14949 + Interview Questions in Maths in Class 11 Page 193 InterviewSolution

9601.	With the usual meaning for a,b,c and s if Deltabe the area of a triangle then the error inDeltaresulting from a small error in the measurement of c, is
Answer» `Delta/4(1/s+1/(s-a)+1/(s-b)-1/(s-c))DELTAC` `1/4(1/s+1/(s-a)+1/(s-b)+1/(s-c))deltac` `Delta/4(1/s+1/(s-a)+1/(s-b)+1/(s-c))` `(1/s+1/(s-a)+1/(s-b)+1/(s-c))deltac` ANSWER :A

Discussion

9602.	Find the Cartesian equation of the plane passing through the points with position vectors bar(i), bar(j) and bar(k).
Answer» ANSWER :`x+y+z=1`

Discussion

9603.	Solve 3x-6>=0 graphically in two dimensional plane.
Answer» Answer :the solution REGION is the shaded region on the RIGHT hand side of the line `X = 2`.

Discussion

9604.	A, B, C are projections oof P(5, -2, 6) on coordinate planes then find the centroid of triangle ABC.
Answer» `(10/3,(-4)/3,4)` `(5/3,(-2)/3,2)` `(15/2,-3,4)` (5,-2,6) ANSWER :B

Discussion

9605.	Find the smallest positive integer n, for which ((1+i)/(1-i))^(n)=1
Answer» ANSWER :n=4

Discussion

9606.	Find the roots of the equations. Q. (x^(2)+8)/(11)=5x-x^(2)-5
Answer» ANSWER :`2(1)/(3),2(1)/(4)`.

Discussion

9607.	Find the mean of the given data 57,64,43,67,49,59,44,47,61,59.
Answer»

Discussion

9608.	Number of solution (s) of the equation sin x = [x] where [] where []denotes greatest integer function is
Answer» 1 2 0 infinite Answer :B

Discussion

9609.	2 le 3x -4le 5
Answer» ANSWER :`[2,3]`

Discussion

9610.	A candidate is required to answer 7 questions out of 12 questions, which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. Find the number of different ways of doing questions.
Answer» ANSWER :780

Discussion

9611.	If two shorter sides of a triangle measure 9 and 18. If the internal angle bisector drawn to the longest side is 8 then length of longest side of the triangle.
Answer» 15 18 21 25 Answer :C

Discussion

9612.	Compute the following limits : Lt_(xtoa)(tanx-tana)/(x-a)
Answer» ANSWER :`SEC^(2)a`

Discussion

9613.	Evaluate the following limits : Lim_(x to oo) [ x - sqrt((x^(2)+x))]
Answer» ANSWER :`1/2`

Discussion

9614.	Write the following as intervals : {x : x ∈ R, 3 ≤ x ≤ 4}
Answer» ANSWER :`=(3, 4)`

Discussion

9615.	Match the following
Answer» 1-a,2-b,3-C 1-c,2-a,3-b 1-b,2-c,3-a 1-c,2-b,3-a Answer :C

Discussion

9616.	A ballon is in the shape of a cone surmounted by a semi sphere. The radius of a sphere is equal to the height of the cone. If the height of the ballon is 2 then the rate of change in its volume is ……..times the rate of change in its height.
Answer» `4PI` `6PI` `12pi` `8pi` ANSWER :C

Discussion

9617.	Evaluate sqrt(((76.24)^(5) xx root(3)(65))/((3.2)^(7) xx sqrt(17))).
Answer» Solution :Let `x = sqrt(((76.24)^(5) xx ROOT(3)(65))/((3.2)^(7) xx sqrt(17)))`. Then, log `x = 1/2 * log {((76.24)^(5) xx (65)^(1/3))/((3.2)^(7) xx (17)^(1/2))}` `= 1/2 * {5 log (76.24) + 1/3 log 65 - 7log (3.2) - 1/2 log 17}` `= 1/2 * {5 xx 1.8822 + 1/3 xx 1.8129- 7 xx 0.5051 - 1/2 xx 1.2304}` `= 1/2 * {9.4110 + 0.6043 - 3.5357 - 0.6152}` `= 1/2 xx (10.0153 - 4.1509) = 1/2 xx 5.8644 = 2.9322` `rArr` x = antilog (2.9322) = 855.5. Hence, the REQUIRED value of the GIVEN expression is 855.5.

