14949 + Interview Questions in Maths in Class 11 Page 25 InterviewSolution

1201.	Evaluate the following limits. Lt_(xto0)(sinx)/(xcos2x)
Answer» ANSWER :1

Discussion

1202.	If the straight line (4,3,5) and (x-4)/(1) = (y -2)/(1) = (z-k)/(2) intersect at a point, then the integer k is equal to
Answer» `-5` `5` 2 `-2` ANSWER :A

Discussion

1203.	The resultant of two forces P and Q is R If Q is doubled and when Q is reversed R is again doubled. Show that P:Q:R
Answer» ANSWER : `2 : 3 : 2`

Discussion

1204.	Write down the contrapositive of the following statements.:If natural number n is divisible by 6, then n is divisible by 2 and 3.
Answer» ANSWER :not DIVISIBLE by 6.

Discussion

1205.	Evaluate the following limits : lim_(x to oo) (2 sin x - sin 2 x)/(x^(3))
Answer» ANSWER :1

Discussion

1206.	{:("Column-I (Equation) ","Column-II (Solution) "),("A) " If max_(theta in R){5 sin theta + 3 sin (theta - alpha)}= 7", then the set of possible values of "alpha is ,"p) " 2 n pi + 3 pi // 4"," n in Z),("B) " x ne (n pi)/(2) and (cos x)^(sin^(2)x-3 sin x + 2)=1,"q) "x = 2 n pi pm (pi)/(3)","n in Z),("C) " sqrt((sin x))+2 ^(1//4) cos x = 0 ,"r) " 2 n pi + cos^(-1)(1//3)","n in Z),("D) " log_(5) tan x = (log_(5) 4) (log_(4)(3 sin x)),"s) No solution "):}
Answer» <P> ANSWER :A- Q; B - s; C - p; D - R

Discussion

1207.	Solve the equations: Q. (x-7)(x-3)(x+1)(x+5)=1680.
Answer» ANSWER :9,-7, `1pmsqrt(-24)`.

Discussion

1208.	Mohan does 50% of the jobs, Vivek does 30% of the jobs and Anand does 20% of the jobs in a company. The probability of an error when Mohan works is 0.03, the probability of an error when Vivek works is 0.04 and that of Anand is 0.05. Suppose an error has occured in the work who would have done the work.
Answer» <P> Answer :Since `P(A_(1)/(B))`has the highest probability ONE can GIVES that MOHAN would have DONE the error in the work.

Discussion

1209.	The sum of 15 terms of A.P. is zero. Its 4th term is 12. Find its 14th term.
Answer» SOLUTION :N/a

Discussion

1210.	For the curvesqrt(x) + sqrt(y) = 1 , (dy)/(dx) " at " ((1)/(4) , (1)/(4)) is
Answer» ` 1/2` 1 `-1` 2 Answer :`-1`

Discussion

1211.	If x=a("cosec" theta + cot theta ) , y=b( " cosec " theta - cot theta ) , then
Answer» `x+y=ab` `x-y=ab` `xy=ab` `xy=0` ANSWER :C

Discussion

1212.	Find the mean deviation from the median for the following data: 34, 66, 30, 38, 44, 50, 40, 60, 42, 51.
Answer» ANSWER :8.7

Discussion

1213.	Number of integral vaules (s) offor which the equation sinx-sqrt(3)cosx=(4m-6)/(4-m) has solutions. x in [0,2pi], is_______________
Answer» ANSWER :4

Discussion

1214.	There are 12 points in a plane of which5 are collinear . Find the number of straight lines obtainedby joining these points in pairs .
Answer» ANSWER :57

Discussion

1215.	If cot^(2) A cot^(2) B = 3, then the value of (2 - cos 2A) (2 - cos 2 B) is _________.
Answer» ANSWER :3

Discussion

1216.	If f(x)= overset(n) underset(i=1) sum (x-a_(i))^(2) has a minimum at x=x_(0) then for a_(1),.....a_(n),x_(0) is the
Answer» GEOMETRIC MEAN HARMONIC mean arithemetic mean A.G.M Answer :C

