14949 + Interview Questions in Maths in Class 11 Page 172 InterviewSolution

8551.	Match the following
Answer» a,B,c,d b,c,d,a c,d,a,b d,a,b,c Answer :B

Discussion

8552.	sin h^(-1) ((x)/(sqrt(1 - x^(2)))) =
Answer» `cos H^(-1) x` `cos h^(-1) (2X)` `TAN h^(-1) x` `tan h^(-1) (2x)` Answer :C

Discussion

8553.	Which of the following sentences are statements? Give reasons for your answer: The sum of all interior angles of a triangle is 180^(@)
Answer» ANSWER :This sentence is always TRUE and therefore, it is a STATEMENT.

Discussion

8554.	State which of the following statements are true and which are false. Justify your answer. 3 in {x \|x^(4)-5x^(3)+2x^(2)-112x+6=0}
Answer» ANSWER :1

Discussion

8555.	U= {h, i, j, k, l, m, n, o, p} then find the complement of the following sets :B= {j, k, l, m}
Answer» <P> ANSWER :`= {H, i, N, o, p}`

Discussion

8556.	If cos(theta - alpha)=a, cos(theta-beta)=b, then sin^(2)(alpha -beta) + 2abcos(alpha-beta)=0
Answer» `a^(2)+B^(2)` `a^(2)-b^(2)` `b^(2)-a^(2)` `-a^(2)-b^(2)` ANSWER :A

Discussion

8557.	If z=4 + 3i, then verify that-\|z\| lt I m (z) le \|z\|
Answer» ANSWER :`-5 LT 3 lt 5`

Discussion

8558.	If points ( x , 0) , ( 0 , y) and ( 1 , 1) are collinear, then(1)/(x) +(1)/(y) = .......
Answer» 0 `1/2` `2` `1 Answer :D

Discussion

8559.	The set A has 3 elements how many relations are there from A to A.
Answer» ANSWER :`DELTA^(9)`s

Discussion

8560.	A straight line parallel to the line y=sqrt(3)x passes through Q(2,3) and cuts the line 2x+4y-27=0 at P. Find the lengh of PQ.
Answer» ANSWER :`2sqrt(3)-1`

Discussion

8561.	If z=x +iy is purely real number such that x lt 0 then arg (z) is
Answer» 0 `(PI)/(2)` `pi` `-pi` ANSWER :C

Discussion

8562.	If A(3,4) and B is a variable point on the lines \|x\|=6.If ABle4 then number of positions of B with integral co ordinates is :
Answer» 10 6 4 5 Answer :D

Discussion

8563.	Express the following expression in the form of a+lb: (5+sqrt(2)i)/(1-sqrt(2)i)
Answer» ANSWER :`1+2sqrt(2)i`

Discussion

8564.	If x sin y = 3 sin y + 4 cos y , then (dy)/(dx) =
Answer» `(-sin^2y)/(4)` `(sin^2y)/(4)` `(-cos^2y)/4` `(cos^2y)/4` ANSWER :A

Discussion

8565.	( a- b) ^(2) cos ^(2) ""(C ) /(2) + ( a+b) ^(2) sin ^(2) "" ( C )/(2)=
Answer» `C ` `( c )/(2)` ` 2C` ` c^(2) ` ANSWER :D

Discussion

8566.	Differentiate the following functions w.r.t. x: cos (2x-3)
Answer» ANSWER :`-2 SIN (2X -3)`

Discussion

8567.	If the point (3, -2) transformed to (-2, 1) when origin shifted to P then P =
Answer» (3, 2) (5, -3) (2, -3) (-1, 2) Answer :B

Discussion

8568.	Two finite sets have m and n elements. The number of subsets of the first set is 112 more than of the second set. The values of m and n are, respectively.
Answer» 4 and 7 7 and 4 4 and 4 7 and 7 Answer :B

Discussion

8569.	Two unbiased dice are thrown . Find the probability that both the dice show the same number .
Answer» ANSWER :`=(1)/(6)`.

