14949 + Interview Questions in Maths in Class 11 Page 239 InterviewSolution

11901.	For the following, using median, calculate mean deviation and coefficient of mean deviation. 100, 150, 200, 250, 360, 490, 500, 600, 671
Answer» ANSWER :M.D = 173.44, COEFFT. of M.D = 0.48

Discussion

11902.	f'(x) = cancel(O)(x) and cancel(O)'(x) = f(x) for all x. Also f(3) = 5 and f'(3) = 4 , then the value of [f(10)^2 - [cancel(O)(10)]^2 is
Answer»

Discussion

11903.	Match list {:(" ", "List I"," " ,"List II"), (i., [{:(a, b), (b, a):}], (a), "identity"), (ii., [{:(0, b), (-b, 0):}], (b), "Singular matrix"), (iii., [{:(a, a), (b, b):}], (c), "Skew-Symmetric"), (iv., [{:(1,0), (0,1):}], (d), "Symmetric"):} The correct match is (i) (ii) (iii) (iv)
Answer» d,C,B,a c,d,b,a b,a,d,c b,d,a,c ANSWER :A

Discussion

11904.	The standard deviation of the numbers 2, 3, 11, 2x is 3""1/2. Calculate the values of x.
Answer» ANSWER :`6, 4""2/3`

Discussion

11905.	Length of latus rectum of hyperbola 16x^2-9y^2 = 144 is ......... .
Answer» ANSWER :`32/3`

Discussion

11906.	If log_(e)(sqrt(5) + 2) = sin^(-1)(k) then k =
Answer» 1 5 3 2 Answer :D

Discussion

11907.	A die is thrown repeatelly until a six comes up. What is thwe sample space for this experiment?
Answer» Answer :{(6, (1, 6), (2, 6), (3, 6), (4, 6), (5, 6), (1, 1, 6), (1, 2, 6), … , (1, 5, 6), (2, 1, 6), (2, 2, 6), … , (2, 5, 6), … , (5, 1, 6), (5, 2, 6), … }

Discussion

11908.	Find lim_(xrarr0)f(x) and lim_(xrarr1)f(x), where f(x)={{:(2x+3",",xle0),(3(x+1)",",xgt0):}
Answer» ANSWER :`underset(x->0)LT y(x) =3`

Discussion

11909.	Examine each of the following relations given below and state in each case, giving resons whether it is function or not? (i) R={(2,1), (3,1), (4,2)}, (ii) R={(2,2), (2,4) ,(3,3),(4,4)} (ii) R={(1,2),(2,3),(3,4),(4,5),(5,6),(6,7)}
Answer» ANSWER :Not FUNCTION

Discussion

11910.	How many triangles may be formed by joining any three of the nine points when five of them are collinear?
Answer» ANSWER :` 74`

Discussion

11911.	Let A=pi/7, B =(2pi)/7, C=(4pi)/7 and cosA cos B cosC=-1//8, then sum tan A tan B=
Answer» 7 `-7` `1//7` 1 Answer :B

Discussion

11912.	Find the derivative of the function e ^(ln (cot x )) + ln (e ^(x ^(2)))
Answer» ANSWER :`-COSEC ^(2) X +2X`

Discussion

11913.	If omega is a cube root of unity, then 1+ omega^(2)= …..
Answer» ANSWER :`-OMEGA`

Discussion

11914.	Find Lt_(xto0)f(x) where f(x)=f(x)={{:(x-1" if "xlt1),(0"if "x=0),(x+1" if "xgt0):}
Answer» ANSWER :`Lt_(xto0)F(X)` doesn't EXIST

Discussion

11915.	A in P(A)
Answer» ANSWER :TRUE STATEMENT

Discussion

11916.	If bara,barb,barc are the position vectors of the vertices of a triangle ABC, then the area of triangle ABC is
Answer» `ABS(BARABARBBARC)` `1/2[barabarbbarc]` `abs(baraxxbarb+barbxxbarc+barcxxbara)` `1/2abs(baraxxbarb+barbxxbarc+barcxxbara)` ANSWER :D

