14949 + Interview Questions in Maths in Class 11 Page 171 InterviewSolution

8501.	R= {(x,y): x, y in N, x + y= 8}. Find the domain and range of R.
Answer» ANSWER :DOMAIN of R = {1, 2, 3,4,5,6,7}

Discussion

8502.	Given the complex number z= (-1 + sqrt3i)/(2) and w= (-1- sqrt3i)/(2) (where i= sqrt-1) Represent z and w accurately on the complex plane.
Answer» <P> Answer :W and Z are represented by `p((-1)/(2), (-sqrt3)/(2)) and Q ((-1)/(2), (sqrt3)/(2))` respectively

Discussion

8503.	Prove that the equation2x^(2)+3xy-2y^(2)-x+3y-1=0 represents a pair of perpendicular straight lines.
Answer» ANSWER :`a=2,c=-3`

Discussion

8504.	A five digit number is formed at random by using the digits 1, 2, 3, 4, 5, 6 and 7. Find the chance that the number formed has none of its digits is repeated.
Answer» SOLUTION :360/2401

Discussion

8505.	3sinx+4cosx=5implies6tan""(x)/(2)-9tan^(2)""(x)/(2) =
Answer» 0 1 3 4 Answer :B

Discussion

8506.	Two sides of a triangle having the joint equation (x-3y+1)(x+y-2)=0 the third side with is variable always passes through the point (-5,-1), then possible value of slope of the third side such that origin is an interior point of triangle are..
Answer» `(-1,(-1)/5)` `((-1)/5,-1)` (0,2) RR Answer :A

Discussion

8507.	Find the value of f(0) so thatf(x) = ((a + x)^(2) sin (a + x) - a^(2) sin a)/(x)is continuous at x = 0 .
Answer» ANSWER :`a^(2)cosa+2a SIN a`

Discussion

8508.	For x,y,z, t in R, sin^(-1)x+cos^(-1)y+sec^(-1)zget^(2)-sqrt(2pi)t+3pi The principal value of cos^(-1)(cos5t^(2)) is
Answer» `(3PI)/2` `pi/2` `pi/3` `(2PI)/3` Answer :C

Discussion

8509.	A= Set of odd natural numbers B = set of even natural numbers F= {(a,b)\| a.bis even natural number, a inA, b in B}Then domain of relation R is set . A
Answer» ANSWER :TRUE STATEMENT

Discussion

8510.	Rewrite each of the following statements in the form of conditional statements: 2b=a+c if a,b and c are in A.P.
Answer» ANSWER :If a,B and C are in airthmatic SEQUENCE then `2b=a+c`.

Discussion

8511.	Maximum valueof f(x)=x+sin2x,x in [0,2pi] is
Answer» `PI` `2PI` `3PI` `pi//2` ANSWER :B

Discussion

8512.	Find the equation to the locus of points equidistant from the points (-3,2),(0,4)
Answer» A true, R true and R is correct EXPLANATION of A A true, R true but R is not correct explanation of A A true, R FALSE A false, R true Answer :1

Discussion

8513.	Find the 13^(th) term in the expansion of ( 9x-1//3sqrtx)^18, x !=0.
Answer» ANSWER :18564

Discussion

8514.	Find lim_(xrarr0)f(x) and lim_(xrarr1)f(x), where f(x)={{:(6x+3",",xle0),(x+6",",xgt0):}
Answer» ANSWER :7

Discussion

8515.	Determine the conjugate and the reciprocal of each complex number given below: sqrt(-9)-1
Answer» ANSWER :`3i-1, -(1)/(10)- (3)/(10)i`

Discussion

8516.	If P(n) be the statement n (n+1)+1 is an integer, then which of the following is even
Answer» <P>`P(4)` `P(4) +2` `P(4) + 4` `P(4) +1` ANSWER :D

Discussion

8517.	Solution set of inequality \|x-1\| lt -1is set R .
Answer» ANSWER :FALSE STATEMENT

Discussion

8518.	Solution of the equation sin(sqrt(1+sin 2 theta))=sin theta+cos thetais ( n in Z)
Answer» `npi -(pi)/4` `npi +(pi)/12` `N pi +(pi)/6` `n pi -(pi)/6` ANSWER :A