Discussion

8570.	The periodof sin (pix )/( n )- cos ((pi x)/( n+1))is
Answer» `(N+1)!` `2(n+1)!` `2(n)!` `((n+1))/(2!)` ANSWER :B

Discussion

8571.	IfA and B be the points (3,4,5) and (-1,3,-7) respectively find the equation of the set of points P such that PA^(2)+PB^(2)=K^(2) where k is a constant
Answer» Answer :`x^(2)+y^(2)+Z^(2)-2x-7y+2z=(K^(2)-109)/(2)`

Discussion

8572.	Explain the use of screw gauge and vernier caliper in measuring smaller distances.
Answer» Solution :(a) Measurement of small distances: (i) The screw gauge is an instrument used for measuring accurately the diameter of a thin wire or thickness of a sheet of metal or glass the dimensions of objects up to a MAXIMUM of about 50 mm. (a) It is used for measuring external dimensions. i.e. diameter. (b) It can take the smallest measurement of 0.01 mm. (c) A vernier caliper is a versatile instrument for measuring the dimensions of an object namely diameter of a hole, or a depth of a hole. i.e. internal & external dimensions. (ii) For measuring larger distances such as the height of a tree, distance of the Moon or a planet from the Earth. Triangulation method, PARALLAX method and radar method are used. Triangulation method for the height of an accessible object : (a) Let AB = h be the height of the tree or tower to be measured. Let C be the point of observation at distance x from B. Place a range finder at C and measure the angle of elevation, `ANGLEACB = theta` as shown in Figure. (b) From right angled triangle ABC, `TAN theta= (AB)/(BC) = h/x` (or) height h = `x tan theta` . (c) Knowing the distance x, the height h can be determined.

Discussion

8573.	If 4 cot 2 theta=cot^(2)theta-tan^(2)theta then theta=
Answer» `npi+-(PI)/6, NIN Z` ` n pi +-(pi)/3, n in z` `n pi +-(pi)/4, n inZ` `(2n+1)+-(pi)/2, n in Z` Answer :C

Discussion

8574.	…….is the interval from of the set {"x"in R \|-5
Answer» ANSWER :`[-5,7]`

Discussion

8575.	A function is matched below agnaist an interval where it is supposed to be increasing. Which of the following pair is incorrectly matched
Answer» `{:("Ineterval","FUCTION"),((-oo,oo),(x^3-3x^2+3x+3)):}` `{:("Ineterval","Fuction"),([2,oo),2x^3-3x^2-12x+6):}` `{:("Ineterval","Fuction"),((-oo,1/3],3x^2-2x+1):}` `{:("Ineterval","Fuction"),((-oo,-4),x^3+6x^2+6):}` ANSWER :C

Discussion

8576.	A (1,2) and B(7,10) are two fixed points. If P(x,y) is such that a point where angleAPB=60^@ and the area of DeltaAPB is maximum then the point P
Answer» is on the line 3x+4y=36 is on any line perpendicular to AB is on perpendicular bisector of AB is on the circle PASSING through(1,2) and (7,10) having RADIUS 10 Answer :A::B::C::D

Discussion

8577.	If f(x)=(x+1)^(2)-1, x ge -1 then the set S={x, f(x)=f^(-1)x} is
Answer» STATEMENT 1 is true, statement 2 is true, statement 2 is a correct EXPLANATION for statement 1. Statement 1 is true, statement 2 is true, statement 2 is not a correct explanation for statement 1. Statement 1 is true, statement 2 is false Statement 1 is false, statement 2 is true Answer :C

Discussion

8578.	Ifa_0 = x, a_( n+1) = f(a_n) , " where"n = 0,1,2……… then answer the following questions If f(x)=""^(m) sqrt( (a- x^(m))), x gt 2=0, m ge 2 , m in Nthen
Answer» `a_(n)=x, n = 2k+1` where k is an INTEGER `a_(n) = f(x)` if `n= 2k`, where k is an integer The inverse of `a_(n)` EXISTS for any value of n and m none of these Answer :D

Discussion

8579.	cos""(2pi)/(15)cos""(4pi)/(15)cos""(8pi)/(15)cos"(16pi)/(15)=(1)/(16)
Answer» ANSWER :TRUE

Discussion

8580.	Write the first five terms of the sequences in obtain the corresponding series: a_(1)= a_(2)= 1, a_(n)= a_(n-1) + a_(n-2), n gt 2
Answer» ANSWER :1,1,2,3,5 SERIES : `1+1+2+ 3+ 5+`…….

Discussion

8581.	Find the slope of a line parallel to the line which passes throughthepoints: (-a, 0) and (0, b)
Answer» ANSWER : `B/(a)`

Discussion

8582.	Given\|vec (x_1) \| = 47.5 , \|vec (x_2)\|= 52.5. and theta = 0Then \| vec (x_1) - vec (x_2)\|=
Answer» `27` ` 5` ` 23.7` ` 26.3` ANSWER :B

Discussion

8583.	The p^(th), q^(th) and r^(th) terms of an A.P. are in geometric progression then common ratio for G.P is…….
Answer» `(p-q)/(q-r)` `(q-r)/(p-q)` pqr None of these Answer :B

Discussion

8584.	If a le cos theta + 3sqrt(2) sin [theta + (pi)/4] + 6 le b, find largest value of a and smallest value of b.
Answer» ANSWER :A::B