Discussion

11917.	If f(g(x)) = x and g(f(x)) = x then g(x) is the inverse of f(x) . (g'(x))f'(x) = 1 implies g'(f(x))=1/(f'(x)) Let g(x) be the inverse of f(x) such that f'(x) =1/(1+x^5) ,then (d^2(g(x)))/(dx^2) is equal to
Answer» `1/(1+(g(X))^5)` `(g'(x))/(1+(g(x))^5)` `5(g(x))^4+(1+(g(x))^5)` `1+g(x))^5` Answer :C

Discussion

11918.	If u=f(x^3),v=g(x^2),f'(x)=cosx, and g'(x)=sinx, then (du)/(dv) is
Answer» `3/2 X cosx^3cosecx^2` `2/3sinx^3secx^2` `TANX` NONE of these Answer :A

Discussion

11919.	A particle is moving in a straight line so that after t seconds its distance is s (in cms) from a fixed point on the line is given by s= f(t)=8t+t^3. Find the velocity at time t= 2sec (ii) the initial velocity can acceleration at t=2 sec
Answer» ANSWER :(i) 20 cm/sec: (ii) 8 cm/sec; (iii) 12 cm/sec`""^(2)`

Discussion

11920.	With the help of tables, find the values, correct to places of decimals, of each of the following : cos280^(@)10'
Answer» ANSWER :`0.1766`

Discussion

11921.	Let f={(1,1),(2,3),(0,-1),(,-1,-3)} be a linear function from Z into Z. Find f(x).
Answer» ANSWER :`F(X)= 2x-1`

Discussion

11922.	24x^(2)-25y^(2)=600
Answer» ANSWER :(i) 10 units ,`4sqrt(6)` units (II) `A(-5,0),B(5,0) ` (iii) `F_(1)(-7,0),F_(2)(7,0)` (IV) `e=1(1)/(5)` (v) `9(3)/(5)`units

Discussion

11923.	The sum of an infinite series is 15 and the sum of the squares of these terms is 45. Find the series.
Answer» ANSWER :`5 +(10)/(3) +(20)/(9) + ....oo`

Discussion

11924.	If cos^(-1)x=tan^(-1)x, then
Answer» `x^(2)=(SQRT(5)-1)/2` `x^(2)=(sqrt(5)+1)/2` `sin(COS^(-1)x)=(sqrt(5)-1)/2` `tan(cos^(-1)x)=(sqrt(5)-1)/2` Answer :A

Discussion

11925.	Find the middle terms in the expansion of (3 - (x^3)/( 6) )^7.
Answer» ANSWER :`(-105)/(x) x^(9) and (35)/(48) x^(12)`

Discussion

11926.	For the line (x-1)/(1) = (y -2)/(2) = (z-3)/(3), which one of the following is incorrect ?
Answer» It LIES in the plane `X - 2y + z=0` It is same as line `x/1 + y/2 = z/3` It passes through `(2,3,5)` It is parallel to the plane `x - 2y + z-6 =0` ANSWER :C

Discussion

11927.	If 1 - Iis a rootof the equationx^(2) + ax +b = 0where ab in Rthen valueof a is
Answer» `-2` 2 0 none of these ANSWER :A

Discussion

11928.	vec(a) and vec(b) are non-zero vectors such that vec(a) xx vec(b)= vec(b) xx vec(a) " then" vec(a), vec(b) are
Answer» this RESULT is ALWAYS true this result is impossible parallel to each other perpendicular to each other Answer :C

Discussion

11929.	Evaluatesum_(k=1)^11(2+3^k)
Answer» ANSWER :`22+3/2(3^(11)-1)`

Discussion

11930.	Compare the following statements : q is a necessary condition for p.
Answer» Answer :All FIVE statements are EQUIVALENTS, i.e.,all are DIFFERENT ways of saying. "If p, then Q."