Discussion

8519.	Write the first six terms of an A.P. in whicha=98 , d=-3
Answer» ANSWER :98, 95, 92, 89, 86, 83

Discussion

8520.	Assertion (A) : If cos(x-y) = 3 cos (x + y) then cotx cotx = 2 Reason (R ) : If (a)/(b) = ( c)/(d) then (a+b)/(a-b) = (c+d)/(c-d)
Answer» A is true, R is correct explanation of A A is true , R is true and R is not CORRECTE explanation of A A is true ,R is FALSE A is false, R is true Answer :A

Discussion

8521.	Express the equation 16x^2-9y^2=144 of a hyperbola in standard form
Answer» SOLUTION :`x^2/9-y^2/16=1`

Discussion

8522.	Lives of LG and Samsung Microwaves that are currently popular were observed to be the following in a survey : Compute coefficients of variance for the lives of LG and Sarmsung Microwaves. Which model do you prefer ? Justify.
Answer» Answer :We should PREFER Samsung, since it has higher average LIFE and lower VARIABILITY.

Discussion

8523.	A bag contains tickets numbered 1 to 30. Three tickets are drawn atrandom from the bag. What is the probability that the maximum number on theselected tickets exceeds 25?
Answer» ANSWER :`(88)/(203)`

Discussion

8524.	Find the equation of a line parallel to X- axis and passing through the origin.
Answer» `X^(2) = 4A (y + a)` `y^(2)= 4a (x - a)` `y^(2) = - 4a (x - a)` `NONE of these Answer :A

Discussion

8525.	A and B are events such that P(A)=0,42, P(B) =0.48 and P(A and B) =0.16. Determine (i) P(not A), (ii) P(not B) and (iii) P(A or B)
Answer» ANSWER :(i) 0.58(II) 0.52(III) 0.74

Discussion

8526.	Let f be a function which is continuous and differentiable for all real x. If f(2) = -4 and f'(x) ge 6 for all x in [2,4], then
Answer» `f(4) LT 8` `f(4) ge8` `f(4) GT 12` `f(4) gt 8` ANSWER :B

Discussion

8527.	Write the parametric equations of the line passing through (3,2) and having inclination135^(@)
Answer» ANSWER :PARAMETER

Discussion

8528.	Draw the graphs of the following : y =f(x) ={{:(2x,if,x lt 1 ),(1-x, if, xge1):}
Answer» ANSWER :`(##AKS_ELT_AI_MAT_XI_VIB_P02_C01_E01_020_A01##)`

Discussion

8529.	If upper quartile and inter-quartile range of a data are 55 and 5 respectively, then find the value of lower quartile
Answer» ANSWER :50

Discussion

8530.	Iff : R to Ris continuous such thatf(x + y) = f(x) + f(y) x in R , y in Rand f(1) = 2 then f(100) =
Answer» 100 50 200 0 Answer :C

Discussion

8531.	Let bara=bari+barj+bark,barb=bari-barj+2bark,barc=xbari+(x-2)barj-bark. If the vector barc lie in the plane of bara and barb then x equals to
Answer» 0 1 `-4` `-2` ANSWER :D

Discussion

8532.	In DeltaABC, AD is the altitude from A, if b gt c, C=23^(0), AD=(abc)/(b^(2)-c^(2)) then angle B=
Answer» `93^(@)` `113^(@)` `27^(@)` `103^(@)` ANSWER :B

Discussion

8533.	If tan theta + tan 2theta = tan 3theta, then theta =
Answer» `NPI` `(npi)/4` `(npi)/2` `(npi)/3` ANSWER :A

Discussion

8534.	A person has one currency not each of Rs 500, Rs 100, Rs 50 , Rs 20and Rs 10 . Then in ..........numbers of ways he can made his payments .
Answer» ANSWER :31

Discussion

8535.	Let f(x)) be an increasing function defined on (0.oo) If f(2a^(2)+a+1)gtf(3a^(2)-4a+1), then the possible integers in the range of a is /are
Answer» 1 2 3 4 Answer :B::C::D

Discussion

8536.	If the tangent to the curve 2y^(3)=ax^(2)+x^(3) atthe point cuts off intercepts alpha and beta on the coordinate axes, where alpha^(2)+beta^(2)=61 then the value of \|a\| is
Answer» 16 28 30 31 Answer :C

Discussion

8537.	Fill in the blanks of the following If \|z+4\| le3, then the greatest and least values of \|z+1\| are ... and .....
Answer» ANSWER :`\|z+1\|` is ZERO.

