14949 + Interview Questions in Maths in Class 11 Page 32 InterviewSolution

1551.	Find the equation of line joining origin to the point of intersection of the pair of lines 3x+y=10 and x-y=2.
Answer» ANSWER :`x-3y=0`

Discussion

1552.	If some or all of n objects are taken at a time then the number of combinations is 2^n-1.
Answer» ANSWER :`=2^n- 1`

Discussion

1553.	Which one of the following equations represents a parabola which is symmetrical about the positive y-axis?
Answer» `y^2=4x` `y^2=-8x` `x^2+4y=0` `x^2-4y=0` ANSWER :D

Discussion

1554.	Let bara=barj-bark and barc= bari -barj-bark. Then the vector barb satisfying bara xx barb + barc = 0 and bara. barb =3 is
Answer» `-bari+barj-2bark` `2bari-barj+2bark` `bari-barj-2bark` `bari+barj-2bark` ANSWER :A

Discussion

1555.	Given point A (6,30) and point B(24,6) equation of line AB is 4x+3y=114 . " point P " (0, lambda) is a point on y-axis such that 0lt lambda lt 38 and pointQ(0,K) is a point on y-axis such that kgt 38. For all position of point P, angle APB is maximum when point P is
Answer» (0,12) (0,15) (0,18) (0,21) ANSWER :C

Discussion

1556.	A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a cetrain point A on the path, he observves that the angle of elevation of the top of the pillar is 30^(@). After walking for 10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is 60^(@). Then the time taken (in minutes ) by him, from B to reach the pillar, is
Answer» 10 20 5 6 Answer :C

Discussion

1557.	If 0ltxltpi and cosx+sinx=1/2 then tanx=
Answer» `-((4+sqrt7))/3` `(1+sqrt7)/4` `(1-sqrt7)/4` `(4-sqrt7)/3` ANSWER :A

Discussion

1558.	Simiplify :((1+i)/(1-i))^(4n+1) (n is a positive integer)
Answer» ANSWER :i

Discussion

1559.	Find the square root of the following complex number ((2+3i)/(5-4i) + (2-3i)/(5+4i))
Answer» ANSWER :`+- (2)/(sqrt41)i`

Discussion

1560.	Find the value of n from each of the following: (i) 10 .^(n)P_(6) = .^(n+1)P_(3) (ii) 16.^(n)P_(3) = 13 .^(n+1)P_(3) (iii) .^(n-1)P_(3): .^(n)P_(4) = 1:9 (iv) .^(n)P_(6) = 30 .^(n)P_(4) (v) .^(2n+1)P_(n-1): .^(2n-1) P_(n) = 3:5 (vi) P(n,4) =30 P (n,2)
Answer» Answer :(i) 9 (ii) 15 (iii) 9 (iv) 10 (v) 4 (VI) 8

Discussion

1561.	Draw the graph of the following quadratic functions. Q. y=-x^(2)+2x+3""-3lexle5.
Answer» ANSWER :`(##SCH_OPM_ISC_MAT_XI_C10_E05_002_A01##)`

Discussion

1562.	If P(AcapB)=(1)/(2),P(A'capB')=(1)/(3),P(A)=a and P(B)=2a, then a =………..
Answer» `(1)/(3)` `(7)/(18)` `(4)/(9)` `(1)/(9)` Answer :B

Discussion

1563.	If Sin^(-1)(cos^(-1)x) lt 1 and cos^(-1)(cos^(-1)x) lt 1" then "x in
Answer» `(SIN1, Sin(sin1))` `(cos(COS1), cos(sin1))` `(cos(sin1), cos(cos1))` `PHI` (empty set) ANSWER :C

Discussion

1564.	The(x+4)/(3) = (y+6)/(5) = (z-1)/(-2) and 3x - 2y + z+5 =0 = 2x + 3y + 4z -k are coplanar for k is equal to
Answer» ANSWER :4

Discussion

1565.	If sin^(-1)x+sin^(-1)y=pi/2 and sin2x=cos2y, then
Answer» `x=pi/8+sqrt(1/2-pi^(2)/64)` `y=sqrt(1/2-pi^(2)/64)-pi/12` `x=pi/12+sqrt(1/2-pi^(2)/64)` `y=sqrt(1/2-pi^(2)/64)-pi/8` ANSWER :A::D