Discussion

9618.	A coin is tossed three times, consider the following events. A : 'No head appears, B : 'Exactly one head appears' and C: 'At least two heads appear'. Do they form a set of mutually exclusive and exhaustive events?
Answer» Answer :YES, they form a set A, B and C are MUTUALLY exclusive and exhaustive EVENTS

Discussion

9619.	If the period of ( cos ( sin(nx)))/(tan""(x//n)), n in N is 6pi then n=
Answer» ANSWER :6

Discussion

9620.	If these coefficients are equal , prove that r=14
Answer» SOLUTION :`"^43C_(r+1]]

Discussion

9621.	The standard deviation of four consecutive numbers in A.P. is sqrt5 .The common difference of A.P. is ………
Answer» `pm 2sqrt5` `pm sqrt2` `pm 2` `pm SQRT5` ANSWER :C

Discussion

9622.	If vec(r ) xx vec(a) = vec(b) xx vec(a), vec(r ) xx vec(b) = vec(a) xx vec(b), vec(a) ne vec(0), vec(b) ne vec(0), vec(a) ne lamda vec(b) and vec(a) is not perpendicular to vec(b), then vec(r )=
Answer» `VEC(a) - vec(B)` `vec(a) + vec(b)` `(vec(a) XX vec(b)) + vec(a)` `(vec(a) xx vec(b)) + vec(b)` ANSWER :B

Discussion

9623.	Evaluate Lim_(x to a ) (x^(3/5) -a^(3/5))/(x^(1/3)-a^(1/3))
Answer» ANSWER :`9/5 a^(4/15)`

Discussion

9624.	Find delta and dy for y = x^(2) + 3x + 6 when x = 10, delta x = 0.01
Answer» Answer :`(2X + 3)DELTA X (x^(2) + 3X + 6)`

Discussion

9625.	Find the equation of the circle with centre (-3,2) and radius 4.
Answer» ANSWER :`(x+3)^(2)+(y-2)^(2)=16`

Discussion

9626.	Write down the equation of the straight line cuttting off intercepts a and b from the axes where a = -k/(m), b= k
Answer» ANSWER : `mx-y+k=0`

Discussion

9627.	In Delta ABC, if tan A, tan B, tan C are in H.P., then a^2,b^2,c^2 are in
Answer» G.P. A.P. H.P. A.G.P Answer :B

Discussion

9628.	Prove that line passes from the points A( 4, -6) and B(-2, -5) makes obtuse angle with X- axis.
Answer» ANSWER :`TAN^(-1)""((2)/(3))`

Discussion

9629.	If sin (y+z-x), sin (z+x-y), sin (x+y-z) are in A. P , then prove that x , tan y, tanz are also in A.P.
Answer» A.P. G.P. H.P. NONE of these ANSWER :A

Discussion

9630.	The side of a cube is equal to the radius of a shpere. If the side and the radius increase at the same rate, then the relation between the rates of change of surface areas of the cube and sphere respectively is
Answer» `LT` `GT` `=` `GE` ANSWER :A

Discussion

9631.	Ifcos alpha = (3)/(5) , cos beta =(5)/(13) , "then " cos^(2) ((alpha - beta )/(2))=
Answer» `1/65` `63/65` `64/65` `2/65` ANSWER :C

Discussion

9632.	The three sides of a trapezium are equal , each being 8 cm . Thearea of the trapezium , when it is maximum , is
Answer» `24sqrt(3)CM^(2)` `48sqrt(3)cm^(2)` `72sqrt(3)cm^(2)` `36sqrt(3)cm^(2)` ANSWER :B

Discussion

9633.	When a is irrational, the number of solutions satisfying the equation 1 + sin^(2) ax = cos x is
Answer» `X=a` `x=0` `x=(a)/(2)` `x=2a` ANSWER :B

