14949 + Interview Questions in Maths in Class 11 Page 157 InterviewSolution

7801.	Two students Anil and Ashima appeared in an examination. The probability that Anil will qualify the examination is 0.05 and that Ashima will qualify the examination is 0.10. The probability that both will qualify the examination is 0.02. Find the probability that (a) Both Anil and Ashima will not qualify the examination. (b) Atleast one of them will not qualify the examination and (c) Only one of them will qualify the examination.
Answer» ANSWER :(a) 0.87 (B) 0.98, (C ) 0.11

Discussion

7802.	Two ships leave a port at the same time. One goes 24 km per hour in the direction N45^(@)Eand other travels 32km per hour in the directions S75^(@)E. Find the distance between the ships at the end of 3 hours.
Answer» ANSWER :`84.53km`

Discussion

7803.	A carpenter was hired to build 192 window frames. The first day he made five frames and each day, thereafter he made two more frames than he made the day before. How many days did it take him to finish the job?
Answer» ANSWER :12

Discussion

7804.	Write the following sets in the set-builder form : {1,4,9, . . .,100}
Answer» ANSWER :`={x : x` is a perfect SQUARE NATURAL NUMBER `1 le x le 10}`

Discussion

7805.	cos[2Sin^(-1)sqrt((1-x)/2)]=
Answer» X `1/x` 2x 3x Answer :A

Discussion

7806.	Write the negation of the following statements: q: There exists a rational number x such that x^(2)=2
Answer» ANSWER :`X^(2)~=2`

Discussion

7807.	Find the Locus of the mid points of the line x cos theta + y sin theta = pintercepted between the axis .
Answer» ANSWER :`p^2(x^2+y^2)`

Discussion

7808.	By eliminating a,b,c from the Homogeneous Equations x=(a)/(b-c),y=(b)/(c-a),z=(c)/(a-b) where a,b,c not all zero then xy+yz+zx=
Answer» 1 `-1` 2 0 Answer :B

Discussion

7809.	Writethe inverse of the given conditionastatement: Ifa number n is even, then n^(2) is even .
Answer» Answer :" If a NUMBER N is ODD , then `n^(2)` is also odd"

Discussion

7810.	Write each of the following statements in the form "if-then" i. You get a job implies that your credentials are good. ii. The bannana trees will bloom if it stays warm for a month. iii. A quadrilateral is a parallelogram if its diagonals bisect each other. iv. to get an A^(+) in the class, it is necessary that you do all the exercises of the book.
Answer» ANSWER :If DIAGONALS of a QUADRILATERAL BISECT each other, then it is a PARALLELOGRAM

