14949 + Interview Questions in Maths in Class 11 Page 252 InterviewSolution

12551.	If y = 2^(-1/x) then dy/dx is:
Answer» `-1/x2^(-1/X-1)` `2^(-1/x)(LOG2)` `(2^(-1/x)(log2))/x^(2)` `(2^(-1/x)/x^(2)` ANSWER :C

Discussion

12552.	IfDelta ABCis right angled at A , thenr_2 + r_3 is equal to
Answer» `r_(1)-R` `r_(1)+r` `r-r_(1)` R Answer :A

Discussion

12553.	A point P is moving on the curve y = 2 x^(2) . Thex coordinate of P is increasing at the rate of 4 units per second . Find the rate at which y coordinate is incerasing when the point is at (2,8).
Answer» ANSWER :32 units/sec

Discussion

12554.	If tantheta=(sinalpha-cosalpha)/(sinalpha+cosalpha), then show that sinalpha+cosalpha=sqrt(2)costheta.
Answer» ANSWER :`SQRT(2)COSTHETA`

Discussion

12555.	If the angles of a triangleare in A.P., a=2c= 4 , then b=
Answer» ` 2SQRT3` ` sqrt(21) ` ` 8` `14` Answer :A

Discussion

12556.	The point A(2,9,12), B(1,8,8),C(-2,11,8) and D(-1,12,12) form
Answer» A PARALLELOGRAM A rhombus A square A rectangle Answer :C

Discussion

12557.	Find the 10th term of the sequence whose sum to n terms is 6n^(2)+7
Answer» ANSWER :114

Discussion

12558.	If x,y,z are non zero real numbers and if x cos theta=y cos (theta+(2pi)/3)=z cos (theta+(4pi)/3) for some theta in R then show that xy+yz+zx=0
Answer» `-1` 1 0 2 Answer :C

Discussion

12559.	Find the number of terms in the following expansions. (vi) (1+ 3 sqrt(5) x )^(9) - (1-3 sqrt(5) x)^(9)
Answer» ANSWER :`=5`

Discussion

12560.	Assertion (A) : In rolling die, getting number Reason (R) : In a die contains only numbers 1, 2, 3, 4, 5, 6
Answer» Both (A) and (R)are TRUE and (R) is the CORRECT rexplanation of (A) Both (A) and (R) are true but (R) is not the correct EXPLANATION of (A) (A) is true (R) is FALSE (A) is false (R) is true Answer :A::D

Discussion

12561.	Find the radian measures corresponding to the following degree measures: (i) 25 ^(@) (ii)- 47^(@)30 (iii) 240^(@) (iv) 520^(@)
Answer» Answer :`(i) (5pi)/(36)` (ii) ` - (19pi)/(72)` (III) ` (4PI)/(3)` (iv) ` (26 pi)/(9)`

Discussion

12562.	If the sides of a triangle are in A.P. and difference between the greatest and least angles is pi/2, then Sin (B/2) =
Answer» `1/2` `1/(2SQRT2)` `1/(SQRT2)` `sqrt3/2` ANSWER :B

Discussion

12563.	If 2x^(2)-5xy+2y^(2)=0 represents two equal sides of an isosceles triangle and the third side passes through (3,1) then equation of third side is
Answer» x+y=2 x+y=0 x-y=2 x-y=4 Answer :C

Discussion

12564.	If the areas of triangles formed by a plane with the positive x, y, y, z, 2, x axes respectively are 12,9, 6 sq. unit respectively then the equation of the plane is
Answer» `(X)/(4)+(y)/(6)+(z)/(3)=1` `(x)/(6)+(y)/(4)+(z)/(3)=1` `(x)/(3)+(y)/(4)+(z)/(6)=1` `(x)/(3)+(y)/(6)+(z)/(4)=1` Answer :A

Discussion

12565.	Find the standard deviation for the following data :
Answer» ANSWER :6.12

Discussion

12566.	How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if. (i) 4 leters are used at a time, (ii) all letters are used at a time (iii) all letters are used but first letter is a vowel ?
Answer» ANSWER :(i) 360, (ii) 720, (iii) 240

Discussion

12567.	Without repetition of the numbers, four digit numbers are formed with the numbers 0, 2, 3, 5. The probability of such a number divisibele by 5 is
Answer» `(1)/(5)` `(4)/(5)` `(1)/(30)` `(5)/(9)` ANSWER :D