Discussion

9634.	if ((n),(r)) + ((n),(r-1)) = ((n + 1),(x)), then x = ....
Answer» N - R r + 1 n n - r + 1 Answer :D

Discussion

9635.	show that the set of all point satisfying \|z-1\|=\|z-i\| represents a line passing through origin with slope -1.
Answer» ANSWER :`-48`

Discussion

9636.	Slopes of the linesmaking an angle 45^(@) with the line x-2y=3 are
Answer» `3,-1//3` `2,-1//2` `-3,1//3` `1,-1` ANSWER :A

Discussion

9637.	Assertion (A) : InDelta ABCa,b, c denotes lengths of the sides and\|{:(a,b,c),(b,c,a),(c,a,b):}\| then the triangle is equilateral triangle Reason (R ): Sum of three non-negativenumber = 0rArreach number is zero
Answer» A is true, R is true and R is correct EXPLANATION of A A is true, R is true and R is not correct explanation of A A is true, R is FALSE A is false, R is true Answer :A

Discussion

9638.	Obtain the equation of the parabola with given conditions:Focus (4,0) and directrix is x + 4 = 0.
Answer» ANSWER :`y^(2) = 16X`

Discussion

9639.	S_(n) is the sum of n terms of an A.P. If S_(2n)= 3S_(n) then prove that (S_(3n))/(S_(n))= 6
Answer» 4 6 8 10 Answer :B

Discussion

9640.	The value of cot(sum_(n=1)^(23)cot^(-1)(1+sum_(k=1)^(n)2k)) is
Answer» `23/25` `25/23` `23/24` `24/23` ANSWER :B::C::D

Discussion

9641.	Find the area of the parallelogram whose adjacent sides are bar(a) = 2 bar(j) - bar(k), bar(b) = -bar(i) + bar(k).
Answer» ANSWER :`2 VEC(i) + vec(J) + 2vec(k)`, 3 SQ. units

Discussion

9642.	Observe the following statements : List-I: (A) If x+y=k then x^2+y^2is minimum if,(B) If x+y=20 then P=xy, what is value of P (C) the minimum value of"64sectheta+27cosectheta" when theta in (0,pi//2),("D) the greatest value of (logx)/xList-2:1) 1252) x=y3) 1004)e5) 1/e
Answer» A-3,B-1,C-2,D-4 A-2,,B-1,C-4,D-3 A-3,B-1,C-2,D-5 A-2,B-3,C-1,D-5 Answer :D

Discussion

9643.	The minimum and maximum values of sin^(2) (60^(@)-x) + sin^(2) ( 60^(@) + x) are
Answer» `- (1)/(2) , (1)/(2)` `(1)/(2) , 1` `(1)/(2) , (3)/(2)` `(3)/(2) , 2` ANSWER :C

Discussion

9644.	Find lim_(xto1)f(x), where f(x)={lim_(-x^(2)-1,xgt1)overset(x^(2)-1,xle1)
Answer» ANSWER :-2

Discussion

9645.	Differentiate the following functions w.r.t. x: cosec""(2)/(3) x
Answer» Answer :`(-2)/(3) cosec"" (2)/(3) X COT""(2)/(3) x`

Discussion

9646.	Find the value of ( sqrt(2) + 1)^(6) + ( sqrt(2) - 1)^(6) and show that the value of ( sqrt(2) + 1)^(6) lies between 197 and 198.
Answer» ANSWER :`=197`

Discussion

9647.	If A, B and C are three disjoint sets such that n(A) = 9, n(B) = 7, n(c) =4 then n(AcupB cupC) = ..... .
Answer» ANSWER :20

Discussion

9648.	IfP standsforP_(r)then the sum of the series1 + P_(1) + 2P_(2) + 3P_(3) + …+ nPn is
Answer» <P>`P_(n+1)` `P_(n+1) -1` `P_(n+1)+1` `.^(n+1)P_(n-1)` ANSWER :B

Discussion

9649.	Represent the complex numbers(1+7i)/((2-i)^(2)) in polar form
Answer» Answer :`sqrt2 ("COS"(3PI)/(4) + "i sin"(3pi)/(4))`