Discussion

7811.	Two dice are thrown. The events A, B and C are as follows: A: getting an even number on the first die. B: getting an odd number on the first die. C: getting the sum of the number on the first dice le5. Describe the events (i) A' (ii) not B (iii) A or B (iv) A and B (v) A but not C (vi) B or C (vii) B and C (viii) AnnB'nnC'
Answer» SOLUTION :In a throw of two dice Sample space `S={{:((1,1)","(1,2)","(1,3)","(1,4)","(1,5)","(1,6)),((2,1)","(2,2)","(2,3)","(2,4)","(2,5)","(2,6)),((3,1)","(3,2)","(3,3)","(3,4)","(3,5)","(3,6)),((4,1)","(4,2)","(4,3)","(4,4)","(4,5)","(4,6)),((5,1)","(5,2)","(5,3)","(5,4)","(5,5)","(5,6)),((6,1)","(6,2)","(6,3)","(6,4)","(6,5)","(6,6)):}}` Now `A=` event of getting an even number on first die `={{:((2,1)","(2,2)","(2,3)","(2,4)","(2,5)","(2,6)),((4,1)","(4,2)","(4,3)","(4,4)","(4,5)","(4,6)),((6,1)","(6,2)","(6,3)","(6,4)","(6,5)","(6,6)):}}` `B=` event of getting an odd number of first die `={{:((1,1)","(1,2)","(1,3)","(1,4)","(1,5)","(1,6)),((3,1)","(3,2)","(3,3)","(3,4)","(3,5)","(3,6)),((5,1)","(5,2)","(5,3)","(5,4)","(5,5)","(5,6)):}}` `C=` event of getting the sum NUMBERS less than or equal to 5 `={(1,1,),(1,2),(2,1),(1,3),(2,2),` `(3,1),(1,4),(2,3),(3,2),(4,1)}` `A'=S-A` `={{:((1,1)","(1,2)","(1,3)","(1,4)","(1,5)","(1,6)),((3,1)","(3,2)","(3,3)","(3,4)","(3,5)","(3,6)),((5,1)","(5,2)","(5,3)","(5,4)","(5,5)","(5,6)):}}` (ii) not `B=S-B` `={{:((2,1)","(2,2)","(2,3)","(2,4)","(2,5)","(2,6)),((4,1)","(4,2)","(4,3)","(4,4)","(4,5)","(4,6)),((6,1)","(6,2)","(6,3)","(6,4)","(6,5)","(6,6)):}}` (iii) A or B `={{:((1,1)","(1,2)","(1,3)","(1,4)","(1,5)","(1,6)),((2,1)","(2,2)","(2,3)","(2,4)","(2,5)","(2,6)),((3,1)","(3,2)","(3,3)","(3,4)","(3,5)","(3,6)),((4,1)","(4,2)","(4,3)","(4,4)","(4,5)","(4,6)),((5,1)","(5,2)","(5,3)","(5,4)","(5,5)","(5,6)),((6,1)","(6,2)","(6,3)","(6,4)","(6,5)","(6,6)):}}` (iv) A and `B=phi` (v) A but not `C=A-C` `{(2,4),(2,5),(2,6),(4,2),(4,3),(4,4),(4,5),` `(4,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}` (vi) B or `C=BuuC` `={{:((1,1)","(1,2)","(1,3)","(1,4)","(1,5)","(1,6)),((2,1)","(2,2)","(2,3)),((3,1)","(3,2)","(3,3)","(3,4)","(3,5)","(3,6)),((4,1)), ((5,1)","(5,2)","(5,3)","(5,4)","(5,5)","(5,6)):}}` (VII) B and `C=BnnC` `={1,1),(1,2),(1,4),(3,1),(3,2)}` (viii) `C=S-C` `={{:((1,5)","(1,6)),((2,4)","(2,5)","(2,6)),((3,3)","(3,4)","(3,5)","(3,6)),((4,2)","(4,3)","(4,4)","(4,5)","(4,6)),((5,1)","(5,2)","(5,3)","(5,4)","(5,5)","(5,6)),((6,1)","(6,2)","(6,3)","(6,4)","(6,5)","(6,6)):}}` Now `AnnB'nnC'` `=AnnC' :' B'=A` (from PART II) `={{:((2,4)","(2,5)","(2,6)),((4,2)","(4,3)","(4,4)","(4,5)","(4,6)),((6,1)","(6,2)","(6,3)","(6,4)","(6,5)","(6,6)):}}`

Discussion

7812.	For the function f(x)=(e^(x))/(1+e^(x)), which of the following hold good ?
Answer» The point (1,-7) is the point of INFLECTION `x=e^(1//3)` is the point of minima the graph is concave downwards in (0,1) the graph is concave UPWARDS in `(1,oo)` Answer :A::B::C::D

Discussion

7813.	Draw the graphs of the following : y = [x] in [-3,3]
Answer» ANSWER :`(##AKS_ELT_AI_MAT_XI_VIB_P02_C01_E01_021_A01##)`

Discussion

7814.	If y = "Tan^(-1) (((3-x)sqrt(x))/(1 - 3x)) then (dy)/(dx) =
Answer» `3/((1 + X)sqrt(x))` `3/(2(1 + x) sqrt(x))` `(-3)/(2(1 + x) sqrt(x))` `0` Answer :B

Discussion

7815.	Find the correct statement: Given vec OA =veca, vecOB=vecb and vecOP = (3veca+5vecb)/(8) implies that : P divides the line joining A nd B in the ratio:
Answer» 3:5 internally 5:3 externally 5:3 internally 3:5 externally Answer :C

Discussion

7816.	Find the point on the curve y = x^(2) + 7x + 2 which is closer to the line y = 3x - 3.
Answer» ANSWER :`(-2,-8)`

Discussion

7817.	Find the centre and radiusof equation of circle inx^(2) + y^(2) -x + 2y - 3 = 0
Answer» Answer :CENTRE `((1)/(2), - 1)`, Radius `(SQRT(17))/(2)`

Discussion

7818.	If2 sin ""( A) /( 2) sin ""( C)/(2) = sin "" ( B) /(2)then a,b,c are in
Answer» <P>` A.P ` ` G.P ` ` H. P ` ` A.G. P ` ANSWER :A

