14949 + Interview Questions in Maths in Class 11 Page 81 InterviewSolution

4001.	The total number of solutions of cos x=sqrt(1-sin2x) in [0,2pi] is equal to
Answer» 2 3 5 4 Answer :A

Discussion

4002.	If thesemivertical angle of a cone is 45^(@)then the rate of change of volume of the cone is
Answer» CURVED AREA times the RATE of CHANGE of r base area times the rate of change of l base area times the rate of change of r base area times the rate of change of `theta` Answer :C

Discussion

4003.	If x_(1), x_(2), x_(3) as well as y_(1), y_(2), y_(3) are in G.P with same common ratio, then thepoints P(x_(1), y_(1)), Q(x_(2), y_(2)) and R(x_(3), y_(3))
Answer» LIE on a STRAIGHT LINE lie on an ellipse lie on a circle are VERTICES of a triangle Answer :A

Discussion

4004.	If a,b,c,d,e,f are in A.P. then d-b= ……
Answer» `2(C-a)` `2(f-c)` `2(d-c)` `2(f-b)` ANSWER :C

Discussion

4005.	Match the following (##ANE_PMP_MAT_0XI_C11_E02_019_Q01##)
Answer» SOLUTION :[MATCH in the FOLLOWING ORDER `y^2=12x, y^2=16x, x^2=-y, y^2=9/2x]`

Discussion

4006.	If vecaand vecb are unit vector which are included at an angle of 360^(@)then \|(3veca+2vecb) X (2veca-vecb)\|.
Answer» 7 `(7)/(2)` 14 none of these Answer :B

Discussion

4007.	Find equation of line passes from point of intersection of 3x+4y=7 and x-y+2=0. whose slope is 5.
Answer» ANSWER :`35x-7y+18=0` which is REQUIRED EQUATION.

Discussion

4008.	Solve the inequality7 le ((3x+11))/(2) le 11.
Answer» ANSWER :`[1, (11)/(3)]`

Discussion

4009.	If bara=2bari +bark, barb=bari +barj+bark, barc=4bari-3barj+7bark then the vector barr satifying barr xx barb = barc xx barb and barr.bara= 0 is
Answer» `bari+8barj+2bark` `bari-8barj+2bark` `bari-8barj-2bark` `-bari-8barj+2bark` ANSWER :D

Discussion

4010.	If tan x = 3/4, pi lt x lt (3pi)/(2), find the value of sin(x)/(2), cos "" x/2 and tan "" x/2.
Answer» ANSWER :`-3`

Discussion

4011.	Find the volume of tetrahedron formed by the four planes barr. (bari + barj) = 0 , barr. (barj + bark) = 0, barr. (bari + bark) = 0 and barr. (bari + barj + bark) = 4.
Answer» ANSWER :`128/3`

Discussion

4012.	For all sets A and B, A - (A - B) = A cap B.
Answer» ANSWER :R.H.S.

Discussion

4013.	If the sum of first 20 terms of an AP is equal to the sum of first 30 terms, then the sum of first 50 terms is.... a)50 b)20 c)0d)80
Answer» 50 20 0 80 Answer :C

Discussion

4014.	A company produces steel pipes in three plants with daily production volumes of 500, 1000 and 2000 units respectively. It is known that the fractions of defective outputs produced by the three plants are 0.005, 0.008 and 0.010 respectively. If a pipe selected from a day's total production is found to be defective, find the probability that it came from the first plant.
Answer» ANSWER :`= 5/61`

Discussion

4015.	The rank of [(1,0,2),(0,1,-2),(1,-1,4),(2,2,8)] is
Answer» ANSWER :3

Discussion

4016.	"sin"^(2)pi/8" + sin"^(2)(3pi)/8" + sin"^(2)(5pi)/8" + sin"^(2)(7pi)/8=
Answer» 1 2 4 6 Answer :B

Discussion

4017.	Write down the negation of following compound statements. 6 is divisible by 2 and 3.
Answer» ANSWER :not DIVISIBLE by 3.