Discussion

8585.	If 'n' is a positive integer then prove that the coefficient fox^(m) in the expansion of (x^(2)+(1)/(x))^(2n) is :
Answer» SOLUTION :N/a

Discussion

8586.	(k+1)^(15) derivative of (x+1)^(k) is:
Answer» 0 `\|_k` `\|_(K+1)` `(x+1)^(k+1)` ANSWER :A

Discussion

8587.	Solve sqrt(5)x^(2) + x+ sqrt(5)=0
Answer» ANSWER :`(-1 + SQRT(19)i)/(2sqrt(5))`

Discussion

8588.	If bara. barb = barb. barc = barc . bara = 0 then [bara barb barc] =
Answer» `barrbotbarcxxbara` `barrbotbaraxxbarb` `barrbotbarbxxbarc` `barr=bar0` ANSWER :A

Discussion

8589.	Obtain equation of the circle which makes intercept of leght 6 unit on X - axis and touches Y - axis at the distance 4 unit from the origin.
Answer» Answer :`x^(2) + y^(2) - 10x pm 8Y + 16 = 0`

Discussion

8590.	A five digit number is formed at random by using the digits 1, 2, 3, 4, 5, 6 and 7. How many five digit numbers formed will have distinct digits?
Answer» SOLUTION :`"^7P_5`

Discussion

8591.	For which value of k will the equations x^(2)-kx-21=0 and x^(2)-3kx+35=0 have one common root ?
Answer» ANSWER :`k=pm4`.

Discussion

8592.	Calculate the standard deviation of the following data:
Answer» ANSWER :1.54

Discussion

8593.	If cos^(-1)[(cos alpha+ cos beta)/(1+cos alpha cos beta)]=2 Tan^(-1)x then x=
Answer» `"tan"(ALPHA)/(2)"tan"(BETA)/(2)` `tan alpha tan beta` `"cot"(alpha)/(2)"cot"(beta)/(2)` `cot alpha cot beta` ANSWER :A

Discussion

8594.	If the acute angle between the pair of lines x^(2)+4sqrt2xy+lamday^(2)=0 is (pi)/(6) then lamda=
Answer» 2 3 4 5 Answer :D

Discussion

8595.	Solve x^(2) + 3x + 5=0
Answer» ANSWER :`(-3+-sqrt(11)i)/2`

Discussion

8596.	Calculate the standard deviation of the following data:
Answer» ANSWER :9.99 APPROX

Discussion

8597.	If vec(a)= 2vec(i) -vec(j) + 3vec(k), vec(b)= p vec(i) + vec(j) + q vec(k) and vec(b) xx vec(a) = vec(0), then
Answer» (p, q)= (2, 3) (p, q)= `(-2, -3)` (p, q)= (1, 2) (p, q)= `(-1, -2)` ANSWER :B

Discussion

8598.	Write the negation of each of the following : (i) sqrt(2) is an irrational number. (ii) 3 is a prime number. (iii) asia is continent. (iv) the product of 3 and 6 is 12. (v) every natural number is an integer. (vi) all triangles are not a right- angled. (vii) all indian speak hindi. (viii) 100 is divisible by 8.
Answer» Solution :(i) `sqrt(2)` is not an irrational number . (II) 3 is not a prime number. (III) asia is not an continent. (iv) the product of 3 and 6 is not 12. (v) at LEAST one natural number is not INTEGER. (vi) at least one triangle is right-angled. (vii) at least one triangle does not speak Hindi. (viii) 100 is not divisible by 8.

Discussion

8599.	All chords of a curve 3x^(2)-y^(2)-2x+4y=0 which subtends a right angle at origin passing through fixed point
Answer» (1,2) (1,-2) (2,1) (2,2,) ANSWER :B

Discussion

8600.	The sum of the intercepts cut offby the axes on line x+y=a, x+y =ar, x+=ar^(2),………. " where " a ne 0 and r=1/2
Answer» 2A `asqrt2` `2sqrt2a` a Answer :C

Discussion

Explore topic-wise InterviewSolutions in .

Match the following

sin h^(-1) ((x)/(sqrt(1 - x^(2)))) =

Which of the following sentences are statements? Give reasons for your answer: The sum of all interior angles of a triangle is 180^(@)

State which of the following statements are true and which are false. Justify your answer. 3 in {x |x^(4)-5x^(3)+2x^(2)-112x+6=0}

U= {h, i, j, k, l, m, n, o, p} then find the complement of the following sets :B= {j, k, l, m}

If cos(theta - alpha)=a, cos(theta-beta)=b, then sin^(2)(alpha -beta) + 2abcos(alpha-beta)=0

If z=4 + 3i, then verify that-|z| lt I m (z) le |z|

If points ( x , 0) , ( 0 , y) and ( 1 , 1) are collinear, then(1)/(x) +(1)/(y) = .......