Discussion

7819.	The projection of the join of the points (3,4,2), (5,1,8) on the line whose d.c's are ((2)/(7),(-3)/(7),(6)/(7)) is
Answer» 7 `(46)/(13)` `(42)/(13)` `(38)/(13)` Answer :A

Discussion

7820.	The projection of vector bari+barj+bark " on the line whose vector equation is "barr=(3+t)bari+(2t-1)barj+3tbark,t being a scalar, is
Answer» `6/14` `6/(SQRT14)` `3/14` `3/(sqrt14)` ANSWER :B

Discussion

7821.	If y=x/a+a/x then dy/dx = …. .
Answer» ANSWER :`1/(a)-a/(x^2)`

Discussion

7822.	If A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, C = {11, 13, 15} andD = {15, 17}, find A ∩ (B ∪ D)
Answer» ANSWER :`{ 7, 9, 11 }`

Discussion

7823.	Describe the sample space for the indicated experiments. A box contins 1 red 3 identical white balls. Two balls re drawn in succession without replacement.
Answer» ANSWER :{RW, WR, WW}

Discussion

7824.	If the coordinates of a point P are transformed to (4,-3) when the axes are rotaated through an angle of 135^(0), then find P.
Answer» ANSWER :`(-(1)/(SQRT2)(,7)/(sqrt2))`

Discussion

7825.	Find the vector area and area of the parallelogram having bar(a) = bar(i) + 2bar(j) - bar(k), bar(b) = 2bar(i) -bar(j) + 2bar(k) as adjacent sides.
Answer» Answer :`3 VEC(i) -4vec(j) -5vec(K), 5 SQRT2`

Discussion

7826.	If y^2 =ax^2 + bx +c, then y^3(d^2y)/(dx^2) is
Answer» a CONSTANT a FUNCTION of X only a function of y only a function of x and y Answer :A

Discussion

7827.	Let P(k)=(1+cos""(pi)/(4k))(1+cos""((2k-1)pi)/(4k))(1+cos""((2k+1pi))/(4k))(1+cos""((4k-1)pi)/(4k)) Then
Answer» `P(3)=1/16` `p(4)=(2-sqrt2)/16` `P(5)=(3-sqrt5)/32` `P(6)=(2-sqrt3)/16` ANSWER :A::B::C::D

Discussion

7828.	d/(dx) ((3^x - 3^(-x))/(3^x + 3^(-x))) =
Answer» `(4 LOG 3)/((3^x + 3^(-x))^2)` `(-4 log 3)/((3^x + 3^(-x))^2)` `(1)/((3^x + 3^(-x))^2)` `(-1)/((3^x + 3^(-x))^2)` Answer :A

Discussion

7829.	If E and F are events such that P(E)=(1)/(4),P(F)=(1)/(2) and P(E and F)=(1)/(8) find (i) P(E or F), (ii) P (not E and not F).
Answer» ANSWER :(i) `(5)/(8)`(II) `(3)/(8)`

Discussion

7830.	P(n) : 2^n gt n^2 , for n = ………it is true.
Answer» ANSWER :`5 in N`.

Discussion

7831.	(1,2),(2,1), ((3+ sqrt(3))/( 2) , (3 + sqrt3)/( 2) ) are verticies of triangle. Then distance between circumcentre and orthocentre is ........ ..
Answer» `0` `SQRT2` `3 + sqrt3` None of these Answer :A

Discussion

7832.	If A = [(4,2),(-1,x)] and such that (A-2I) (A-3I) = 0, find the value of x.
Answer» ANSWER :X = 1

Discussion

7833.	If the domain of the function f(x)=sqrt(3cos^(-1)(4x)-pi) is [a,b], then the value of (4a+64b) is
Answer» ANSWER :7

Discussion

7834.	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) at least one will be green ?
Answer» ANSWER :(i) `(""^(20)C_(5))/(""^(60)C_(5))` (ii) `1 - (""^(30)C_(5))/(""^(60)C_(4))`

Discussion

7835.	Solvesintheta +costheta +sin3theta +cos3theta
Answer» ANSWER :`theta=pi/16 +(NPI)/4`

Discussion

7836.	The position vector of the points P, Q, R, S are bar(i)+bar(j)+bar(k), 2bar(i)+5bar(j), 3bar(i)+2bar(j)-3bar(k) and bar(i)-6bar(j)-bar(k) respectively. Prove that bar(PQ) and bar(RS) are parallel and find the ratio of their lengths.
Answer» ANSWER :`1:2`