Discussion

1566.	P(1, 1, 1) and Q(1, 1, 1) are two points in the space such that PQ=sqrt(27), the value of l can be
Answer» `-4` `-2` 2 0 Answer :B

Discussion

1567.	Foot of the perpendicular drawn from the point A (1,0,3)to the join of the points B (4,7,1) and C (3,5,3) is
Answer» `(1,2,-2)` `((5)/(3), (7)/(3) , (17)/(3))` `((1)/(3) , (2)/(3) , (-2)/(3))` `((-5)/(3), (-7)/(3), (-17)/(3))` ANSWER :B

Discussion

1568.	BY the principle of mathematicalinduction ,prove that for nge 1 1^(2) + 3^(2) + 5^(2) + ….+ ( 2n-1)^(2) = (n(2n-1) (2n+1))/3
Answer» <P> ANSWER :p (N)

Discussion

1569.	Find the sum to infinity in each of the following G.P 1, (1)/(3), (1)/(9),…….
Answer» ANSWER :`(3)/(2)`

Discussion

1570.	The value of f(0) so that f(x)=(log(1+x//a)-log(1-x//b))/(x) is continuous at x=0 is
Answer» ANSWER :`(a+b)/(AB)`

Discussion

1571.	If the function f(x)=(Ksinx+2cosx)/(sinx+cosx) is increasing for all values of x then
Answer» `Klt1` `KGT1` `Klt2` `Kgt2` ANSWER :D

Discussion

1572.	If f(x)=ax^(2)+bx^(3)+cx -5 ( a, b, c are real constants and f(-7)=7, then the range of f(7)+17cos x is
Answer» `[-34, 0]` `[0, 34]` `[-34, 34]` `{-34, 34}` ANSWER :A

Discussion

1573.	Greatest value of ((1)/(x))^(x) is
Answer» E `(e)^((1)/(e))` `((1)/(e))^(e)` `(1)/(e)` ANSWER :B

Discussion

1574.	Find the mean deviation about the mean for the data is Question:
Answer» SOLUTION : MEAN `BARX=(sumf_(i)x_(i))/(sumf_(i))=350/25=14` Mean DEVIATION `=(sumf_(i)d_(i))/(sumf_(i))=158/25=6.32`

Discussion

1575.	Find the mean deviation about the mean for the data is Question:
Answer» SOLUTION : MEAN `BARX=(sumf_(i)x_(i))/(sumf_(i))=4000/80=50` Mean DEVIATION `=(sumf_(i)\|x_(i)-barx\|)/(sumf_(i))=1280/80=16`

Discussion

1576.	Locate the following points : (i) (1, -1, 3) (ii) (-1, 2, 4) (iii) (-2, -4, -7) (iv) (-4, 2, -5)
Answer» ANSWER :X-increment = Y-increment = Z-increment = 1.

Discussion

1577.	The value of x for which the function f(x)=int_(0)^(x)(1-t^(2))e^(-t^(2)//2)dt has an extremum is
Answer» 0 1 `-1` 2 Answer :B::C

Discussion

1578.	If A(cos alpha, sin alpha, 0) B(cos beta, sin beta, 0) C(cos gamma, sin gamma, 0) are vertices of DeltaABC and let cos alpha+cos beta+cos gamma=3a, sin alpha+sin beta +sin gamma=3b then correct matching of the following is : {:("List-1","List-II"),((A)"Circumcentre",(1)"(3a, 3b, 0)"),((B)"Centroid",(2)"(0, 0, 0)"),((C )"Ortho centre",(4)"(2a,2b,0)"):}
Answer» `{:(A,B,C),(2,3,4):}` `{:(A,B,C),(2,3,1):}` `{:(A,B,C),(1,2,3):}` `{:(A,B,C),(2,3,4):}` ANSWER :b

