14949 + Interview Questions in Maths in Class 11 Page 147 InterviewSolution

7301.	For the statement ''19 is real number or a positive integer", "Or" is
Answer» (a) inclusive (b) EXCLUSIVE (C) both (a) and (b) (d) NONE of these Answer :A

Discussion

7302.	Find the direction cosines of the two lines which are connected by the relations l + m + n = 0 an mn - 2nl - 2lm = 0.
Answer» Answer :Thus the d.c's of the TOW LINES are `((1)/(SQRT(6)),(1)/(sqrt(6)),(-2)/(sqrt(6)));((1)/(sqrt(6)),(-2)/(sqrt(6)),(1)/(sqrt(6)))`

Discussion

7303.	If A = {3, 6, 9, 12, 15, 18, 21}, B = { 4, 8, 12, 16, 20 }, C = { 2, 4, 6, 8, 10, 12, 14, 16 }, D = {5, 10, 15, 20 }, find C – B
Answer» ANSWER :`={2, 6, 10, 14}`

Discussion

7304.	The value of log_729 81 is ___
Answer» 2 3 `2/3` `3//2` ANSWER :C

Discussion

7305.	The transformed equation of x^(2) + y^(2) = r^(2) when the axes rotated through an angle 36^(@) is
Answer» `SQRT(5) X^(2) - 4XY + 3Y^(2) = R^(2)` `X^(2) + 2XY - sqrt(5) Y^(2) = r^(2)` `X^(2) + Y^(2) = 2r^(2)` `X^(2) + Y^(2) = r^(2)` ANSWER :D

Discussion

7306.	e^(\|sin x\|)+ e^(-\|sin x\|) + 4 a = 0will have exactly four different solutions in [0, 2 pi] is
Answer» `a in R` `a in [-(E)/(4),-(1)/(4)]` `a in [- (1 - e^(2))/(4 e), infty]` NONE of these Answer :D

Discussion

7307.	Match the following
Answer» ANSWER :MATCH in the FOLLOWING ORDER 1, -1, -i, i

Discussion

7308.	Show that the statement . p : 'If x is a real number such thatx^(3)+ 4x=0, then x=0' is true by Method of contradiction
Answer» Answer :METHOD of CONTRADICTION : LET x ≠0, and let x=p,p`in` R and p is a root of`x^(3)+4x=0=>p^(3)+4p=0=>p(p^(2)+4)=0.` but p ≠ 0 (assumption),also`p^(2)+4 ≠ 0=> p(p^(2)+4),i.e., p^(3)+4p ≠ 0` This contradicts the given statement. So our assurnption that x≠0is wrong Hence, x =0.

Discussion

7309.	Show that the statement . p : 'If x is a real number such thatx^(3)+ 4x=0, then x=0' is true by Method of contrapositive
Answer» <P> Answer :METHOD of contrapositive : Let x=0 be not TRUE. Let x =p ≠ 0.Then, `p^(3)+4 p=0,p` being the root of`x^(2)+4=0=>p(p^(2)+4)=0.` Now, p ≠ 0, Also, `p^(2)+4 ≠ 0 => p(p^(2)+4)≠0 :. x=0` is the root of`x^(3)+4x=0`

Discussion

7310.	The scores of a batsman in ten innings are: 48, 80, 58, 44, 52, 65, 73, 56, 64, 54. Find the mean deviation from the median.
Answer» ANSWER :8.6

Discussion

7311.	Find the value of cos^(-1)sqrt(2/3)-cos^(-1)""(sqrt(6)+1)/(2sqrt(3))
Answer» `pi/2` `pi/4` `pi/6` `pi/8` ANSWER :C

Discussion

7312.	Liney = mx + 3 is tangent to parabola 3y^(2) = 2x then m = ……..
Answer» `-(1)/(18)` 18 `(1)/(18)` NONE of these Answer :C

Discussion

7313.	If the function f:R rarr B defined by f(x)=sqrt(x^(2)) is surjective then B is
Answer» `(-OO, 0]` `[0, oo)` `(0, oo)` R Answer :B