Discussion

9650.	Using binomial theorem, expand each of the following:(1+x/2-2/x)^(4),x!=0
Answer» Solution :`(1+x/2-2/x)^(4) = {1 + (x/2-2/x)}^(4)` `(1+y)^(4) " where " (x/2 - 2/x)=y` `=^(4) C_(0) + .^(4)C_(1)y + .^(4)C_(2)y^(2) + .^(4) C _(3)y^(3) + .^(4)C_(4)y^(4)` `1+ 4y+ 6y^(2) + 4y^(3) + y^(4)` ` 1+ 4 (x/2-2/x)+ 6 ( x/2-2/x)^(2) + 4(x/2- 2/x)^(3) + ( x/2-2/x)^(4)` `=1+ ( 2x - 8/x) + 6 ( x^(2)/4 + 4/x^(2)-2) + 4[.^(3)C_(0)(x/2)^(3)-.^(3)C_(1) (x/2)^(2) (2/x)+.^(3)C_(2)(x/2)(2/x)^(2) -.^(3) C_(3) (2/x)^(3)]` `[.^(4) C_(0) (x/2)^(4)-.^(4)C_(1)(x/2)^(3) (2/x)+.^(4)C_(2)(x/2)^(2)(2/x)^(2)-.^(4)C_(3) (x/2)(2/x)^(3) + .^(4)C_(4)(2/x)^(4)]` `= 1+(2x-8/x)+((3X^(2))/2+ 24/x^(2) - 12 ) + 4 [ x^(3)/8 - 3/2 x +6.x - 8/x^(3)] + [x^(4)/16 - x^(2) + 6 - 16/x^(2) + 16/x^(4)]` `=1 + (2x-8/x)+ ((3x^(2))/2 +24/x^(2) - 12)+(x^(3)/2-6x+24/x-32/x^(3)) +(x^(4)/16 - x^(2) + 6 - 16/x^(2) + 16/x^(4))` `x^(4)/16 + x^(3)/2 + x^(2)/2 - 4x - 5 + 16/x +8/x^(2) - 32/x^(3) + 16/x^(4)`

Discussion

Explore topic-wise InterviewSolutions in .

With the usual meaning for a,b,c and s if Deltabe the area of a triangle then the error inDeltaresulting from a small error in the measurement of c, is

Find the Cartesian equation of the plane passing through the points with position vectors bar(i), bar(j) and bar(k).

Solve 3x-6>=0 graphically in two dimensional plane.

A, B, C are projections oof P(5, -2, 6) on coordinate planes then find the centroid of triangle ABC.

Find the smallest positive integer n, for which ((1+i)/(1-i))^(n)=1

Find the roots of the equations. Q. (x^(2)+8)/(11)=5x-x^(2)-5

Find the mean of the given data 57,64,43,67,49,59,44,47,61,59.

Number of solution (s) of the equation sin x = [x] where [*] where [*]denotes greatest integer function is

2 le 3x -4le 5

A candidate is required to answer 7 questions out of 12 questions, which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. Find the number of different ways of doing questions.

If two shorter sides of a triangle measure 9 and 18. If the internal angle bisector drawn to the longest side is 8 then length of longest side of the triangle.

Compute the following limits : Lt_(xtoa)(tanx-tana)/(x-a)

Evaluate the following limits : Lim_(x to oo) [ x - sqrt((x^(2)+x))]

Write the following as intervals : {x : x ∈ R, 3 ≤ x ≤ 4}

Match the following

A ballon is in the shape of a cone surmounted by a semi sphere. The radius of a sphere is equal to the height of the cone. If the height of the ballon is 2 then the rate of change in its volume is ……..times the rate of change in its height.

Evaluate sqrt(((76.24)^(5) xx root(3)(65))/((3.2)^(7) xx sqrt(17))).

A coin is tossed three times, consider the following events. A : 'No head appears, B : 'Exactly one head appears' and C: 'At least two heads appear'. Do they form a set of mutually exclusive and exhaustive events?