Discussion

11931.	Express each of the following in the form b or bi, where b is a real number (6)/(-i)
Answer» ANSWER :6I

Discussion

11932.	Equation of the plane passing through thepoints with position vectors (3, -5, -1), (-1, 5, 7) and parallel to the vector (3, -1, 7) is
Answer» ·3x+2y+z=0 3x+2y-z=0 3x-2y-z =0 x+2y+3z=0 Answer :B

Discussion

11933.	If tanalpha = p/qwhere alpha = 2beta, alpha being an acute angle then 1/(2)[p"cosec"2beta sec2beta] is equal to
Answer» `SQRT(p^2+q^2)` `sqrt(p^2-q^2)` `sqrt(2p^2+q^2)` `2sqrt(p^2+q^2)` ANSWER :A

Discussion

11934.	Arc at the circle with length 37.4 cm subtends and angle of 60^@ at centre . Then its radius r = .........
Answer» ANSWER :`35.7 CM`

Discussion

11935.	Line 2x - 3y + 8 = 0 intersects parabola y^(2) = 8x of points P and Q then point of bar(PQ) is ……..
Answer» (2,4) (8,8) (5,6) (6,5) ANSWER :C

Discussion

11936.	Find the distance between P(x_(1), y_(1)) and Q(x_(2), y_(2)) when : i. PQ is parallel to the y-axis, ii. PQ is parallel to the x-axis.
Answer» ANSWER :`(i) \| y_(2) - y_(1)\|, (II) \|x_(2) - x_(1)\|`

Discussion

11937.	Given thatf(x) =[(x^5 -1)/(x-1) ]if x ne 1.
Answer» ANSWER :5

Discussion

11938.	Find equation of line passes from middle of two parallel lines 9x + 6y - 7 = 0 and 3x + 2y + 6 = 0.
Answer» ANSWER :`18X + 12y+11=0`

Discussion

11939.	The points (1, 3) and (5, 1) are two opposite vertices of a rectangle. The other two verticeslie on the line y=2x+c.The remaining vertices are
Answer» ANSWER :(4,4)

Discussion

11940.	Write the negation of each of the following statements. It is not true that 3 is less than 4.
Answer» ANSWER :3 LESS than 4

Discussion

11941.	{:("Column - I (Equations) ","Column - II (No.of solutions) " ),("A) " x^(3) + x^(2) + 4 x + 2 sin x = 0 I n x in [ 0, 2 pi ],"p)4 "),("B) " sin (e^(x)) cos (e^(x)) = 2 ^(x - 2) + 2^(- x - 2),"q)1 "),("C) " sin 2 x + cos 4 x = 2 ,"r)2 "),("D) " 30 \| sin x\| = x " when " x in [ 0, 2 pi ],"s)0 "):}
Answer» <P> ANSWER :A - Q; B - s; C - S; D - p

Discussion

11942.	If tanA=tan alpha tanh beta and tanB=cot alpha tan h betathen tan(A+B)=
Answer» `sinh2beta COS 2ALPHA` `sin2beta "cosec"2alpha` `cosh 2betasec 2alpha` `cosh2beta SIN 2alpha` Answer :B

Discussion

11943.	If the tangent at any point on the curve ((x)/(a))^(2//3)+((y)/(b))^(2//3)=1 makes the intercepts, p,q and the axes then (p^(2))/(a^(2))+(q^(2))/(b^(2))=
Answer» 1 2 0 2pq Answer :A

Discussion

11944.	Let P(x) be a quadratic polynomial with real coefficient such that for all real 'x' the relation 2(1+p(x))=p(x-1)+p(x+1) holds of p(0)=8 and p(2)=32 then If the range of p(x) in [m, oo) then the value of 'm' is
Answer» -5 -12 -15 -17 Answer :D

Discussion

11945.	(x+cos x)(x-tanx)
Answer» ANSWER :`-TAN^(2)X(x+cosx)+(x-tanx)(1-sinx)(because 1 +tan^(2)x=sec^(2)x)`