Discussion

4018.	Iff(x) = \|x + 100\| +x^(2)test whether f( -100) exists or (b) Examine the differentiabilityof functionsinRRby drawingthe diagrams (i) \| sin x\| (ii)\| cos x \|
Answer» ANSWER :(a)X= -1 00 (B) ` `pi/2`

Discussion

4019.	A tower subtendsanglesalpha, 2alpha, 3alphaat A,B and C all lying on the horizontalline throughthe foot of the tower the AB/BC =
Answer» ` (sin 3 ALPHA )/(sin 2 alpha) ` ` 1+ 2 cos 2ALPHA ` ` 2 + cos 2 alpha` ` ( sin 2 alpha )/( sin alpha ) ` Answer :B

Discussion

4020.	Express each of the following decimals in the following p/q form5.682
Answer» ANSWER :(a) 52 (B) `1/52` (C) (i) `1/13` (II) `1/2`

Discussion

4021.	Express each of the following in the form b or bi, where b is a real number sqrt(-144)
Answer» ANSWER :12I

Discussion

4022.	If S=(1//2)ab""sinC and alpha is the error in C then, relative error in S is
Answer» `alphacotC` `alphasinC` `alphatanC` `alphacosC` ANSWER :A

Discussion

4023.	If A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}, find ( A ∩ B ) ∩ ( B ∪ C )
Answer» ANSWER :`{7, 9, 11 }`

Discussion

4024.	A man has 6 friends. In how many ways can be invite one or more of his friends to a party ?
Answer» ANSWER :63

Discussion

4025.	Assertion (A) : If semi vertical angle of a cone is 45^(@) and height is 30.05 cm then approximate volume of cone is 9045.08 pic.c Reason(R ): When semi vertical angle is 45^(@) approximate error in volume is deltav=pir^(2)deltah
Answer» A is FALSE R is TRUE A is true R is false A,R are true and `RrArrA` A,R both false ANSWER :A

Discussion

4026.	Two sides of the triangle are along the lines 3x-2y+6=0 and 4x+5y-20=0. If ortho centre of the triangle is (1,1). Find the equation of third side of the triangle.
Answer» ANSWER :`26.x - 122y - 1675 = 0`

Discussion

4027.	If Delta is the area of triangle whose sides are a,b,c then the area of the triangle with 2a,2b,2c as the sides is
Answer» `2DELTA` `4Delta` `8Delta` `16Delta` ANSWER :B

Discussion

4028.	If (1+x)^(n)=C_(0)+C_(1).x+C_(2).x^(2)+â€¦.+C_(n).x^(n). then prove that (i) C_(0)+2C_(1)+3C_(2)+â€¦+(n-1)C_(n)=(n+2).2^(n-1) (ii)C_(0)+3C_(1)+5C_(2)+...+(2n+1)C_(n)=(n+1).2^(n) (iii)C_(0)+(C_(2))/(3)+(C_(4))/(5) +....+(2^(n))/(n+1) (iv) 2C_(0)+(2^(2).C_(1))/(2) +(2^(3).C_(2))/(3)+...+(2^(n+1).C_(n))/(n+1) =(3^(n+1)-1)/(n+1) (v) (C_(0)+C_(1))(C_(1)+C_(2))(C_(2)+C_(3))......(C_(n-1)+C_(n)) =(C_(1)C_(2)C_(3)........C_(n)(n+1)^(n))/(\|uln)
Answer» SOLUTION :N/a

Discussion

4029.	Using binomial theorem, evaluate(96)^3
Answer» ANSWER :11040808032

Discussion

4030.	If A+B+C=pi then \|{:(tan(A+B+C),tanB,tanC),(tan(A+C),0,tanA),(tan(A+B),-tanA,0):}\|=
Answer» 1 `-1` `2tanA TAN B TANC` 0 Answer :D