Discussion

7314.	A flag staff of 5 mts high stands on a building of 25 mt high. At an observerat a height of 30 mt the flag staff and the building subtend equal angles. The distance of the observer from the top of the flag staff is
Answer» `10sqrt(2)` `20sqrt(2)` `30sqrt(2)` `40sqrt(2)` ANSWER :A

Discussion

7315.	The distance of the orthocentre from the vertices A,B,C are in the ratio
Answer» `SinA:SinB:SINC` `CosA: CosB: COSC` `SECA: SecB: SecC` `a:B:c` ANSWER :B

Discussion

7316.	Find the derivative of y=sqrt(2x-3)+sqrt(7-3x).
Answer» Answer :`(1)/(SQRT ( 2x -3)) -(3)/( 2 sqrt(7 - 3X))`

Discussion

7317.	If the position vectors of the four points A, B, C, D are 2bar(a), bar(b), 6bar(b) and 2bar(a)+5bar(b) then ABCD is
Answer» square rectangle rhombus parallelogram Answer :D

Discussion

7318.	If f(0)=0, f(1)=1, f(2)=2 and f(x)=f(x-2)+f(x-3) " for " x=3, 4, 5, ………….., then f(9)=
Answer» 12 13 14 10 Answer :D

Discussion

7319.	If a,b,c(altbltc) are positive prime factors of 2001, then find the equation of the plane passing through (1,1,1) in which (b,c,a) are direction ratios of a normal line.
Answer» ANSWER :55

Discussion

7320.	A variable line L si drawn through O(0,0) to meet lines L_1 and L_2 " given by " y-x-10=0 and y-x-20=0 at point A and B, respectively. A point P IS taken on L such that 2//OP=1//OA+1//OB. Then the locus of P is
Answer» `3x+3y=40` `3x+3y+40=0` `3x-3y=40` `3y-3x=40` ANSWER :D

Discussion

7321.	A variable line L si drawn through O(0,0) to meet lines L_1 and L_2 " given by " y-x-10=0 and y-x-20=0 at point A and B, respectively. Locus of P, if OP^2=OAxxOB, is
Answer» `(y-x)^2=200` `(y+x)^2=50` `(y-x)^2=64` NONE of these Answer :D

Discussion

7322.	A variable line L si drawn through O(0,0) to meet lines L_1 and L_2 " given by " y-x-10=0 and y-x-20=0 at point A and B, respectively. Locus of P if(1//OP^2)=(1//OA^2), is
Answer» `(y-x)^2=80` `(y-x)^2=100` `(y-x)^2=64` NONE of these Answer :B

Discussion

7323.	Expand the following expressions : (ax-b/x)^(6)
Answer» ANSWER :`a^(6)x^(6)-6a^(5)x^(4)b+15 a^(4)x^(2)b^(2)-20a^(3)b^(3)+(15a^(2)b^(4))/(x^(2))-(6AB^(5))/(x^(4))+(b^(6))/(x^(6))`

Discussion

7324.	If the direction cosines of a line L are (ab, b,b) and the angle between L and X-axis is (pi)/(3) then a pair of possible values for a, b are
Answer» `sqrt((2)/(3)), sqrt((3)/(8))` `sqrt((8)/(3)), sqrt((2)/(3))` 2, 5 3, 4 ANSWER :A

Discussion

7325.	Write cos4 thetain terms ofcos theta.
Answer» ANSWER :`8 cos ^(4) THETA - 8 cos ^(2) theta +1 `

Discussion

7326.	If tan px = cot qx, then the solutions are in A.P. with common difference
Answer» `(PI)/((p+q))` `(2PI)/((p+q))` `(pi)/((p-q))` `(2pi)/((p-q))` ANSWER :A

Discussion

7327.	If A = {a_(1),a_(2), ……,a_(10)} and B = {b_(1),b_(2),b_(3),…….b_(10)} then the number of bijections that can be defined from A to B is
Answer» `10^(10)` 10! `10^(2)` `10^(9)` ANSWER :B

Discussion

7328.	Using section formula, show that the points A(2, -3, 4), B(-1, 2, 1) and C(0,1/3,2) are collinear.
Answer» ANSWER :K = 2 POINTS are COLLINER.