Discussion

11946.	Differentiate the following function w.r.t. x: sqrt (x) cosec (5x +7)
Answer» ANSWER :`- 5 sqrt(x) COSEC (5x + 7) COT (5x + 7) + (1)/( 2 sqrt(x) ) cosec (5x + 7)`

Discussion

11947.	Solve sin 2x - sin 4x + sin 6x =0.
Answer» ANSWER :`X =(MPI)/(4)`

Discussion

11948.	3(sin x + cos x )^(4) + 6(sin x - cos x )^(2) + 4(sin^(6) x + cos^(6) x )=
Answer» 10 11 12 13 Answer :D

Discussion

11949.	Let P(x) be a quadratic polynomial with real coefficient such that for all real 'x' the relation 2(1+p(x))=p(x-1)+p(x+1) holds of p(0)=8 and p(2)=32 then Sumof all the coefficients of p(x) is
Answer» 15 17 19 21 Answer :C

Discussion

11950.	Find the component statements of the following compound statements and check whether they are true or false. All integers are positive or negative.
Answer» ANSWER :All INTEGERS are POSITIVE; all integers are NEGATIVE (FALSE).

Discussion

Explore topic-wise InterviewSolutions in .

For the following, using median, calculate mean deviation and coefficient of mean deviation. 100, 150, 200, 250, 360, 490, 500, 600, 671

f'(x) = cancel(O)(x) and cancel(O)'(x) = f(x) for all x. Also f(3) = 5 and f'(3) = 4 , then the value of [f(10)^2 - [cancel(O)(10)]^2 is

Match list {:(" ", "List I"," " ,"List II"), (i., [{:(a, b), (b, a):}], (a), "identity"), (ii., [{:(0, b), (-b, 0):}], (b), "Singular matrix"), (iii., [{:(a, a), (b, b):}], (c), "Skew-Symmetric"), (iv., [{:(1,0), (0,1):}], (d), "Symmetric"):} The correct match is (i) (ii) (iii) (iv)

The standard deviation of the numbers 2, 3, 11, 2x is 3""1/2. Calculate the values of x.

Length of latus rectum of hyperbola 16x^2-9y^2 = 144 is ......... .

If log_(e)(sqrt(5) + 2) = sin^(-1)(k) then k =

A die is thrown repeatelly until a six comes up. What is thwe sample space for this experiment?

Find lim_(xrarr0)f(x) and lim_(xrarr1)f(x), where f(x)={{:(2x+3",",xle0),(3(x+1)",",xgt0):}

Examine each of the following relations given below and state in each case, giving resons whether it is function or not? (i) R={(2,1), (3,1), (4,2)}, (ii) R={(2,2), (2,4) ,(3,3),(4,4)} (ii) R={(1,2),(2,3),(3,4),(4,5),(5,6),(6,7)}

How many triangles may be formed by joining any three of the nine points when five of them are collinear?

Let A=pi/7, B =(2pi)/7, C=(4pi)/7 and cosA cos B cosC=-1//8, then sum tan A tan B=

Find the derivative of the function e ^(ln (cot x )) + ln (e ^(x ^(2)))

If omega is a cube root of unity, then 1+ omega^(2)= …..

Find Lt_(xto0)f(x) where f(x)=f(x)={{:(x-1" if "xlt1),(0"if "x=0),(x+1" if "xgt0):}

A in P(A)

If bara,barb,barc are the position vectors of the vertices of a triangle ABC, then the area of triangle ABC is

If f(g(x)) = x and g(f(x)) = x then g(x) is the inverse of f(x) . (g'(x))f'(x) = 1 implies g'(f(x))=1/(f'(x)) Let g(x) be the inverse of f(x) such that f'(x) =1/(1+x^5) ,then (d^2(g(x)))/(dx^2) is equal to

If u=f(x^3),v=g(x^2),f'(x)=cosx, and g'(x)=sinx, then (du)/(dv) is

A particle is moving in a straight line so that after t seconds its distance is s (in cms) from a fixed point on the line is given by s= f(t)=8t+t^3. Find the velocity at time t= 2sec (ii) the initial velocity can acceleration at t=2 sec

With the help of tables, find the values, correct to places of decimals, of each of the following : cos280^(@)10'

Let f={(1,1),(2,3),(0,-1),(,-1,-3)} be a linear function from Z into Z. Find f(x).