Discussion

1217.	Insert 5 geometric means between (1)/(3) and 243.
Answer» ANSWER :1,2,3,927,81

Discussion

1218.	If s = 12 and A=90^(@)then find the value of r_(1)
Answer» ANSWER :`12`

Discussion

1219.	If the d.c.s of the line joining the oints P(4,3,5) and Q(1,1,k) are (3)/(7),(2)/(7),(6)/(7) then k =
Answer» -1 11 1 -11 Answer :A

Discussion

1220.	The sum of the digits in unit place of all the numbers formed with the help of 3, 4, 5 and 6 taken all a time is
Answer» 432 108 36 18 Answer :A

Discussion

1221.	P is a point on the segment joining the feet of two vertical poles of heights a and b. The angles of elevation of the tops of the poles from P are 45^(@) each. Then, thesquare of the distance between the tops of the poles is
Answer» `(a^(2)+B^(2))/2` `a^(2)+b^(2)` `2(a^(2)+b^(2))` `4(a^(2)+b^(2))` ANSWER :C

Discussion

1222.	If a = 5, b= 12,c = 13then R =
Answer» ` 13//2` ` 13//4` ` 13//8` ` 13//6` ANSWER :A

Discussion

1223.	The co-efficients of x^2 and x^3 in the expansion of (3+kx)^9 are equal. Then the value of k is
Answer» ANSWER :a= `9/7`

Discussion

1224.	For problems Let cos^(-1)(4x^(3)-3x)=a+bcos^(-1)x If xin (1/2, 1], then the value of lim_(y to a)bcos(y) is
Answer» `-1/3` -3 `1/3` 3 Answer :D

Discussion

1225.	Find the derivative of f(x)=1+x+x^(2)+x^(3)+……+x^(50) at x=1
Answer» ANSWER :1275

Discussion

1226.	A rod of length 2 units whose one end is (1, 0, -1) and other end touches the plane x - 2y + 2z + 4=0, then
Answer» the rod sweeps the figure WHOSE volume is `pi` cubic units the area of the regio which the rod traces on the plnae is `2pi` the length of projection of the rod on the PLANE is `sqrt3` units the centre of the region which the rod traces on the plane is `((2)/(3), (2)/(3),(-5)/(3))` ANSWER :A::C::D

Discussion

1227.	(baraxxbari).(barjxxbark)+(baraxxbarj).(barkxxbari)+(baraxxbark).(barixxbarj)=
Answer» 0 `BAR0` `BARA` 1 Answer :A

Discussion

1228.	Determine the sum of the first 35 terms of an A.P. if a_(2), = 2 and a_(7), =22.
Answer» ANSWER :2310

Discussion

1229.	Solve each of the following equation for real x and y : (x+ yi) + (3-2i) =1 + 4i
Answer» ANSWER :x=2, y=6

Discussion

1230.	If f(x)=x^(2)-x+5, x gt (1)/(2) and g(x) is its inverse function, then g'(7) equals
Answer» `-(1)/(3)` `(1)/(13)` `(1)/(3)` `-(1)/(13)` ANSWER :C

Discussion

1231.	Find points A,B where A lies on a line through (6,7,4) with d.rs 3,-1,1 and B lies on a line through (0,-9,2) with d.rs -3,2,4 such that AB is perpendicular to both lines.
Answer» ANSWER :A(3,8,3) and B(-3,-7,6)

Discussion

1232.	Define the function f: R to R by y=f(x)=x^(2), x in R. Complete the Table given below by using this defination. What is the domain and range of this function? Draw the graph of f.
Answer» Answer :DOMAIN F= `{X: x in R}` RANGE `= {x^(2); x in R}`