Discussion

8538.	The periodof ((1)/(3))^(sinx) + ((1)/(3))^(cos x) is
Answer» `PI` `(pi)/(2)` `(pi)/(4)` `2PI` ANSWER :D

Discussion

8539.	If y=(sqrt(a+x)-sqrt(a-x))/(sqrt(a+x)+sqrt(a-x)), then dy/dx is equal to
Answer» `(AY)/(xsqrt(a^2-x^2))` `(ay)/SQRT(a^2-x^2)` `(ay)/(xsqrt(x^2-a^2))` `(ay)/(xsqrt(x^2+a^2))` ANSWER :A

Discussion

8540.	With the help of tables, find the values, correct to places of decimals, of each of the following : sin(-263^(@))
Answer» ANSWER :`0.9925`

Discussion

8541.	If A+B+C=180^(0) then match the following
Answer» 1-c, 2-a,3-d ,4-b 1-d,2-b,3-a,4-c 1-a, 2-c, 3-b, 4-d 1-b, 2-d, 3-c, 4-a Answer :A

Discussion

8542.	If sec x + sec^(2) x = 1 then the value of tan^(8) x - tan^(4) x - 2 tan^(2) x +1 will be equal to 0
Answer» 0 1 2 3 Answer :C

Discussion

8543.	Find the mean deviation from the mean for the following data:
Answer» ANSWER :2.09

Discussion

8544.	Two dice are thrown simultaneously. Find the probability of getting an even number as the sum
Answer» ANSWER :`(18)/(36),i.e.,(1)/(2)`

Discussion

8545.	"cot 7" (1^(0))/(2) - "cot 37" (1^(0))/(2) - "cot 52" (1^(0))/(2) + "cot 82" (1^(0))/(2)=
Answer» `4 SQRT(2)` 4 2 1 Answer :A

Discussion

8546.	Express the following as functions of angles less than 45^(@) : cos189^(@)
Answer» ANSWER :`-COS9^(@)`

Discussion

8547.	Biconditional phArrq is ..
Answer» <P>CONJUCTION of `p implies Q` and `q implies p` Disjunctionn `p implies q` and `q implies p` Converse of `p implies q` Contrapositive of `q implies p` Answer :A

Discussion

8548.	A bell tent consists of a conical portion above a cylinder portion near the ground For a given vloume and a circular base of a given radius , the amount of the canvas usedis a minimumwhenthe semi - vertical angle of the cone is
Answer» `COS^(-1)2//3` `SIN^(-1)2//3` `cos^(-1)1//3` `cos^(-1)1//2` ANSWER :A

Discussion

8549.	Write the set {(1)/(2),(2)/(3),(3)/(4),(4)/(5),(5)/(6),(6)/(7)} in the set-builder form.
Answer» ANSWER :`{X : x =(n)/(n+1)," where n is a natural NUMBER and "1 le n le 6}`

Discussion

8550.	Find the number ofpermutations of the letter of the words 'CHANDIGARH'
Answer» ANSWER :` 907200 `

Discussion

Explore topic-wise InterviewSolutions in .

R= {(x,y): x, y in N, x + y= 8}. Find the domain and range of R.

Given the complex number z= (-1 + sqrt3i)/(2) and w= (-1- sqrt3i)/(2) (where i= sqrt-1) Represent z and w accurately on the complex plane.

Prove that the equation2x^(2)+3xy-2y^(2)-x+3y-1=0 represents a pair of perpendicular straight lines.

A five digit number is formed at random by using the digits 1, 2, 3, 4, 5, 6 and 7. Find the chance that the number formed has none of its digits is repeated.

3sinx+4cosx=5implies6tan""(x)/(2)-9tan^(2)""(x)/(2) =

Two sides of a triangle having the joint equation (x-3y+1)(x+y-2)=0 the third side with is variable always passes through the point (-5,-1), then possible value of slope of the third side such that origin is an interior point of triangle are..

Find the value of f(0) so thatf(x) = ((a + x)^(2) sin (a + x) - a^(2) sin a)/(x)is continuous at x = 0 .

For x,y,z, t in R, sin^(-1)x+cos^(-1)y+sec^(-1)zget^(2)-sqrt(2pi)t+3pi The principal value of cos^(-1)(cos5t^(2)) is

A= Set of odd natural numbers B = set of even natural numbers F= {(a,b)| a.bis even natural number, a inA, b in B}Then domain of relation R is set . A

Rewrite each of the following statements in the form of conditional statements: 2b=a+c if a,b and c are in A.P.