Discussion

12568.	If (Tan^(-1)x)^(2)+(Cot^(-1)x)^(2)=(5pi^(2))/8 then =
Answer» -1 1 0 2 Answer :A

Discussion

12569.	How many number between 99 and 1000 are there if (i) Last digit is 0 ? (ii) Last digit is 5 ?
Answer» ANSWER :90 , 90

Discussion

12570.	sin^(-1)(4/5)+sin^(-1)(5/13)+sin^(-1)(16/65)=
Answer» 1)`(pi)/4` 2)`(pi)/2` 3)`(pi)/3` 4)`(pi)/6` ANSWER :B

Discussion

12571.	Express each of the following complex number in the form a+ib: i^(998)
Answer» ANSWER :`1+0.i`

Discussion

12572.	Set A has 3 elements. Set B has 4 elements. The number of surjections that can be defined from A to B is
Answer» 144 12 0 64 Answer :C

Discussion

12573.	Observe the following statements Assertion (A) : The general solution for costheta=(3)/(2) is theta=2npipmcos^(-1)(3//2) Reason (R ) : The general solution for costheta=k is theta=2npipmalpha, n inz where 'alpha' is principal value, alpha in[0,pi] and \|k\|le1. Then the true statement among the following is
Answer» A is true, R is false A is false, R is true A is true, R is true, R IMPLIES A A is false, R is false Answer :B

Discussion

12574.	Reduce the equation in the Normal form -x+y+4=0 . Findits perpendicular distance from the origin and angle between perpendicular and the positive x- axis .
Answer» ANSWER :`2sqrt(2),315^(@)`

Discussion

12575.	The maximum value of cos^(2)(45^(@)+x)(sin x - cos x)^(2) is _______
Answer» ANSWER :3

Discussion

12576.	The sides of a cyclic quadrilateral are 3,3,4,4 when its area is greatest then radius of circle inscribed in it is
Answer» `(1)/(7)` `(6)/(7)` `(12)/(7)` `(22)/(7)` Answer :C

Discussion

12577.	Let C be incircle of DeltaABC. If the tangents of lengths t_(1),t_(2) and t_(3) are drawn inside the given triangle parallel to sides a, b and c, respectively, then (t_(1))/(a)+(t_(2))/(b)+(t_(3))/(c) is equal to
Answer» 0 1 2 3 Answer :B

Discussion

12578.	The range of f(x)= [ sin x+ [ tan x+ [secx ]]] , x in (0, (pi )/(4))where [.]denotes greatest integer function is
Answer» [0, 1] [-1, 0, 1] {1} {0} ANSWER :C

Discussion

12579.	A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn from the box, what is the probability that (i) all will be blue? (ii) atleast one will be green?
Answer» Answer :(i) `(""^(20)C_(5))/(""^(60)C_(5))` (ii) `1 - (""^(30)C_(5))/(""^(60)C_(4))`

Discussion

12580.	Find the values of theta lying between 0^(@) and 360^(@) when costheta=sin 285^(@).
Answer» ANSWER :`165^(@),195^(@)`

Discussion

12581.	A and B are two fixed points the vertex C and DeltaABC move such that cotA+cotB is contant the locus of C is
Answer» a LINE PERPENDICULAR to AB a line PARALLEL to AB a parabola not a STRAIGHT line Answer :A

Discussion

12582.	Find the derivative from the left and from the right at x=1 (if they exist) of the following functions. Are the functions differentiable at x=1? (i) f(x) = \|x-1\| (ii) f(x) = sqrt(1-x^2) (iii) f(x) = {{:(x, x le 1),(x^2, x gt 1):}
Answer» ANSWER :(i) `therefore F` is not DIFFERENTIABLE at `x=1`. (II) `therefore f` is not differentiable at `x=1`. (iii)`therefore f` is not differentiable at `x=1`.

Discussion

12583.	A coin is toosed three times consider the following events. A:'No head appears', B: 'Exactly one head appears' and C: 'Atleast two heads appear'.
Answer» ANSWER :` = 0.1 + 0.2 + 0.3 + 0.4 + 0.5 + 0.6 = 2.1`

Discussion

12584.	Lt_(xto0)(2x-log(1+2x))/x^(2)
Answer» ANSWER :2

Discussion

12585.	Calculate Kari Pearson's coefficient of correlation between the values of x and y for the following data : n = 10, sum x = 55, sum y = 40, sum x^(2) = 385, sum y^(2) = 192 and sum (x + y)^(2) = 947
Answer» ANSWER :`-0.68`