If the period of ( cos ( sin(nx)))/(tan""(x//n)), n in N is 6pi then n=

If these coefficients are equal , prove that r=14

The standard deviation of four consecutive numbers in A.P. is sqrt5 .The common difference of A.P. is ………

If vec(r ) xx vec(a) = vec(b) xx vec(a), vec(r ) xx vec(b) = vec(a) xx vec(b), vec(a) ne vec(0), vec(b) ne vec(0), vec(a) ne lamda vec(b) and vec(a) is not perpendicular to vec(b), then vec(r )=

Evaluate Lim_(x to a ) (x^(3/5) -a^(3/5))/(x^(1/3)-a^(1/3))

Find delta and dy for y = x^(2) + 3x + 6 when x = 10, delta x = 0.01

Find the equation of the circle with centre (-3,2) and radius 4.

Write down the equation of the straight line cuttting off intercepts a and b from the axes where a = -k/(m), b= k

In Delta ABC, if tan A, tan B, tan C are in H.P., then a^2,b^2,c^2 are in

Prove that line passes from the points A( 4, -6) and B(-2, -5) makes obtuse angle with X- axis.

If sin (y+z-x), sin (z+x-y), sin (x+y-z) are in A. P , then prove that x , tan y, tanz are also in A.P.

The side of a cube is equal to the radius of a shpere. If the side and the radius increase at the same rate, then the relation between the rates of change of surface areas of the cube and sphere respectively is

Ifcos alpha = (3)/(5) , cos beta =(5)/(13) , "then " cos^(2) ((alpha - beta )/(2))=

The three sides of a trapezium are equal , each being 8 cm . Thearea of the trapezium , when it is maximum , is

When a is irrational, the number of solutions satisfying the equation 1 + sin^(2) ax = cos x is

if ((n),(r)) + ((n),(r-1)) = ((n + 1),(x)), then x = ....

show that the set of all point satisfying |z-1|=|z-i| represents a line passing through origin with slope -1.

Slopes of the linesmaking an angle 45^(@) with the line x-2y=3 are

Assertion (A) : InDelta ABCa,b, c denotes lengths of the sides and|{:(a,b,c),(b,c,a),(c,a,b):}| then the triangle is equilateral triangle Reason (R ): Sum of three non-negativenumber = 0rArreach number is zero

Obtain the equation of the parabola with given conditions:Focus (4,0) and directrix is x + 4 = 0.

S_(n) is the sum of n terms of an A.P. If S_(2n)= 3S_(n) then prove that (S_(3n))/(S_(n))= 6

The value of cot(sum_(n=1)^(23)cot^(-1)(1+sum_(k=1)^(n)2k)) is

Find the area of the parallelogram whose adjacent sides are bar(a) = 2 bar(j) - bar(k), bar(b) = -bar(i) + bar(k).

Observe the following statements : List-I: (A) If x+y=k then x^2+y^2is minimum if,(B) If x+y=20 then P=xy, what is value of P (C) the minimum value of"64sectheta+27cosectheta" when theta in (0,pi//2),("D) the greatest value of (logx)/xList-2:1) 1252) x=y3) 1004)e5) 1/e

The minimum and maximum values of sin^(2) (60^(@)-x) + sin^(2) ( 60^(@) + x) are

Find lim_(xto1)f(x), where f(x)={lim_(-x^(2)-1,xgt1)overset(x^(2)-1,xle1)

Differentiate the following functions w.r.t. x: cosec""(2)/(3) x

Find the value of ( sqrt(2) + 1)^(6) + ( sqrt(2) - 1)^(6) and show that the value of ( sqrt(2) + 1)^(6) lies between 197 and 198.

If A, B and C are three disjoint sets such that n(A) = 9, n(B) = 7, n(c) =4 then n(AcupB cupC) = ..... .

IfP standsforP_(r)then the sum of the series1 + P_(1) + 2P_(2) + 3P_(3) + …+ nPn is

Represent the complex numbers(1+7i)/((2-i)^(2)) in polar form

Using binomial theorem, expand each of the following:(1+x/2-2/x)^(4),x!=0

Number of solution (s) of the equation sin x = [x] where [] where []denotes greatest integer function is