Maximum valueof f(x)=x+sin2x,x in [0,2pi] is

Find the equation to the locus of points equidistant from the points (-3,2),(0,4)

Find the 13^(th) term in the expansion of ( 9x-1//3sqrtx)^18, x !=0.

Find lim_(xrarr0)f(x) and lim_(xrarr1)f(x), where f(x)={{:(6x+3",",xle0),(x+6",",xgt0):}

Determine the conjugate and the reciprocal of each complex number given below: sqrt(-9)-1

If P(n) be the statement n (n+1)+1 is an integer, then which of the following is even

Solution set of inequality |x-1| lt -1is set R .

Solution of the equation sin(sqrt(1+sin 2 theta))=sin theta+cos thetais ( n in Z)

Write the first six terms of an A.P. in whicha=98 , d=-3

Assertion (A) : If cos(x-y) = 3 cos (x + y) then cotx cotx = 2 Reason (R ) : If (a)/(b) = ( c)/(d) then (a+b)/(a-b) = (c+d)/(c-d)

Express the equation 16x^2-9y^2=144 of a hyperbola in standard form

Lives of LG and Samsung Microwaves that are currently popular were observed to be the following in a survey : Compute coefficients of variance for the lives of LG and Sarmsung Microwaves. Which model do you prefer ? Justify.

A bag contains tickets numbered 1 to 30. Three tickets are drawn atrandom from the bag. What is the probability that the maximum number on theselected tickets exceeds 25?

Find the equation of a line parallel to X- axis and passing through the origin.

A and B are events such that P(A)=0,42, P(B) =0.48 and P(A and B) =0.16. Determine (i) P(not A), (ii) P(not B) and (iii) P(A or B)

Let f be a function which is continuous and differentiable for all real x. If f(2) = -4 and f'(x) ge 6 for all x in [2,4], then

Write the parametric equations of the line passing through (3,2) and having inclination135^(@)

Draw the graphs of the following : y =f(x) ={{:(2x,if,x lt 1 ),(1-x, if, xge1):}

If upper quartile and inter-quartile range of a data are 55 and 5 respectively, then find the value of lower quartile

Iff : R to Ris continuous such thatf(x + y) = f(x) + f(y) x in R , y in Rand f(1) = 2 then f(100) =

Let bara=bari+barj+bark,barb=bari-barj+2bark,barc=xbari+(x-2)barj-bark. If the vector barc lie in the plane of bara and barb then x equals to

In DeltaABC, AD is the altitude from A, if b gt c, C=23^(0), AD=(abc)/(b^(2)-c^(2)) then angle B=

If tan theta + tan 2theta = tan 3theta, then theta =

A person has one currency not each of Rs 500, Rs 100, Rs 50 , Rs 20and Rs 10 . Then in ..........numbers of ways he can made his payments .

Let f(x)) be an increasing function defined on (0.oo) If f(2a^(2)+a+1)gtf(3a^(2)-4a+1), then the possible integers in the range of a is /are

If the tangent to the curve 2y^(3)=ax^(2)+x^(3) atthe point cuts off intercepts alpha and beta on the coordinate axes, where alpha^(2)+beta^(2)=61 then the value of |a| is

Fill in the blanks of the following If |z+4| le3, then the greatest and least values of |z+1| are ... and .....

The periodof ((1)/(3))^(sinx) + ((1)/(3))^(cos x) is

If y=(sqrt(a+x)-sqrt(a-x))/(sqrt(a+x)+sqrt(a-x)), then dy/dx is equal to

With the help of tables, find the values, correct to places of decimals, of each of the following : sin(-263^(@))

If A+B+C=180^(0) then match the following

If sec x + sec^(2) x = 1 then the value of tan^(8) x - tan^(4) x - 2 tan^(2) x +1 will be equal to 0

Find the mean deviation from the mean for the following data:

Two dice are thrown simultaneously. Find the probability of getting an even number as the sum

"cot 7" (1^(0))/(2) - "cot 37" (1^(0))/(2) - "cot 52" (1^(0))/(2) + "cot 82" (1^(0))/(2)=

Express the following as functions of angles less than 45^(@) : cos189^(@)

Biconditional phArrq is ..

A bell tent consists of a conical portion above a cylinder portion near the ground For a given vloume and a circular base of a given radius , the amount of the canvas usedis a minimumwhenthe semi - vertical angle of the cone is

Write the set {(1)/(2),(2)/(3),(3)/(4),(4)/(5),(5)/(6),(6)/(7)} in the set-builder form.

Find the number ofpermutations of the letter of the words 'CHANDIGARH'