Discussion

7837.	Which of the above lines is farther from the origin ?
Answer» SOLUTION :X- 4Y - 7 = 0

Discussion

7838.	If (0,0) shifted to a point on the x axis then 2x + 3y - 6 = 0reduced as lx + my = 0then shifted origin is
Answer» (3,0) (0,3) (-3, 0) (0,-3) ANSWER :A

Discussion

7839.	Evaluate Lt_(x to 0)("sec" x - 1)/(x^2)
Answer» ANSWER :`1/2`

Discussion

7840.	If x = a Sin 2 theta (1+Cos2 theta) , y = b Cos2 theta (1-Cos2 theta) , then (dy)/(dx) =
Answer» `a/B TAN THETA` `b/atantheta` `a/b COT theta` `b/acottheta` ANSWER :B

Discussion

7841.	A(3, 2, -4), B(9, 8, -10) and C(5, 4, -6) are given points. In which ratio point C divides bar(AB) ?
Answer» ANSWER :`1:2`

Discussion

7842.	If f(x)is an even functions and satisfies the relationx^(2) .f(x)- 2 f((1)/(x))= g(x)where g(x)is an odd functions . Then the value of f(5) is
Answer» 0 `37/55` 4 5 Answer :A

Discussion

7843.	Find the derivative of the w.r.to x. x ^(x sqrtx)
Answer» ANSWER :`X ^(x SQRTX +1//2) [1 + (3)/(2) log x ]`

Discussion

7844.	"Cos"(2pi)/15."Cos"(4pi)/15."Cos"(8pi)/15."Cos"(14pi)/15=
Answer» `1/2` `1/4` `1/8` `1/16` ANSWER :D

Discussion

7845.	For the given data the calculation corresponding to all values of series (x,y) is as following sum(x-barx)^(2)=35, sum(y-bary)^(2)=25, sum(x-barx)(y-bary)=20 Find Karl Pearson's correlation coefficient.
Answer» ANSWER :0.66

Discussion

7846.	Convert the following into simplest form (ii) Cot((21pi)/(2) - theta)
Answer» ANSWER :`TAN THETA`

Discussion

7847.	The probabilities that a typist will make 0, 1, 2, 3, 4, 5 or more mistakes in typing a report are, respectively, 0.12, 0.25, 0.36, 0.14, 0.08, 0.11.
Answer» ANSWER :A

Discussion

7848.	Let f(x) be an even function forall x in RIf f(x) is continuous at x = a, prove that it is continuous at x = - a.
Answer» ANSWER :`-a`

Discussion

7849.	Determine if f defined by f(x)={{:(x^(2)sin""(1)/(x)," if "x ne 0),(0," if "x= 0):} is a continuous function?
Answer» ANSWER :YES X is continousfor all x `in` R

Discussion

7850.	If alpha+beta=(pi)/(4), then the value of (1+tanalpha)(1+tanbeta) is
Answer» 1 2 `-2` Not defined Answer :B

Discussion

Explore topic-wise InterviewSolutions in .

Two ships leave a port at the same time. One goes 24 km per hour in the direction N45^(@)Eand other travels 32km per hour in the directions S75^(@)E. Find the distance between the ships at the end of 3 hours.

A carpenter was hired to build 192 window frames. The first day he made five frames and each day, thereafter he made two more frames than he made the day before. How many days did it take him to finish the job?

Write the following sets in the set-builder form : {1,4,9, . . .,100}

cos[2Sin^(-1)sqrt((1-x)/2)]=

Write the negation of the following statements: q: There exists a rational number x such that x^(2)=2

Find the Locus of the mid points of the line x cos theta + y sin theta = pintercepted between the axis .

By eliminating a,b,c from the Homogeneous Equations x=(a)/(b-c),y=(b)/(c-a),z=(c)/(a-b) where a,b,c not all zero then xy+yz+zx=

Writethe inverse of the given conditionastatement: Ifa number n is even, then n^(2) is even .

For the function f(x)=(e^(x))/(1+e^(x)), which of the following hold good ?

Draw the graphs of the following : y = [x] in [-3,3]

If y = "Tan^(-1) (((3-x)sqrt(x))/(1 - 3x)) then (dy)/(dx) =

Find the correct statement: Given vec OA =veca, vecOB=vecb and vecOP = (3veca+5vecb)/(8) implies that : P divides the line joining A nd B in the ratio:

Find the point on the curve y = x^(2) + 7x + 2 which is closer to the line y = 3x - 3.