Discussion

1579.	Given that (1 + i)/(1 + 2^(2)i) xx (1 + 3^(2) i)/(1 + 4^(2) i) xx….xx (1 + (2n-1)^(2)i)/(1+(2n)^(2)i)= (a + bi)/(c+di), show that (2)/(17) xx (82)/(257) xx ….xx ((2n-1)^(4) + 1)/((2n)^(4) + 1) = (a^(2) + b^(2))/(c^(2) + d^(2))
Answer» ANSWER :`(a^(2) + B^(2))/(C^(2) + d^(2))`

Discussion

1580.	Differentiate the following w.r.t. x or t or u as the case may be: 7. y= (2x -3)/( 3x + 4)
Answer» ANSWER :`(DY)/( DX ) = (17)/( (3x +4)^2)`

Discussion

1581.	If y=sqrt((1-x)/(1+x)) then (1-x^2)dy/dx is equal to
Answer» `y^2` `1/y` `-y` `-y//x` ANSWER :C

Discussion

1582.	If f is continuous on [a,b] and differentiable in (a,b) (ab gt0 ) , then there exists c in (a,b) such that (f(b)-f(a))/((1)/(b) - ( 1)/(a))=
Answer» `-C^(2)f (c )` `c^(2) f (c )` `- c f' ((1)/( c ))` `CF' ((1)/( c^(2)))` Answer :A

Discussion

1583.	(i) Find the values of 'a' for which the expression x^(2)-(3a-1)x+2a^(2)+2a-11 is always positive (ii) If x^(2)+4ax+2 gt0 for all values of x, then a lies in the interval. (a) (-2,4) (b) (1,2) (c) (-sqrt(2),sqrt(2)) (d) (-(1)/(sqrt(2)),(1)/(sqrt(2))) (e) (-4,2).
Answer» ANSWER :(i) `5 LT a lt 9` (II) (d)

Discussion

1584.	Fourcards are drawn at random from a pack of 52 playing cards. Find the probability of getting four honours of the same suit.
Answer» ANSWER :`(""^(4)C_(1))/(""^(52)C_(4))=(4)/(270725)`

Discussion

1585.	Expand (1+x)^((2)/(3)) up to four terms for \|x\|lt 1.
Answer» Answer :`=1+(2)/(3)X-(1)/(9)x^(2)+(4)/(81)x^(3)+….`

Discussion

1586.	Let f(n)=1 + 1/2 + 1/3 +......+1/n, Then f(1)+f(2)+f(3)+.....+f(n) is equal to
Answer» `NF(N)-1` `(n+1)F(n)-n` `(n+1)f(n)+n` `nf(n)+n` ANSWER :B

Discussion

1587.	If y = "log cos "( tan^(-1)((e^x - e^(-x))/(2))), then (dy)/(dx) =
Answer» `- tan HX` `sin hx` `COS hx` `COT H x` Answer :A

Discussion

1588.	Use the graph to find the limits (if it exists).If the limit does not exist ,explain why? lim_(xrarr1)(x^2 +2)
Answer» ANSWER :3

Discussion

1589.	Solve the system of equations2x-y+3z=9,x+y+z=6,x-y+z=2 using Gauss Jordan method.
Answer» ANSWER :`Z=(-13)/(4)` .

Discussion

1590.	If sin theta and theta are the roots of px^(2) + qx + r = 0 then q^(2) - p^(2)=
Answer» 0 `-2pr` 2pr 2rp Answer :D

Discussion

1591.	If y = cos ^(-1) (cosx) , then (dy)/(dx)atx = (5pi)/4 is
Answer» 1 `-1` `1/sqrt2` `(5PI)/4` ANSWER :B

Discussion

1592.	2+ 3.2 + 4.2^(2) + …... upto n terms =
Answer» `(N+1) 2^(n-1)` `N2^(n+1)` `n2^(n)` `(n+1)2^(n)` ANSWER :C

Discussion

1593.	A plane passing through (- 1, 2, 3) and whose normal makes equal angles with the coordinate axes is
Answer» `x+y+z+4=0` `x-y+z+4=0` `x+y+z-4=0` `x+y+z=0` ANSWER :C

