» `40(sqrt6+sqrt2)` `20(sqrt6-sqrt2)` `40(sqrt6-sqrt2)` `10(sqrt6-sqrt2)` ANSWER :C

Discussion

10075.	If A = 35^(@), B = 15^(@), C = 40^(@), then tan A tan B +tan B tan C + tan C tan A = ……
Answer» 0 1 -1 `SQRT(3)` ANSWER :B

Discussion

10076.	For any vector vec(a), the value of (vec(a) xx vec(i))^(2) + (vec(a) xx vec(j))^(2) + (vec(a) xx vec(k))^(2)=
Answer» `4vec(a)^(2)` `2vec(a)^(2)` `VEC(a)^(2)` `3vec(a)^(2)` ANSWER :B

Discussion

10077.	Find the sum of the series whose n^(th) term is as following: n^(3)-3n
Answer» ANSWER :`[(N(n+1))/(2)]^(2) - (3)/(2) (3n-1)`

Discussion

10078.	Find the ratio in which the YZ-plane divides the line segment formed by joining the points (-2, 4, 7) and (3, -5, 8).
Answer» ANSWER :`2:3`

Discussion

10079.	Find the derivative of the following functions :(It is to be understood that a,b,c,d,p,q,r and s are fixed non-zero constants and m and n are intergers): (x+a)
Answer» Answer :`1=(because (d)/(DX)(x^(N)=NX^(n-1)`) and derivative of constant is zero)

Discussion

10080.	If alpha, beta, gamma are acute angles and cos theta = sin beta//sin alpha, cos phi = sin gamma//sin alpha and cos(theta-phi)=sin beta sin gamma then the value of of tan^(2)alpha - tan^(2)beta- tan^(2)gamma is equal to
Answer» `-1` 0 1 2 Answer :B

Discussion

10081.	The maximum distance of a point on the graph of the function y=sqrt(3)sinx+cosx from X-axis is …………...
Answer» ANSWER :2

Discussion

10082.	The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On rechecking, it was found that an observation 8 was incorrect. Calculate the correct mean and standard deviation in each of the following cases: (i) If wrong item is omitted. (ii) If it is replaced by 12.
Answer» ANSWER :(i) 10,1, 1.99 (II) 10.2, 1.98

Discussion

10083.	How many terms of the A.P. 18, 16, 14, 12,…. are needed to give the sum 78?
Answer» ANSWER :6 or 13

Discussion

10084.	If a and b are chosen randomly from the set {1, 2, 3, 4} with replacement, then the probability of the real roots of the equation x^(2) + ax + b = 0 is
Answer» `3/16` `5/16` `7/16` `11/16` ANSWER :A::C

Discussion

10085.	If cos theta - sin theta=1/5, where 0 lt theta lt pi/4, then:
Answer» ANSWER :A::B::C::D

Discussion

10086.	Which of he following are sets ? Justify your answer (i) The collection of all the months of a year beginning with the letter J (ii) The collection of ten most talented writers of India (iii) A team of eleven best-cricket batsman of the world (iv) The collection of all body in your class (v) The collection of all natural numbers less than 100 (vi) A collection of novels written by the writer Munshi Premchand (vii) The collection of all even integers (viii) The collection of questions in this Chapter (ix) A collection of most dangerous animals of the world.
Answer» Solution :(i) Months starting from J are January, June, July. These months are well-defined Therefore, the collection of all months starting from J is a set (ii) `because` It has no scale to SAY whether a writer is TALENTED or not i.e., this collection is not well-defined. Thus, the collection of ten most talented WRITERS of India is not a set (iii) `because` There is no scale to decide whether a batsman is best or not i.e., this collection is not well defined. thus the collection of a team of eleven best-cricket batsmen is not a set (iv) The number of boys in a class is fixed, so their collection is well-defined. Thus, the collection of all boys in your class is a set (v) Collection of all natural numbers less than 100 is `{1,2,3,4,....,99}` which is well-defined. Thus, the collection of all natural numbers less than 100 is a set (vi) `because` The number of novels written by Munshi Premchand is definite, which is well-defined. Thus, this collection is a set. (vii) The properties of the collection of integers 2,4,6,8,10,12.... is definite and well-defined. Thus, the collection of even integers is a set. (viii) Each question given in the chapter is well defined. Thus, this collection is a set (ix) There is no scale to decide whether an ANIMAL is dangerous or not. Thus, the collection of most dangerous ANIMALS of the world is not a set.