Discussion

4031.	Express the following expression in the form of a+ib. ((3+isqrt(5))(3-isqrt(5))//((sqrt(3) + sqrt2i)-(sqrt(3)-isqrt(2)))
Answer» ANSWER :`0-I (7sqrt(2))/2`

Discussion

4032.	The range of f(x)=sin^(-1)((x^(2)+1)/(x^(2)+2)) is
Answer» `[0, pi//2]` `(0, pi//6)` `[pi//6, pi//2)` NONE of these Answer :C

Discussion

4033.	[(sqrt(3)+1)^(6)]= ……… Where "[]" is a greatest integar function .
Answer» 415 416 417 418 Answer :A

Discussion

4034.	Consider a quadrilateral whose vertices are A (- 4,2),B (2,6), C (8,5) and D (9,7) Find the mid point of the sides of the quadrilateral.
Answer» SOLUTION :`(-1,4) ( 5,11/2),(17/2,-1),(5/2,-5/2)`

Discussion

4035.	Find equation of the line through the point(0, 2) making an angle (2pi)/3with the positive x-axis. Also, find the equation of line parallel to it and crossing the y-axis at a distance of 2 units below the origin.
Answer» ANSWER :`SQRT3 X + y - 2 = 0 " and " sqrt3 x + y + 2 = 0 `

Discussion

4036.	Find the range of values of x for which the expression 12x^(2)+7x-10 is negative.
Answer» Answer :`(-5)/(4) lt X lt (2)/(3)`.

Discussion

4037.	Consider the following population and year graph, find the slope of the line AB and using it, find what will be the population in the year 2010?
Answer» ANSWER :104.5 CRORES

Discussion

4038.	The two lines x = ay+ b , z = cy + d and x = a' y + b', z = c ' y + d' will be perpendicular, if and only if
Answer» `aa' + BB' + C c' + 1=0` ` aa' +bb' +c c=0` `(a + a ') (B + b') (c + c'') =0` `aa ' + c c' +1=0` ANSWER :D

Discussion

4039.	The area of the triangle formed by the straight line x + y = 3 and the angle bisectors of the pair of straight lines x^(2)-y^(2)+2y=1 is
Answer» 2 SQ. units 4 sq. units 6 sq. units 8 sq. units Answer :A

Discussion

4040.	Assertion (A) : In a Delta ABC if r_(1)=2r_(2)=3r_(3) then a:b=5:4 Reason (R) : In a DeltaABC, if xr_(1)=yr_(2)=zr_(3)= (x+y+z) r, then a:b:c=y+z:z+x:x+y
Answer» A is true, r is true and R is CORRECT EXPLANATION of A A is true, R is true and R is not correct explanation of A A is TRE, R is false A is false, R is true Answer :A

Discussion

4041.	Find the locus of the feet of the perpendiculars drawn from the point (b, 0) on tangents to the circle x^(2) + y^(2) =a^(2)
Answer» ANSWER :`a^(2){y^(2)+(a-b)^(2)}`

Discussion

4042.	Name the octants in which thefollowing points lie (1,2,3),(4,-2,3),(4,-2,-5),(4,2,-5),(-4,2,-5),(-4,2,5),(-3,-1,6) (-2,-4,-7)
Answer» ANSWER :I,IV,VIII,V,VI,II,III,VII

Discussion

4043.	Let y = t^(10) +1 and x = t^8 +1. Then (d^2y)/(dx^2) is
Answer» `5/2t` `20t^8` `5/(16t^6)` `5/16t^8` ANSWER :C

Discussion

4044.	If F(x)=[(cosx,-sinx,0),(sinx,cosx,0),(0,0,1)] and G(x)=[(cosx,0,sinx),(0,1,0),(-sinx,0,cosx)] then [F(x)G(x)]^(-1)=
Answer» `G(-X)F(-x)` `{F(x)}^(-1){G(x)}^(-1)` `[G(x)]{F(x)}` `F(x).G(x)` ANSWER :A