Discussion

1594.	The point which is equidistant from A (3,4,-1) and B (1,-2,5) on y-axis is
Answer» `(0,1,0)` `(1, 1//3, 0)` `(0, -1//3, 0)` `(0, -5//3 , 0)` ANSWER :C

Discussion

1595.	Find the slope and inclination of the line through each pair of the following points: (1, 2) and (5, 6)
Answer» ANSWER : `1, 45^(@)`

Discussion

1596.	Find the term independent of x in the expansion of the following binomials: (i) (x-(1)/(x) )^(14)
Answer» ANSWER :`T_8 = -3432`

Discussion

1597.	IF 3 sin^(-1)((2x)/(1+x^(2)))-4cos^(-1)((1-x^(2))/(1+x^(2)))+ 2tan^(-1)((2x)/(1-x^(2)))=(pi)/3 then x=
Answer» `1)1/(sqrt(3))` 2)`1/(sqrt(2))` 3)`1//3` 4)`1//2` Answer :A

Discussion

1598.	The polar form of the complex number (i^(25))^(3) is
Answer» `cos.(PI)/(3)-isin.(pi)/(3)` `cos(-(pi)/(2)+isin(-(pi)/(2))` `cos.(pi)/(6)-isin.(pi)/(6)` `cos.(pi)/(6)+isin.(pi)/(6)` ANSWER :B

Discussion

1599.	Let \|vec(a) + vec(b)\| = \|vec(a)-vec(b)\|. If \|vec(a) xx vec(b)\|= lamda \|vec(a)\|, then lamda=
Answer» `\|VEC(a)\|` `\|vec(B)\|` 1 2 Answer :B

Discussion

1600.	Find the standard deviation for the following data :
Answer» ANSWER :6.12

Discussion

Explore topic-wise InterviewSolutions in .

Find the equation of line joining origin to the point of intersection of the pair of lines 3x+y=10 and x-y=2.

If some or all of n objects are taken at a time then the number of combinations is 2^n-1.

Which one of the following equations represents a parabola which is symmetrical about the positive y-axis?

Let bara=barj-bark and barc= bari -barj-bark. Then the vector barb satisfying bara xx barb + barc = 0 and bara. barb =3 is

Given point A (6,30) and point B(24,6) equation of line AB is 4x+3y=114 . " point P " (0, lambda) is a point on y-axis such that 0lt lambda lt 38 and pointQ(0,K) is a point on y-axis such that kgt 38. For all position of point P, angle APB is maximum when point P is

If 0ltxltpi and cosx+sinx=1/2 then tanx=

Simiplify :((1+i)/(1-i))^(4n+1) (n is a positive integer)

Find the square root of the following complex number ((2+3i)/(5-4i) + (2-3i)/(5+4i))

Find the value of n from each of the following: (i) 10 .^(n)P_(6) = .^(n+1)P_(3) (ii) 16.^(n)P_(3) = 13 .^(n+1)P_(3) (iii) .^(n-1)P_(3): .^(n)P_(4) = 1:9 (iv) .^(n)P_(6) = 30 .^(n)P_(4) (v) .^(2n+1)P_(n-1): .^(2n-1) P_(n) = 3:5 (vi) P(n,4) =30 P (n,2)

Draw the graph of the following quadratic functions. Q. y=-x^(2)+2x+3""-3lexle5.

If P(AcapB)=(1)/(2),P(A'capB')=(1)/(3),P(A)=a and P(B)=2a, then a =………..

If Sin^(-1)(cos^(-1)x) lt 1 and cos^(-1)(cos^(-1)x) lt 1" then "x in

The(x+4)/(3) = (y+6)/(5) = (z-1)/(-2) and 3x - 2y + z+5 =0 = 2x + 3y + 4z -k are coplanar for k is equal to

If sin^(-1)x+sin^(-1)y=pi/2 and sin2x=cos2y, then

P(1, 1, 1) and Q(1, 1, 1) are two points in the space such that PQ=sqrt(27), the value of l can be

Foot of the perpendicular drawn from the point A (1,0,3)to the join of the points B (4,7,1) and C (3,5,3) is

BY the principle of mathematicalinduction ,prove that for nge 1 1^(2) + 3^(2) + 5^(2) + ….+ ( 2n-1)^(2) = (n(2n-1) (2n+1))/3

Find the sum to infinity in each of the following G.P 1, (1)/(3), (1)/(9),…….