Discussion

1233.	Express the following in the form a+bi, where a and b are real numbers ((1 + i)/(1-i))^(3)
Answer» ANSWER :`0= 1I`

Discussion

1234.	If ((a^(2)+1)^(2))/(2a-i) =x+iy then what is the value of x^(2)+y^(2)?
Answer» ANSWER :`((a^(2)+1)^(4))/((4A^(2)+1))`

Discussion

1235.	Sameer throws , an ordinary die . What is the probability that he throws 2 or 5 ?
Answer» ANSWER :`(1)/(3)`

Discussion

1236.	Let bara= 4bari-3barj+5bark . A vector b is coplanar with bari, barj" and orthogonal to " bara " and has magnitude " absbara, " then " barb is
Answer» `pmsqrt2(3bari+4barj)` `pmsqrt2(bari+4barj)` `pmsqrt2(3bari+barj)` `pmsqrt2(3bari+5barj)` ANSWER :A

Discussion

1237.	Let f(x) be continuous on [a,b], differentiablein (a,b) and f(x) cancel(=)0 for all x in [a,b]. Then , there exists theta in (a,b), such that(f'(theta))/(f(theta)) is equal to
Answer» `(1)/(a + THETA) - ( 1)/( B- theta )` `( 1)/( a- theta ) + ( 1)/( b - theta )` `(1)/( a+theta) + ( 1)/( b - theta )` `( a+ b) theta ` ANSWER :B

Discussion

1238.	f(x) = {{:((1 + \|sin x\|)^((p)/(\|sinx\|)) " if" - pi //6 lt x lt 0 ),(e^((sin 2x )/(sin3x) )"if" 0 lt x lt pi //6 ):} andf(0) = q is continuous at x = 0 then
Answer» ` p = (2)/(3) , q = E^(2//3)` `p = - (2)/(3) , q = e^(2//3)` ` p = (2)/(3) , q = e^(-2//3)` `p = -(2)/(3) , q = e^(-2//3)` ANSWER :A

Discussion

1239.	Find the centre and radius of each of the following circle : (i) x^(2)+y^(2)+4x-4y+1=0 (ii) 2x^(2)+2y^(2)-6x+xy-1=0 (iii) 2x^(2)+2y^(2)=3k(x+k) (iv) 3x^(2)+3y^(2)-5x-6y+4=0 (v) x^(2)+y^(2)-2ax-2by+a^(2)=0
Answer» Answer :(i) `C(-2,2)r=SQRT(7)` , (ii) `C((3)/(2),-(3)/(2)),r=sqrt(5)` (iii) `C((3k)/(4),0),r=(sqrt(33))/(4)` , (IV) `C((5)/(6),1),r=(sqrt(13))/(6)` (v) C(a,b),r=b

Discussion

1240.	(i) dot product of two vectors is not commutative(ii) If veci,vecj,veck are unit vectors the \|veci+vecj+veck\|= sqrt 3 (iii) (veca,vecb) X vecc is not defined.(iv)The magnitude of 2veci+vecj-2veck is sqrt3Find which pair of statements are correct.
Answer» (i) and (II) are TRUE (i) and (IV) are true (III) and (iv) are true (ii) and (iii) are true Answer :D

Discussion

1241.	Write the truth value of the following statement: 1^(3)=1 or 3^(2)=9
Answer» ANSWER :1

Discussion

1242.	Show that the points O(0,0,0), A(2,-3,3) B(-2,3,-3) are collinear. Find the ratio in which each point divides the segment joining the other two.
Answer» ANSWER :`(OA)/(AB)=(-1)/2; (AB)/(BO)=(-2)/1; (OB)/(OA)=1`

Discussion

1243.	Ifr r_2 = r_1 r_3 " then "angle A + angle C =
Answer» `135 ^(@) ` ` 120 ^(@) ` ` 60 ^(@) ` ` 90 ^(@) ` ANSWER :D

Discussion

1244.	Write the negation of the following statements. r : Not all natural number are integers
Answer» SOLUTION :~R: All NATURAL NUMBERS are INTEGERS