24x^(2)-25y^(2)=600

The sum of an infinite series is 15 and the sum of the squares of these terms is 45. Find the series.

If cos^(-1)x=tan^(-1)x, then

Find the middle terms in the expansion of (3 - (x^3)/( 6) )^7.

For the line (x-1)/(1) = (y -2)/(2) = (z-3)/(3), which one of the following is incorrect ?

If 1 - Iis a rootof the equationx^(2) + ax +b = 0where ab in Rthen valueof a is

vec(a) and vec(b) are non-zero vectors such that vec(a) xx vec(b)= vec(b) xx vec(a) " then" vec(a), vec(b) are

Evaluatesum_(k=1)^11(2+3^k)

Compare the following statements : q is a necessary condition for p.

Express each of the following in the form b or bi, where b is a real number (6)/(-i)

Equation of the plane passing through thepoints with position vectors (3, -5, -1), (-1, 5, 7) and parallel to the vector (3, -1, 7) is

If tanalpha = p/qwhere alpha = 2beta, alpha being an acute angle then 1/(2)[p"cosec"2beta sec2beta] is equal to

Arc at the circle with length 37.4 cm subtends and angle of 60^@ at centre . Then its radius r = .........

Line 2x - 3y + 8 = 0 intersects parabola y^(2) = 8x of points P and Q then point of bar(PQ) is ……..

Find the distance between P(x_(1), y_(1)) and Q(x_(2), y_(2)) when : i. PQ is parallel to the y-axis, ii. PQ is parallel to the x-axis.

Given thatf(x) =[(x^5 -1)/(x-1) ]if x ne 1.

Find equation of line passes from middle of two parallel lines 9x + 6y - 7 = 0 and 3x + 2y + 6 = 0.

The points (1, 3) and (5, 1) are two opposite vertices of a rectangle. The other two verticeslie on the line y=2x+c.The remaining vertices are

Write the negation of each of the following statements. It is not true that 3 is less than 4.

{:("Column - I (Equations) ","Column - II (No.of solutions) " ),("A) " x^(3) + x^(2) + 4 x + 2 sin x = 0 I n x in [ 0, 2 pi ],"p)4 "),("B) " sin (e^(x)) cos (e^(x)) = 2 ^(x - 2) + 2^(- x - 2),"q)1 "),("C) " sin 2 x + cos 4 x = 2 ,"r)2 "),("D) " 30 | sin x| = x " when " x in [ 0, 2 pi ],"s)0 "):}

If tanA=tan alpha tanh beta and tanB=cot alpha tan h betathen tan(A+B)=

If the tangent at any point on the curve ((x)/(a))^(2//3)+((y)/(b))^(2//3)=1 makes the intercepts, p,q and the axes then (p^(2))/(a^(2))+(q^(2))/(b^(2))=

Let P(x) be a quadratic polynomial with real coefficient such that for all real 'x' the relation 2(1+p(x))=p(x-1)+p(x+1) holds of p(0)=8 and p(2)=32 then If the range of p(x) in [m, oo) then the value of 'm' is

(x+cos x)(x-tanx)

Differentiate the following function w.r.t. x: sqrt (x) cosec (5x +7)

Solve sin 2x - sin 4x + sin 6x =0.

3(sin x + cos x )^(4) + 6(sin x - cos x )^(2) + 4(sin^(6) x + cos^(6) x )=

Let P(x) be a quadratic polynomial with real coefficient such that for all real 'x' the relation 2(1+p(x))=p(x-1)+p(x+1) holds of p(0)=8 and p(2)=32 then Sumof all the coefficients of p(x) is

Find the component statements of the following compound statements and check whether they are true or false. All integers are positive or negative.