The value of f(0) so that f(x)=(log(1+x//a)-log(1-x//b))/(x) is continuous at x=0 is

If the function f(x)=(Ksinx+2cosx)/(sinx+cosx) is increasing for all values of x then

If f(x)=ax^(2)+bx^(3)+cx -5 ( a, b, c are real constants and f(-7)=7, then the range of f(7)+17cos x is

Greatest value of ((1)/(x))^(x) is

Find the mean deviation about the mean for the data is Question:

Find the mean deviation about the mean for the data is Question:

Locate the following points : (i) (1, -1, 3) (ii) (-1, 2, 4) (iii) (-2, -4, -7) (iv) (-4, 2, -5)

The value of x for which the function f(x)=int_(0)^(x)(1-t^(2))e^(-t^(2)//2)dt has an extremum is

Given that (1 + i)/(1 + 2^(2)i) xx (1 + 3^(2) i)/(1 + 4^(2) i) xx….xx (1 + (2n-1)^(2)i)/(1+(2n)^(2)i)= (a + bi)/(c+di), show that (2)/(17) xx (82)/(257) xx ….xx ((2n-1)^(4) + 1)/((2n)^(4) + 1) = (a^(2) + b^(2))/(c^(2) + d^(2))

Differentiate the following w.r.t. x or t or u as the case may be: 7. y= (2x -3)/( 3x + 4)

If y=sqrt((1-x)/(1+x)) then (1-x^2)dy/dx is equal to

If f is continuous on [a,b] and differentiable in (a,b) (ab gt0 ) , then there exists c in (a,b) such that (f(b)-f(a))/((1)/(b) - ( 1)/(a))=

(i) Find the values of 'a' for which the expression x^(2)-(3a-1)x+2a^(2)+2a-11 is always positive (ii) If x^(2)+4ax+2 gt0 for all values of x, then a lies in the interval. (a) (-2,4) (b) (1,2) (c) (-sqrt(2),sqrt(2)) (d) (-(1)/(sqrt(2)),(1)/(sqrt(2))) (e) (-4,2).

Fourcards are drawn at random from a pack of 52 playing cards. Find the probability of getting four honours of the same suit.

Expand (1+x)^((2)/(3)) up to four terms for |x|lt 1.

Let f(n)=1 + 1/2 + 1/3 +......+1/n, Then f(1)+f(2)+f(3)+.....+f(n) is equal to

If y = "log cos "( tan^(-1)((e^x - e^(-x))/(2))), then (dy)/(dx) =

Use the graph to find the limits (if it exists).If the limit does not exist ,explain why? lim_(xrarr1)(x^2 +2)

Solve the system of equations2x-y+3z=9,x+y+z=6,x-y+z=2 using Gauss Jordan method.

If sin theta and theta are the roots of px^(2) + qx + r = 0 then q^(2) - p^(2)=

If y = cos ^(-1) (cosx) , then (dy)/(dx)atx = (5pi)/4 is

2+ 3.2 + 4.2^(2) + …... upto n terms =

A plane passing through (- 1, 2, 3) and whose normal makes equal angles with the coordinate axes is

The point which is equidistant from A (3,4,-1) and B (1,-2,5) on y-axis is

Find the slope and inclination of the line through each pair of the following points: (1, 2) and (5, 6)

Find the term independent of x in the expansion of the following binomials: (i) (x-(1)/(x) )^(14)

IF 3 sin^(-1)((2x)/(1+x^(2)))-4cos^(-1)((1-x^(2))/(1+x^(2)))+ 2tan^(-1)((2x)/(1-x^(2)))=(pi)/3 then x=

The polar form of the complex number (i^(25))^(3) is

Let |vec(a) + vec(b)| = |vec(a)-vec(b)|. If |vec(a) xx vec(b)|= lamda |vec(a)|, then lamda=

Find the standard deviation for the following data :