Discussion

12586.	Let f and g be two diffrentiable functions on R such that f'(x) gt 0 and g'(x) lt 0 for all x in R. Then for all x
Answer» `F(G(X)) GT f(g(x-1))` `f(g(x)) gt f(g(x+1))` `g(f(x)) gt g(f(x+1))` `g(f(x)) gt g(f(x+1))` Answer :B

Discussion

12587.	Find the derivative of the following functions from first principle: sin(x+1)
Answer» ANSWER :`COS(x+1)`

Discussion

12588.	Everybody in a room shakes hands with everybody else. If the total number of hand shakes is 66, then the total number of personsin the room is
Answer» 11 12 13 14 Answer :A::B

Discussion

12589.	If (2, 1), (-1, -2), (3, 3) are midpoints of sides BC, CA, AB of DeltaABC, then the equation of AB is
Answer» `x-y=1` `x+y=1` `x-y=9` `x-y=0` ANSWER :D

Discussion

12590.	Find the value of \|(1+i)((2+i))/((3+i))\|
Answer» ANSWER :1

Discussion

12591.	f(x) is linear function of the type mx + c and f(-1) = -5 and f(3) = 3 then values of m and c are ….and ….. .
Answer» `a=-3, B= -1` `a= 2, b= -3` `a=0, b=2` `a= 2, b= 3` ANSWER :B

Discussion

12592.	If 0 lt cos^(-1)x lt 1 and 1+sin(cos^(-1)x)+sin^(2)(cos^(-1)x)+sin^(3)(cos^(-1)x)+…infty=2, then the value of 12x is
Answer» ANSWER :6ROOT(3)

Discussion

12593.	If the sides of the triangle are 13,14,15 then the radius of the incircle is
Answer» `(65)/(8)` `(65)/(4)` 4 24 Answer :C

Discussion

12594.	Sin^(-1)(4/5)+2Tan^(-1)""1/3=
Answer» `PI` `(pi)/2` `(pi)/4` `(3PI)/4` Answer :B

Discussion

12595.	2^(2n)-3n-1 is divisible by ........... .
Answer» ANSWER :9

Discussion

12596.	Find the sum of the series 81 -27 +9 - ...... -(1)/(27) .
Answer» ANSWER :`60 (20)/(27)`

Discussion

12597.	Show that the products of the corresponding terms of the sequences a, ar, ar^2 ,…ar^(n – 1)and A, AR, "AR"^22, … "AR"^(n – 1)form a G.P, and find the common ratio.
Answer» ANSWER :RR

Discussion

12598.	If Sin^(-1)(3/x)+Sin^(-1)(4/x)=pi/2 then x =
Answer» 3 5 7 11 Answer :B

Discussion

12599.	Solve\|(a-x,a+x,a+x),(a+x,a-x,a+x),(a+x,a+x,a-x)\|=0.Using factor theorem
Answer» ANSWER :x=0,x=-3a

Discussion

12600.	The sum of four consecutive terms of an A.P is 32. The product of the second and the third term is 60. Find these terms.
Answer» ANSWER :`2,6,10,14`

Discussion

Explore topic-wise InterviewSolutions in .

If y = 2^(-1/x) then dy/dx is:

IfDelta ABCis right angled at A , thenr_2 + r_3 is equal to

A point P is moving on the curve y = 2 x^(2) . Thex coordinate of P is increasing at the rate of 4 units per second . Find the rate at which y coordinate is incerasing when the point is at (2,8).

If tantheta=(sinalpha-cosalpha)/(sinalpha+cosalpha), then show that sinalpha+cosalpha=sqrt(2)costheta.

If the angles of a triangleare in A.P., a=2c= 4 , then b=

The point A(2,9,12), B(1,8,8),C(-2,11,8) and D(-1,12,12) form

Find the 10th term of the sequence whose sum to n terms is 6n^(2)+7

If x,y,z are non zero real numbers and if x cos theta=y cos (theta+(2pi)/3)=z cos (theta+(4pi)/3) for some theta in R then show that xy+yz+zx=0

Find the number of terms in the following expansions. (vi) (1+ 3 sqrt(5) x )^(9) - (1-3 sqrt(5) x)^(9)

Assertion (A) : In rolling die, getting number Reason (R) : In a die contains only numbers 1, 2, 3, 4, 5, 6

Find the radian measures corresponding to the following degree measures: (i) 25 ^(@) (ii)- 47^(@)30 (iii) 240^(@) (iv) 520^(@)

If the sides of a triangle are in A.P. and difference between the greatest and least angles is pi/2, then Sin (B/2) =

If 2x^(2)-5xy+2y^(2)=0 represents two equal sides of an isosceles triangle and the third side passes through (3,1) then equation of third side is

If the areas of triangles formed by a plane with the positive x, y, y, z, 2, x axes respectively are 12,9, 6 sq. unit respectively then the equation of the plane is

Find the standard deviation for the following data :

How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if. (i) 4 leters are used at a time, (ii) all letters are used at a time (iii) all letters are used but first letter is a vowel ?