Discussion

7329.	If z=x+iy lies in the third quadrant, then (bar(z))/(z) also lies in the third quadrant, if
Answer» `X gt y gt 0` `x lt y lt 0` `y lt x lt 0` `G gt x gt 0` ANSWER :B

Discussion

7330.	Find Lt_(xto0)log_(tanx)tan2x
Answer» ANSWER :1

Discussion

7331.	Ramesh travells at the speed of 40km/hr. If he decreases his speed 4km each hour, then how much time he will taken to cover 216km?
Answer» ANSWER :9 HOURS

Discussion

7332.	If rgt0,-pilethetalepi and r,theta satisfy rsintheta=3, r=4(1+sintheta) then no. of possible solutions of (r, theta) is
Answer» 2 4 0 infinite Answer :A

Discussion

7333.	The value of tan(sin^(-1)(cos(sin^(-1)x)))tan(cos^(-1)(sin(cos^(-1)x)))." where "x in (0, 1) is equal to
Answer» 0 1 `-1` 2 Answer :B::C::D

Discussion

7334.	Find k if the function is continuous at x=(pi)/(2) if(a) f(x)={{:((k cos x )/(pi-2x),x ne (pi)/(2)),(3,if x=(pi)/(2)):} at x=(pi)/(2) (b) f(x)={{:(kx+1, if x le 2),(cos x,if x gt 2):} at x=2 (c ) if f(x)={{:(k^(2)x-k,if x le 1),(2 , if x lt 1):} is continous on R then find the value(s) of k
Answer» ANSWER :k\2,-1

Discussion

7335.	Evaluate the following limits : Lim_(x to 0) 5^(x) sin (a/(5^(x)))
Answer» ANSWER :a

Discussion

7336.	The radius of a sphere is measured as 14cm. Later it was found that there is an error 0.02cm in measuring the radius. Find the approximate error in surface area of the sphere
Answer» ANSWER :7.04sq.cm

Discussion

7337.	Find the values of a and bif f(x)={{:(ax-b,"for" x le -1),(3x^(2)-4ax+2ab,"for" -1 lt x lt 1 "is continous on R"),(-21,"for" x ge1):}is continuous on R.
Answer» ANSWER :a=3,b=-6

Discussion

7338.	Three squares of chess board are selected at random. Find the probability of getting 2 squares of one colour and other of a different colour.
Answer» ANSWER :`(16)/(21)`

Discussion

7339.	Evaluate the following limits : Lt_(ntooo)(1+2+3+......+n)/n^(2)
Answer» ANSWER :`1/2`

Discussion

7340.	The integer is selected at random from 1 to 25. The probability that it is a prime number is
Answer» ANSWER :`(9)/(25)`

Discussion

7341.	If x^4 + 7 x^2y^2+9y^4 =24 xy^3 then (dy)/(dx) =
Answer» `x/y` `y/x` `-x/y` `-y/x` ANSWER :B

Discussion

7342.	A particle moving along a straight line has the relation s =t^2 +3, connecting the distance s described by the particle in time 1. Find the velocity and acceleration of the particle at t=4 seconds.
Answer» ANSWER :50 units/sec, 24units/sec`""^(2)`

Discussion

7343.	If (sin^(4))/(2)+(cos^(4))/(3)=(1)/(5) then
Answer» `TAN^(2) x = (2)/(3)` `(sin^(8))/(8)+(cos^(8)x)/(27)=(1)/(125)` `tan^(2)x=(1)/(3)` `(sin^(2))/(8)+(cos^(8))/(27)=(2)/(125)` Answer :A::B

Discussion

7344.	Evaluate : lim_(x to -1) x/([x])
Answer» ANSWER :`1/2`

Discussion

7345.	L_1 : 3x+4y+8=0 , L_2 : 2x+7y-1=0 If D is the midpoint of BC and E is the mid point of CA then DE is equal to
Answer» `1//4` `1//2` 1 12 Answer :C