Discussion

4045.	f(x) = {{:(4-3x " if " x le 0),(2a + x " if " x ge 0):} is continuous at x = 0 then a =
Answer» 1 2 3 4 Answer :B

Discussion

4046.	The vertices of a DeltaABC are A(1, 1), B(7, 3) and C(3, 6). State the slope ofthe altitude to BC
Answer» ANSWER : `4/(3)`

Discussion

4047.	Construct the index number for 1991 taking 1990 as the base year from the following data by simple average of price relative method.
Answer» ANSWER :`122.32`

Discussion

4048.	Perpendicular distance from (-3,-4) to the line 12x - 5y + 81 = 0is ..........
Answer» ANSWER :5

Discussion

4049.	Find the sum of the series 2^(2)+4^(2)+6^(2)+...to n terms.
Answer» ANSWER :`(2N(n+1)(2n-:1))/(3)`

Discussion

4050.	If x=sum_(n=0)^(oo) cos^(2n) theta, y=sum_(n=theta)^(oo) sin^(2n) theta and z=sum_(n=0)^(oo) theta sin^(2n) theta, 0 lt theta lt pi/2. Then show that xyz=x+y+z.
Answer» ANSWER :`(1)/((SIN^(2) THETA cos^(2) theta) (1-sin^(2) theta cos^(2) theta))`

Discussion

Explore topic-wise InterviewSolutions in .

The total number of solutions of cos x=sqrt(1-sin2x) in [0,2pi] is equal to

If thesemivertical angle of a cone is 45^(@)then the rate of change of volume of the cone is

If x_(1), x_(2), x_(3) as well as y_(1), y_(2), y_(3) are in G.P with same common ratio, then thepoints P(x_(1), y_(1)), Q(x_(2), y_(2)) and R(x_(3), y_(3))

If a,b,c,d,e,f are in A.P. then d-b= ……

Match the following (##ANE_PMP_MAT_0XI_C11_E02_019_Q01##)

If vecaand vecb are unit vector which are included at an angle of 360^(@)then |(3veca+2vecb) X (2veca-vecb)|.

Find equation of line passes from point of intersection of 3x+4y=7 and x-y+2=0. whose slope is 5.

Solve the inequality7 le ((3x+11))/(2) le 11.

If bara=2bari +bark, barb=bari +barj+bark, barc=4bari-3barj+7bark then the vector barr satifying barr xx barb = barc xx barb and barr.bara= 0 is

If tan x = 3/4, pi lt x lt (3pi)/(2), find the value of sin(x)/(2), cos "" x/2 and tan "" x/2.

Find the volume of tetrahedron formed by the four planes barr. (bari + barj) = 0 , barr. (barj + bark) = 0, barr. (bari + bark) = 0 and barr. (bari + barj + bark) = 4.

For all sets A and B, A - (A - B) = A cap B.

If the sum of first 20 terms of an AP is equal to the sum of first 30 terms, then the sum of first 50 terms is.... a)50 b)20 c)0d)80

The rank of [(1,0,2),(0,1,-2),(1,-1,4),(2,2,8)] is

"sin"^(2)pi/8" + sin"^(2)(3pi)/8" + sin"^(2)(5pi)/8" + sin"^(2)(7pi)/8=

Write down the negation of following compound statements. 6 is divisible by 2 and 3.

Iff(x) = |x + 100| +x^(2)test whether f( -100) exists or (b) Examine the differentiabilityof functionsinRRby drawingthe diagrams (i) | sin x| (ii)| cos x |

A tower subtendsanglesalpha, 2alpha, 3alphaat A,B and C all lying on the horizontalline throughthe foot of the tower the AB/BC =

Express each of the following decimals in the following p/q form5.682

Express each of the following in the form b or bi, where b is a real number sqrt(-144)

If S=(1//2)ab""sinC and alpha is the error in C then, relative error in S is

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

A man has 6 friends. In how many ways can be invite one or more of his friends to a party ?