Without repetition of the numbers, four digit numbers are formed with the numbers 0, 2, 3, 5. The probability of such a number divisibele by 5 is

If (Tan^(-1)x)^(2)+(Cot^(-1)x)^(2)=(5pi^(2))/8 then =

How many number between 99 and 1000 are there if (i) Last digit is 0 ? (ii) Last digit is 5 ?

sin^(-1)(4/5)+sin^(-1)(5/13)+sin^(-1)(16/65)=

Express each of the following complex number in the form a+ib: i^(998)

Set A has 3 elements. Set B has 4 elements. The number of surjections that can be defined from A to B is

Reduce the equation in the Normal form -x+y+4=0 . Findits perpendicular distance from the origin and angle between perpendicular and the positive x- axis .

The maximum value of cos^(2)(45^(@)+x)(sin x - cos x)^(2) is _______

The sides of a cyclic quadrilateral are 3,3,4,4 when its area is greatest then radius of circle inscribed in it is

Let C be incircle of DeltaABC. If the tangents of lengths t_(1),t_(2) and t_(3) are drawn inside the given triangle parallel to sides a, b and c, respectively, then (t_(1))/(a)+(t_(2))/(b)+(t_(3))/(c) is equal to

The range of f(x)= [ sin x+ [ tan x+ [secx ]]] , x in (0, (pi )/(4))where [.]denotes greatest integer function is

A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn from the box, what is the probability that (i) all will be blue? (ii) atleast one will be green?

Find the values of theta lying between 0^(@) and 360^(@) when costheta=sin 285^(@).

A and B are two fixed points the vertex C and DeltaABC move such that cotA+cotB is contant the locus of C is

Find the derivative from the left and from the right at x=1 (if they exist) of the following functions. Are the functions differentiable at x=1? (i) f(x) = |x-1| (ii) f(x) = sqrt(1-x^2) (iii) f(x) = {{:(x, x le 1),(x^2, x gt 1):}

A coin is toosed three times consider the following events. A:'No head appears', B: 'Exactly one head appears' and C: 'Atleast two heads appear'.

Lt_(xto0)(2x-log(1+2x))/x^(2)

Calculate Kari Pearson's coefficient of correlation between the values of x and y for the following data : n = 10, sum x = 55, sum y = 40, sum x^(2) = 385, sum y^(2) = 192 and sum (x + y)^(2) = 947

Let f and g be two diffrentiable functions on R such that f'(x) gt 0 and g'(x) lt 0 for all x in R. Then for all x

Find the derivative of the following functions from first principle: sin(x+1)

Everybody in a room shakes hands with everybody else. If the total number of hand shakes is 66, then the total number of personsin the room is

If (2, 1), (-1, -2), (3, 3) are midpoints of sides BC, CA, AB of DeltaABC, then the equation of AB is

Find the value of |(1+i)((2+i))/((3+i))|

f(x) is linear function of the type mx + c and f(-1) = -5 and f(3) = 3 then values of m and c are ….and ….. .

If 0 lt cos^(-1)x lt 1 and 1+sin(cos^(-1)x)+sin^(2)(cos^(-1)x)+sin^(3)(cos^(-1)x)+…infty=2, then the value of 12x is

If the sides of the triangle are 13,14,15 then the radius of the incircle is

Sin^(-1)(4/5)+2Tan^(-1)""1/3=

2^(2n)-3n-1 is divisible by ........... .

Find the sum of the series 81 -27 +9 - ...... -(1)/(27) .

Show that the products of the corresponding terms of the sequences a, ar, ar^2 ,…ar^(n – 1)and A, AR, "AR"^22, … "AR"^(n – 1)form a G.P, and find the common ratio.

If Sin^(-1)(3/x)+Sin^(-1)(4/x)=pi/2 then x =

Solve|(a-x,a+x,a+x),(a+x,a-x,a+x),(a+x,a+x,a-x)|=0.Using factor theorem

The sum of four consecutive terms of an A.P is 32. The product of the second and the third term is 60. Find these terms.