Discussion

7346.	If cos h^(-1)(k) = log_(e)(3+2sqrt(2)) then k =
Answer» 1 2 3 4 Answer :C

Discussion

7347.	i) If bar(a), bar(b), bar(c) are non coplanar vectors, then prove that the vectors 5bar(a)-6bar(b)+7bar(c), 7bar(a)-8bar(b)+9bar(c) and bar(a)-3bar(b)+5bar(c) are coplanar.
Answer» Collinear Coplanar but NON collinear non coplanar cannot be determined Answer :B

Discussion

7348.	Evaluate the following limits : Lim_(x to oo) (4x-3)/(2x+7)
Answer» ANSWER :2

Discussion

7349.	A problem is Mathematics is given to three sutdents whose chance of solving it are in the ratio 6:4:3 respectively. What is the probability that (i)the problem is solved(ii)what is the probability that none of them could solve the problem.
Answer» ANSWER :`(3)/(4)`,'(23)/(24)'

Discussion

7350.	Find the coordinates of the point equidistant from the four pointsA(0,0,0) , B (a,0,0) , C(0,b,0) and D(0,0,c) .
Answer» ANSWER :`(a/2, b/2, c/2)`

Discussion

Explore topic-wise InterviewSolutions in .

For the statement ''19 is real number or a positive integer", "Or" is

Find the direction cosines of the two lines which are connected by the relations l + m + n = 0 an mn - 2nl - 2lm = 0.

If A = {3, 6, 9, 12, 15, 18, 21}, B = { 4, 8, 12, 16, 20 }, C = { 2, 4, 6, 8, 10, 12, 14, 16 }, D = {5, 10, 15, 20 }, find C – B

The value of log_729 81 is ___

The transformed equation of x^(2) + y^(2) = r^(2) when the axes rotated through an angle 36^(@) is

e^(|sin x|)+ e^(-|sin x|) + 4 a = 0will have exactly four different solutions in [0, 2 pi] is

Match the following

Show that the statement . p : 'If x is a real number such thatx^(3)+ 4x=0, then x=0' is true by Method of contradiction

Show that the statement . p : 'If x is a real number such thatx^(3)+ 4x=0, then x=0' is true by Method of contrapositive

The scores of a batsman in ten innings are: 48, 80, 58, 44, 52, 65, 73, 56, 64, 54. Find the mean deviation from the median.

Find the value of cos^(-1)sqrt(2/3)-cos^(-1)""(sqrt(6)+1)/(2sqrt(3))

Liney = mx + 3 is tangent to parabola 3y^(2) = 2x then m = ……..

If the function f:R rarr B defined by f(x)=sqrt(x^(2)) is surjective then B is

A flag staff of 5 mts high stands on a building of 25 mt high. At an observerat a height of 30 mt the flag staff and the building subtend equal angles. The distance of the observer from the top of the flag staff is

The distance of the orthocentre from the vertices A,B,C are in the ratio

Find the derivative of y=sqrt(2x-3)+sqrt(7-3x).

If the position vectors of the four points A, B, C, D are 2bar(a), bar(b), 6bar(b) and 2bar(a)+5bar(b) then ABCD is

If f(0)=0, f(1)=1, f(2)=2 and f(x)=f(x-2)+f(x-3) " for " x=3, 4, 5, ………….., then f(9)=

If a,b,c(altbltc) are positive prime factors of 2001, then find the equation of the plane passing through (1,1,1) in which (b,c,a) are direction ratios of a normal line.