The set A has 3 elements how many relations are there from A to A.

A straight line parallel to the line y=sqrt(3)x passes through Q(2,3) and cuts the line 2x+4y-27=0 at P. Find the lengh of PQ.

If z=x +iy is purely real number such that x lt 0 then arg (z) is

If A(3,4) and B is a variable point on the lines |x|=6.If ABle4 then number of positions of B with integral co ordinates is :

Express the following expression in the form of a+lb: (5+sqrt(2)i)/(1-sqrt(2)i)

If x sin y = 3 sin y + 4 cos y , then (dy)/(dx) =

( a- b) ^(2) cos ^(2) ""(C ) /(2) + ( a+b) ^(2) sin ^(2) "" ( C )/(2)=

Differentiate the following functions w.r.t. x: cos (2x-3)

If the point (3, -2) transformed to (-2, 1) when origin shifted to P then P =

Two finite sets have m and n elements. The number of subsets of the first set is 112 more than of the second set. The values of m and n are, respectively.

Two unbiased dice are thrown . Find the probability that both the dice show the same number .

The periodof sin (pix )/( n )- cos ((pi x)/( n+1))is

IfA and B be the points (3,4,5) and (-1,3,-7) respectively find the equation of the set of points P such that PA^(2)+PB^(2)=K^(2) where k is a constant

Explain the use of screw gauge and vernier caliper in measuring smaller distances.

If 4 cot 2 theta=cot^(2)theta-tan^(2)theta then theta=

…….is the interval from of the set {"x"in R |-5

A function is matched below agnaist an interval where it is supposed to be increasing. Which of the following pair is incorrectly matched

A (1,2) and B(7,10) are two fixed points. If P(x,y) is such that a point where angleAPB=60^@ and the area of DeltaAPB is maximum then the point P

If f(x)=(x+1)^(2)-1, x ge -1 then the set S={x, f(x)=f^(-1)x} is

Ifa_0 = x, a_( n+1) = f(a_n) , " where"n = 0,1,2……… then answer the following questions If f(x)=""^(m) sqrt( (a- x^(m))), x gt 2=0, m ge 2 , m in Nthen

cos""(2pi)/(15)cos""(4pi)/(15)cos""(8pi)/(15)cos"(16pi)/(15)=(1)/(16)

Write the first five terms of the sequences in obtain the corresponding series: a_(1)= a_(2)= 1, a_(n)= a_(n-1) + a_(n-2), n gt 2

Find the slope of a line parallel to the line which passes throughthepoints: (-a, 0) and (0, b)

Given|vec (x_1) | = 47.5 , |vec (x_2)|= 52.5. and theta = 0Then | vec (x_1) - vec (x_2)|=

The p^(th), q^(th) and r^(th) terms of an A.P. are in geometric progression then common ratio for G.P is…….

If a le cos theta + 3sqrt(2) sin [theta + (pi)/4] + 6 le b, find largest value of a and smallest value of b.

If 'n' is a positive integer then prove that the coefficient fox^(m) in the expansion of (x^(2)+(1)/(x))^(2n) is :

(k+1)^(15) derivative of (x+1)^(k) is:

Solve sqrt(5)x^(2) + x+ sqrt(5)=0

If bara. barb = barb. barc = barc . bara = 0 then [bara barb barc] =

Obtain equation of the circle which makes intercept of leght 6 unit on X - axis and touches Y - axis at the distance 4 unit from the origin.

A five digit number is formed at random by using the digits 1, 2, 3, 4, 5, 6 and 7. How many five digit numbers formed will have distinct digits?

For which value of k will the equations x^(2)-kx-21=0 and x^(2)-3kx+35=0 have one common root ?

Calculate the standard deviation of the following data:

If cos^(-1)[(cos alpha+ cos beta)/(1+cos alpha cos beta)]=2 Tan^(-1)x then x=

If the acute angle between the pair of lines x^(2)+4sqrt2xy+lamday^(2)=0 is (pi)/(6) then lamda=

Solve x^(2) + 3x + 5=0

Calculate the standard deviation of the following data:

If vec(a)= 2vec(i) -vec(j) + 3vec(k), vec(b)= p vec(i) + vec(j) + q vec(k) and vec(b) xx vec(a) = vec(0), then

All chords of a curve 3x^(2)-y^(2)-2x+4y=0 which subtends a right angle at origin passing through fixed point

The sum of the intercepts cut offby the axes on line x+y=a, x+y =ar, x+=ar^(2),………. " where " a ne 0 and r=1/2