Discussion

1245.	Evaluate the following limits : Lim_(n to oo) (1+2+3+...+n)/(n^(2)) ( or Lim_(x to oo) (Sigman)/(n^(2)))
Answer» ANSWER :`1/2`

Discussion

1246.	If f and g are two real valued functions defined as f(x)= 2x+1 and g(x)= x^(2)+1, then find fg
Answer» Answer :`2X^(3) + X^(2) + 2x + 1`

Discussion

1247.	sin 5 theta = cos 2 theta , 0^(@) lt theta lt 180^(@). Find value of theta
Answer» ANSWER :`(1^(@))/(7)`

Discussion

1248.	Find the component statements of the compound statement given below:"20 is a prime number and 20 is less than 21."
Answer» ANSWER :Compound STATEMENT : 20 is a prime NUMBER. 20 is LESS than 21

Discussion

1249.	The point (2,1,5),(3,2,3),(4,0,4) form
Answer» EQUILATERAL triangle ISOSCELES triangle right ANGLED triangle right angled isosceles triangle Answer :A

Discussion

1250.	For a positive integer (n gt 1), Let a (n) = 1+ (1)/(2) + (1)/(3) + (1)/(4) ….... + (1)/( (2^(n) )-1) Then
Answer» `a (100) lt 100` `a ( 100 ) GT 100` `a (20 ) = 100` `a (200) ge 100` ANSWER :A

Discussion

Explore topic-wise InterviewSolutions in .

Evaluate the following limits. Lt_(xto0)(sinx)/(xcos2x)

If the straight line (4,3,5) and (x-4)/(1) = (y -2)/(1) = (z-k)/(2) intersect at a point, then the integer k is equal to

The resultant of two forces P and Q is R If Q is doubled and when Q is reversed R is again doubled. Show that P:Q:R

Write down the contrapositive of the following statements.:If natural number n is divisible by 6, then n is divisible by 2 and 3.

Evaluate the following limits : lim_(x to oo) (2 sin x - sin 2 x)/(x^(3))

Solve the equations: Q. (x-7)(x-3)(x+1)(x+5)=1680.

The sum of 15 terms of A.P. is zero. Its 4th term is 12. Find its 14th term.

For the curvesqrt(x) + sqrt(y) = 1 , (dy)/(dx) " at " ((1)/(4) , (1)/(4)) is

If x=a("cosec" theta + cot theta ) , y=b( " cosec " theta - cot theta ) , then

Find the mean deviation from the median for the following data: 34, 66, 30, 38, 44, 50, 40, 60, 42, 51.

Number of integral vaules (s) offor which the equation sinx-sqrt(3)cosx=(4m-6)/(4-m) has solutions. x in [0,2pi], is_______________

There are 12 points in a plane of which5 are collinear . Find the number of straight lines obtainedby joining these points in pairs .

If cot^(2) A cot^(2) B = 3, then the value of (2 - cos 2A) (2 - cos 2 B) is _________.

If f(x)= overset(n) underset(i=1) sum (x-a_(i))^(2) has a minimum at x=x_(0) then for a_(1),.....a_(n),x_(0) is the

Insert 5 geometric means between (1)/(3) and 243.

If s = 12 and A=90^(@)then find the value of r_(1)

If the d.c.s of the line joining the oints P(4,3,5) and Q(1,1,k) are (3)/(7),(2)/(7),(6)/(7) then k =

The sum of the digits in unit place of all the numbers formed with the help of 3, 4, 5 and 6 taken all a time is

P is a point on the segment joining the feet of two vertical poles of heights a and b. The angles of elevation of the tops of the poles from P are 45^(@) each. Then, thesquare of the distance between the tops of the poles is

If a = 5, b= 12,c = 13then R =

The co-efficients of x^2 and x^3 in the expansion of (3+kx)^9 are equal. Then the value of k is