A variable line L si drawn through O(0,0) to meet lines L_1 and L_2 " given by " y-x-10=0 and y-x-20=0 at point A and B, respectively. A point P IS taken on L such that 2//OP=1//OA+1//OB. Then the locus of P is

A variable line L si drawn through O(0,0) to meet lines L_1 and L_2 " given by " y-x-10=0 and y-x-20=0 at point A and B, respectively. Locus of P, if OP^2=OAxxOB, is

A variable line L si drawn through O(0,0) to meet lines L_1 and L_2 " given by " y-x-10=0 and y-x-20=0 at point A and B, respectively. Locus of P if(1//OP^2)=(1//OA^2), is

Expand the following expressions : (ax-b/x)^(6)

If the direction cosines of a line L are (ab, b,b) and the angle between L and X-axis is (pi)/(3) then a pair of possible values for a, b are

Write cos4 thetain terms ofcos theta.

If tan px = cot qx, then the solutions are in A.P. with common difference

If A = {a_(1),a_(2), ……,a_(10)} and B = {b_(1),b_(2),b_(3),…….b_(10)} then the number of bijections that can be defined from A to B is

Using section formula, show that the points A(2, -3, 4), B(-1, 2, 1) and C(0,1/3,2) are collinear.

If z=x+iy lies in the third quadrant, then (bar(z))/(z) also lies in the third quadrant, if

Find Lt_(xto0)log_(tanx)tan2x

Ramesh travells at the speed of 40km/hr. If he decreases his speed 4km each hour, then how much time he will taken to cover 216km?

If rgt0,-pilethetalepi and r,theta satisfy rsintheta=3, r=4(1+sintheta) then no. of possible solutions of (r, theta) is

The value of tan(sin^(-1)(cos(sin^(-1)x)))tan(cos^(-1)(sin(cos^(-1)x)))." where "x in (0, 1) is equal to

Find k if the function is continuous at x=(pi)/(2) if(a) f(x)={{:((k cos x )/(pi-2x),x ne (pi)/(2)),(3,if x=(pi)/(2)):} at x=(pi)/(2) (b) f(x)={{:(kx+1, if x le 2),(cos x,if x gt 2):} at x=2 (c ) if f(x)={{:(k^(2)x-k,if x le 1),(2 , if x lt 1):} is continous on R then find the value(s) of k

Evaluate the following limits : Lim_(x to 0) 5^(x) sin (a/(5^(x)))

The radius of a sphere is measured as 14cm. Later it was found that there is an error 0.02cm in measuring the radius. Find the approximate error in surface area of the sphere

Find the values of a and bif f(x)={{:(ax-b,"for" x le -1),(3x^(2)-4ax+2ab,"for" -1 lt x lt 1 "is continous on R"),(-21,"for" x ge1):}is continuous on R.

Three squares of chess board are selected at random. Find the probability of getting 2 squares of one colour and other of a different colour.

Evaluate the following limits : Lt_(ntooo)(1+2+3+......+n)/n^(2)

The integer is selected at random from 1 to 25. The probability that it is a prime number is

If x^4 + 7 x^2y^2+9y^4 =24 xy^3 then (dy)/(dx) =

A particle moving along a straight line has the relation s =t^2 +3, connecting the distance s described by the particle in time 1. Find the velocity and acceleration of the particle at t=4 seconds.

If (sin^(4))/(2)+(cos^(4))/(3)=(1)/(5) then

Evaluate : lim_(x to -1) x/([x])

L_1 : 3x+4y+8=0 , L_2 : 2x+7y-1=0 If D is the midpoint of BC and E is the mid point of CA then DE is equal to

If cos h^(-1)(k) = log_(e)(3+2sqrt(2)) then k =

i) If bar(a), bar(b), bar(c) are non coplanar vectors, then prove that the vectors 5bar(a)-6bar(b)+7bar(c), 7bar(a)-8bar(b)+9bar(c) and bar(a)-3bar(b)+5bar(c) are coplanar.

Evaluate the following limits : Lim_(x to oo) (4x-3)/(2x+7)

A problem is Mathematics is given to three sutdents whose chance of solving it are in the ratio 6:4:3 respectively. What is the probability that (i)the problem is solved(ii)what is the probability that none of them could solve the problem.

Find the coordinates of the point equidistant from the four pointsA(0,0,0) , B (a,0,0) , C(0,b,0) and D(0,0,c) .