Discussion

10087.	The value of x for which Cos^(-1)(cos4) gt 3x^(2)-4x is
Answer» `(0,(2+sqrt(6pi-8))/3)` `((2+sqrt(6pi-8))/3,0)` `(-2,2)` `((2-sqrt(6pi-8))/3,(2+sqrt(6pi-8))/3)` ANSWER :D

Discussion

10088.	( a+b + c) [tan ""(A)/(2) + tan "" ( B)/(2) ] =
Answer» ` 2C COT C//2` `c(cot ""( C)/(2))` ` 3c ( cot ""( C)/(2))` ` 4c ( cot "" ( C)/(2)) ` Answer :A

Discussion

10089.	If f(x)=mx+c and f(0)=1=f'(0) then f(-2)=(i) 1(ii) -1(iii) 3(iv) +-1
Answer» 1 `-1` 3 `+-1` ANSWER :B

Discussion

10090.	In Delta ABC, if 3 tan ""A/2 tan""C/2=1 then a,b,c are in
Answer» <P>` A.G. P ` ` H. P ` ` A.P ` ` G.P ` ANSWER :C

Discussion

10091.	Out of 100 students, 55 passed in Mathematics and 67 passed in Physics 100 students passed at least one of these two subjects. Find how many students passed in Physics only?
Answer» ANSWER :`= 45`

Discussion

10092.	Delta^("le")ABC is right angled at A the point P and Q are on the hypotenuse BC suh that BP=PQ=QC if AP=3.Aq=4 then length BC
Answer» `SQRT(27)` `sqrt(36)` `sqrt(45)` `sqrt(54)` Answer :C

Discussion

10093.	For x in R, x != 0, x != 1, let f_(0)(x)= (1)/(1-x) and f_(n+1)(x)=f_(0)(f_(n)(x)), n = 0, 1, 2,.... Then the value of f_(100)(3)+f_(1)(2/3)+f_(2)(3/2) is equal to
Answer» `8/3` `5/3` `4/3` `1/3` ANSWER :B

Discussion

10094.	Find the value of 0.23434343434..... regarding it as a geometric series.
Answer» ANSWER :`(116)/(495)`

Discussion

10095.	Write the first three terms in each of the following sequences defined by the following: (i) a_n =2n +5, (ii) a_n = (n-3)/4
Answer» Answer :(i) 11 the FIRST three terms are `- (1)/(2) , - (1)/(4) and 0`

Discussion

10096.	When the origin is shifted to (4,-5) by the translation of axes, find the coordinates of the point (4,-5) with reference to new axes.
Answer» ANSWER :(0,0)

Discussion

10097.	4 cos A * cos B * sin (A-B)
Answer» `4 COS A * cos B * cos(A-B)` `4 SIN A * sin B sin(A-B)` `4 sin A cos B sin(A-B)` `4 cos A sin B *cos(A-B)` ANSWER :A

Discussion

10098.	Find the coordinates of vertex of the parabola y^(2)=4(x+y)
Answer» ANSWER :`(-1,2)`

Discussion

10099.	Bytranslation of axes the equation xy - x + 2y - 6 = 0changed as xy = c then c =
Answer» 4 5 6 7 Answer :A

Discussion

10100.	Find the equation of a circle passing through the points (-1,5) and (-7,5) and its centre lies on the line 3x+4y+8=0.
Answer» ANSWER :`X^(2)+y^(2)+8x-2y-8=0`

Discussion

Explore topic-wise InterviewSolutions in .

Find the square roots of the following : 1+i

What is science?

The value of (0.32)^128 is ________

Let z_(1) =2-I, z_(2) =-2 + i, Find (i) (Re(z_(1)z_(2))/barz_(1)), (ii) Im(1/(z_(1)barz_(1)))

If sinx + cos x + tanx + cotx + secx + "cosec "x =7, 0 lt x lt pi//2 and sin2x=a-bsqrt(7) then (a,b in Z^(+))

y=mx is one of the lines represented by ax^2+2hxy+by^2=0 if a+2hm+bm^2=

Statement 1: If -2h =a+b, then one line of the pair of lines ax^(2)+2hxy+by^(2)=0bisects the angle between coordinate axes in positive quadrant. Statement 2: If ax + y (2h + a) = 0 is a factor ofax^(2)+2hxy+by^(2)=0,then b + 2h +a=0

Show that the line are tangent to the given hyperbolas and determine the points of contact. x - 2y + 1 =0, x ^(2) -6y ^(2) =3

Show that the function f:NtoN defined by f(x)=2x-1 is one-one but not onto.

Write down the slopes of the following lines: 2x+3y+1=0

If ((20) ,(r))=((20),(r+2)) then ((r),(2))=........ .