Assertion (A) : If semi vertical angle of a cone is 45^(@) and height is 30.05 cm then approximate volume of cone is 9045.08 pic.c Reason(R ): When semi vertical angle is 45^(@) approximate error in volume is deltav=pir^(2)deltah

Two sides of the triangle are along the lines 3x-2y+6=0 and 4x+5y-20=0. If ortho centre of the triangle is (1,1). Find the equation of third side of the triangle.

If Delta is the area of triangle whose sides are a,b,c then the area of the triangle with 2a,2b,2c as the sides is

Using binomial theorem, evaluate(96)^3

If A+B+C=pi then |{:(tan(A+B+C),tanB,tanC),(tan(A+C),0,tanA),(tan(A+B),-tanA,0):}|=

Express the following expression in the form of a+ib. ((3+isqrt(5))(3-isqrt(5))//((sqrt(3) + sqrt2i)-(sqrt(3)-isqrt(2)))

The range of f(x)=sin^(-1)((x^(2)+1)/(x^(2)+2)) is

[(sqrt(3)+1)^(6)]= ……… Where "[]" is a greatest integar function .

Consider a quadrilateral whose vertices are A (- 4,2),B (2,6), C (8,5) and D (9,7) Find the mid point of the sides of the quadrilateral.

Find equation of the line through the point(0, 2) making an angle (2pi)/3with the positive x-axis. Also, find the equation of line parallel to it and crossing the y-axis at a distance of 2 units below the origin.

Find the range of values of x for which the expression 12x^(2)+7x-10 is negative.

Consider the following population and year graph, find the slope of the line AB and using it, find what will be the population in the year 2010?

The two lines x = ay+ b , z = cy + d and x = a' y + b', z = c ' y + d' will be perpendicular, if and only if

The area of the triangle formed by the straight line x + y = 3 and the angle bisectors of the pair of straight lines x^(2)-y^(2)+2y=1 is

Assertion (A) : In a Delta ABC if r_(1)=2r_(2)=3r_(3) then a:b=5:4 Reason (R) : In a DeltaABC, if xr_(1)=yr_(2)=zr_(3)= (x+y+z) r, then a:b:c=y+z:z+x:x+y

Find the locus of the feet of the perpendiculars drawn from the point (b, 0) on tangents to the circle x^(2) + y^(2) =a^(2)

Name the octants in which thefollowing points lie (1,2,3),(4,-2,3),(4,-2,-5),(4,2,-5),(-4,2,-5),(-4,2,5),(-3,-1,6) (-2,-4,-7)

Let y = t^(10) +1 and x = t^8 +1. Then (d^2y)/(dx^2) is

If F(x)=[(cosx,-sinx,0),(sinx,cosx,0),(0,0,1)] and G(x)=[(cosx,0,sinx),(0,1,0),(-sinx,0,cosx)] then [F(x)G(x)]^(-1)=

f(x) = {{:(4-3x " if " x le 0),(2a + x " if " x ge 0):} is continuous at x = 0 then a =

The vertices of a DeltaABC are A(1, 1), B(7, 3) and C(3, 6). State the slope ofthe altitude to BC

Construct the index number for 1991 taking 1990 as the base year from the following data by simple average of price relative method.

Perpendicular distance from (-3,-4) to the line 12x - 5y + 81 = 0is ..........

Find the sum of the series 2^(2)+4^(2)+6^(2)+...to n terms.

If x=sum_(n=0)^(oo) cos^(2n) theta, y=sum_(n=theta)^(oo) sin^(2n) theta and z=sum_(n=0)^(oo) theta sin^(2n) theta, 0 lt theta lt pi/2. Then show that xyz=x+y+z.