Find the centre and radiusof equation of circle inx^(2) + y^(2) -x + 2y - 3 = 0

If2 sin ""( A) /( 2) sin ""( C)/(2) = sin "" ( B) /(2)then a,b,c are in

The projection of the join of the points (3,4,2), (5,1,8) on the line whose d.c's are ((2)/(7),(-3)/(7),(6)/(7)) is

The projection of vector bari+barj+bark " on the line whose vector equation is "barr=(3+t)bari+(2t-1)barj+3tbark,t being a scalar, is

If y=x/a+a/x then dy/dx = …. .

If A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, C = {11, 13, 15} andD = {15, 17}, find A ∩ (B ∪ D)

Describe the sample space for the indicated experiments. A box contins 1 red 3 identical white balls. Two balls re drawn in succession without replacement.

If the coordinates of a point P are transformed to (4,-3) when the axes are rotaated through an angle of 135^(0), then find P.

Find the vector area and area of the parallelogram having bar(a) = bar(i) + 2bar(j) - bar(k), bar(b) = 2bar(i) -bar(j) + 2bar(k) as adjacent sides.

If y^2 =ax^2 + bx +c, then y^3(d^2y)/(dx^2) is

Let P(k)=(1+cos""(pi)/(4k))(1+cos""((2k-1)pi)/(4k))(1+cos""((2k+1pi))/(4k))(1+cos""((4k-1)pi)/(4k)) Then

d/(dx) ((3^x - 3^(-x))/(3^x + 3^(-x))) =

If E and F are events such that P(E)=(1)/(4),P(F)=(1)/(2) and P(E and F)=(1)/(8) find (i) P(E or F), (ii) P (not E and not F).

P(n) : 2^n gt n^2 , for n = ………it is true.

(1,2),(2,1), ((3+ sqrt(3))/( 2) , (3 + sqrt3)/( 2) ) are verticies of triangle. Then distance between circumcentre and orthocentre is ........ ..

If A = [(4,2),(-1,x)] and such that (A-2I) (A-3I) = 0, find the value of x.

If the domain of the function f(x)=sqrt(3cos^(-1)(4x)-pi) is [a,b], then the value of (4a+64b) 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) at least one will be green ?

Solvesintheta +costheta +sin3theta +cos3theta

The position vector of the points P, Q, R, S are bar(i)+bar(j)+bar(k), 2bar(i)+5bar(j), 3bar(i)+2bar(j)-3bar(k) and bar(i)-6bar(j)-bar(k) respectively. Prove that bar(PQ) and bar(RS) are parallel and find the ratio of their lengths.

Which of the above lines is farther from the origin ?

If (0,0) shifted to a point on the x axis then 2x + 3y - 6 = 0reduced as lx + my = 0then shifted origin is

Evaluate Lt_(x to 0)("sec" x - 1)/(x^2)

If x = a Sin 2 theta (1+Cos2 theta) , y = b Cos2 theta (1-Cos2 theta) , then (dy)/(dx) =

A(3, 2, -4), B(9, 8, -10) and C(5, 4, -6) are given points. In which ratio point C divides bar(AB) ?

If f(x)is an even functions and satisfies the relationx^(2) .f(x)- 2 f((1)/(x))= g(x)where g(x)is an odd functions . Then the value of f(5) is

Find the derivative of the w.r.to x. x ^(x sqrtx)

"Cos"(2pi)/15."Cos"(4pi)/15."Cos"(8pi)/15."Cos"(14pi)/15=

For the given data the calculation corresponding to all values of series (x,y) is as following sum(x-barx)^(2)=35, sum(y-bary)^(2)=25, sum(x-barx)(y-bary)=20 Find Karl Pearson's correlation coefficient.

Convert the following into simplest form (ii) Cot((21pi)/(2) - theta)

The probabilities that a typist will make 0, 1, 2, 3, 4, 5 or more mistakes in typing a report are, respectively, 0.12, 0.25, 0.36, 0.14, 0.08, 0.11.

Let f(x) be an even function forall x in RIf f(x) is continuous at x = a, prove that it is continuous at x = - a.

Determine if f defined by f(x)={{:(x^(2)sin""(1)/(x)," if "x ne 0),(0," if "x= 0):} is a continuous function?

If alpha+beta=(pi)/(4), then the value of (1+tanalpha)(1+tanbeta) is