Find the derivative of 99x at x=100.

Find the component statements of the following compound statements: All rational numbers are real and all real numbers are complex.

Prove that (sin theta + sin 2 theta )/(1+cos 0 + cos 2 theta )= tan theta

Prove that the equation 2x^(2)+3xy-2y^(2)+3x+y+1=0 represents a pair of perpendicular lines and find the lines.

If sin^(-1)(12/13)+sec^(-1)(13/x)=(pi)/2 then x=

Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces : {x : x is an equilateral triangle in a plane} . . .{x : x is a triangle in the same plane}

e^(sin h^(-1) (cot theta))

If 2bar(i)-bar(j)+bar(k), bar(i)-3bar(j)-5bar(k), 3bar(i)-4bar(j)-4bar(k) are the vertices of a triangle then the vector equation of the median passing through 2bar(i)-bar(j)+bar(k) is

Expand the following Cos(A-B-C)

Find the derivative of the function (x ^(2) - 3) (4x ^(3) +1)

Find the value of(i) sin. (5pi)/(3)

Evaluate the following limits : Lim_(x to oo) sqrt(((x+sin x)/(x- cos x))) is equal to

A vertical tower stands on a declivity which is inclinde at 15^(@) to the horizon. From the foot of the tower a man ascends the declivity from 80 feet and then finds that the towersubteds an angle of 30^(@). The height of the tower is

If A = 35^(@), B = 15^(@), C = 40^(@), then tan A tan B +tan B tan C + tan C tan A = ……

For any vector vec(a), the value of (vec(a) xx vec(i))^(2) + (vec(a) xx vec(j))^(2) + (vec(a) xx vec(k))^(2)=

Find the sum of the series whose n^(th) term is as following: n^(3)-3n

Find the ratio in which the YZ-plane divides the line segment formed by joining the points (-2, 4, 7) and (3, -5, 8).

Find the derivative of the following functions :(It is to be understood that a,b,c,d,p,q,r and s are fixed non-zero constants and m and n are intergers): (x+a)

If alpha, beta, gamma are acute angles and cos theta = sin beta//sin alpha, cos phi = sin gamma//sin alpha and cos(theta-phi)=sin beta sin gamma then the value of of tan^(2)alpha - tan^(2)beta- tan^(2)gamma is equal to

The maximum distance of a point on the graph of the function y=sqrt(3)sinx+cosx from X-axis is …………...

The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On rechecking, it was found that an observation 8 was incorrect. Calculate the correct mean and standard deviation in each of the following cases: (i) If wrong item is omitted. (ii) If it is replaced by 12.

How many terms of the A.P. 18, 16, 14, 12,…. are needed to give the sum 78?

If a and b are chosen randomly from the set {1, 2, 3, 4} with replacement, then the probability of the real roots of the equation x^(2) + ax + b = 0 is

If cos theta - sin theta=1/5, where 0 lt theta lt pi/4, then:

The value of x for which Cos^(-1)(cos4) gt 3x^(2)-4x is

( a+b + c) [tan ""(A)/(2) + tan "" ( B)/(2) ] =

If f(x)=mx+c and f(0)=1=f'(0) then f(-2)=(i) 1(ii) -1(iii) 3(iv) +-1

In Delta ABC, if 3 tan ""A/2 tan""C/2=1 then a,b,c are in

Out of 100 students, 55 passed in Mathematics and 67 passed in Physics 100 students passed at least one of these two subjects. Find how many students passed in Physics only?

Delta^("le")ABC is right angled at A the point P and Q are on the hypotenuse BC suh that BP=PQ=QC if AP=3.Aq=4 then length BC

For x in R, x != 0, x != 1, let f_(0)(x)= (1)/(1-x) and f_(n+1)(x)=f_(0)(f_(n)(x)), n = 0, 1, 2,.... Then the value of f_(100)(3)+f_(1)(2/3)+f_(2)(3/2) is equal to

Find the value of 0.23434343434..... regarding it as a geometric series.

Write the first three terms in each of the following sequences defined by the following: (i) a_n =2n +5, (ii) a_n = (n-3)/4

When the origin is shifted to (4,-5) by the translation of axes, find the coordinates of the point (4,-5) with reference to new axes.

4 cos A * cos B * sin (A-B)

Find the coordinates of vertex of the parabola y^(2)=4(x+y)

Bytranslation of axes the equation xy - x + 2y - 6 = 0changed as xy = c then c =

Find the equation of a circle passing through the points (-1,5) and (-7,5) and its centre lies on the line 3x+4y+8=0.