For problems Let cos^(-1)(4x^(3)-3x)=a+bcos^(-1)x If xin (1/2, 1], then the value of lim_(y to a)bcos(y) is

Find the derivative of f(x)=1+x+x^(2)+x^(3)+……+x^(50) at x=1

A rod of length 2 units whose one end is (1, 0, -1) and other end touches the plane x - 2y + 2z + 4=0, then

(baraxxbari).(barjxxbark)+(baraxxbarj).(barkxxbari)+(baraxxbark).(barixxbarj)=

Determine the sum of the first 35 terms of an A.P. if a_(2), = 2 and a_(7), =22.

Solve each of the following equation for real x and y : (x+ yi) + (3-2i) =1 + 4i

If f(x)=x^(2)-x+5, x gt (1)/(2) and g(x) is its inverse function, then g'(7) equals

Find points A,B where A lies on a line through (6,7,4) with d.rs 3,-1,1 and B lies on a line through (0,-9,2) with d.rs -3,2,4 such that AB is perpendicular to both lines.

Define the function f: R to R by y=f(x)=x^(2), x in R. Complete the Table given below by using this defination. What is the domain and range of this function? Draw the graph of f.

Express the following in the form a+bi, where a and b are real numbers ((1 + i)/(1-i))^(3)

If ((a^(2)+1)^(2))/(2a-i) =x+iy then what is the value of x^(2)+y^(2)?

Sameer throws , an ordinary die . What is the probability that he throws 2 or 5 ?

Let bara= 4bari-3barj+5bark . A vector b is coplanar with bari, barj" and orthogonal to " bara " and has magnitude " absbara, " then " barb is

Let f(x) be continuous on [a,b], differentiablein (a,b) and f(x) cancel(=)0 for all x in [a,b]. Then , there exists theta in (a,b), such that(f'(theta))/(f(theta)) is equal to

f(x) = {{:((1 + |sin x|)^((p)/(|sinx|)) " if" - pi //6 lt x lt 0 ),(e^((sin 2x )/(sin3x) )"if" 0 lt x lt pi //6 ):} andf(0) = q is continuous at x = 0 then

Find the centre and radius of each of the following circle : (i) x^(2)+y^(2)+4x-4y+1=0 (ii) 2x^(2)+2y^(2)-6x+xy-1=0 (iii) 2x^(2)+2y^(2)=3k(x+k) (iv) 3x^(2)+3y^(2)-5x-6y+4=0 (v) x^(2)+y^(2)-2ax-2by+a^(2)=0

(i) dot product of two vectors is not commutative(ii) If veci,vecj,veck are unit vectors the |veci+vecj+veck|= sqrt 3 (iii) (veca,vecb) X vecc is not defined.(iv)The magnitude of 2veci+vecj-2veck is sqrt3Find which pair of statements are correct.

Write the truth value of the following statement: 1^(3)=1 or 3^(2)=9

Show that the points O(0,0,0), A(2,-3,3) B(-2,3,-3) are collinear. Find the ratio in which each point divides the segment joining the other two.

Ifr r_2 = r_1 r_3 " then "angle A + angle C =

Write the negation of the following statements. r : Not all natural number are integers

Evaluate the following limits : Lim_(n to oo) (1+2+3+...+n)/(n^(2)) ( or Lim_(x to oo) (Sigman)/(n^(2)))

If f and g are two real valued functions defined as f(x)= 2x+1 and g(x)= x^(2)+1, then find fg

sin 5 theta = cos 2 theta , 0^(@) lt theta lt 180^(@). Find value of theta

Find the component statements of the compound statement given below:"20 is a prime number and 20 is less than 21."

The point (2,1,5),(3,2,3),(4,0,4) form

For a positive integer (n gt 1), Let a (n) = 1+ (1)/(2) + (1)/(3) + (1)/(4) ….... + (1)/( (2^(n) )-1) Then