14949 + Interview Questions in Maths in Class 11 Page 192 InterviewSolution

9551.	Four cards are drawn from a full pack of cards . Find the probability thatall are diamonds ,
Answer» ANSWER :`=(11)/(4165)`.

Discussion

9552.	If (x)/(y) = (cos A)/( cos B) then (x tan A +y tan B)/(x +y) =
Answer» `TAN "" (A+B)/(2)` `tan ""(A-B)/(2)` `COT "" (T+ B)/(2)` `cot "" ( A -B)/(2)` ANSWER :A

Discussion

9553.	Two unbiased dice are thrown . Find the probability that the total of the numbers on the dice is any number from 2 to 12 , both inclusive.
Answer» ANSWER :`=1`.

Discussion

9554.	The value of x which satisfies sin(cot^(-1)x)=cos(tan^(-1)(1+x)) is
Answer» `-1/2` `1/2` `-1` 1 Answer :A

Discussion

9555.	Find the distance between parallel lines (i) 15x + 8y - 34 = 0 " and " 15x + 8y + 31 = 0(ii) l (x + y) + p = 0 " and " l (x + y) - r = 0 .
Answer» ANSWER :`(i) 65/17 ` units, (ii) `1/sqrt 2 \|(p + R)/L\|` units.

Discussion

9556.	2 (x-1) lt x + 5, 3 (x+2) gt 2-x
Answer» ANSWER :`(-1,7)` `(##NCERT_TEL_MAT_XI_C06_E04_008_A01##)`

Discussion

9557.	Aray of light passing through the point (1, 2) reflects on the x-axis at point and the reflected ray passes through the point (5,3). Find the coordinates of A.
Answer» ANSWER :`(13/5, 0)`

Discussion

9558.	Which of the following sets are empty sets ? {x : x in N, x^(2)= 9}
Answer» ANSWER :it is not an EMPTY SET

Discussion

9559.	If sin ^(2) x + (1)/(4) sin^(2) 3x = sin x sin^(2) 3 xthenx =
Answer» `(n pi)/(2), n in Z` `2 n pi PM (pi)/(3) , n in Z` `n pi, n in Z` `n pi + (-1) ^(n)(pi)/(6), n in Z` Answer :C::D

Discussion

9560.	Let A be a square matrix. Then A+A^(T) will be
Answer» SYMMETRIC matrix skew symmetric scalar IDENTITY matrix Answer :A

Discussion

9561.	The points A91,3) and C (5,1) are the opposite vertices of a rectange. The equation of line passing through other two vertices and of gradient 2, is
Answer» `2X+y-8 =0` `2x -y-4 =0` `x+3y+4=0` `x+2y-1=0` ANSWER :B

Discussion

9562.	Lett_(1)=(sin^(-1)x)^(sin^(-1)x),t_(2)=(sin^(-1)X)(cos^(-1)x),t_(3)=(cos^(-1)x)^(sin^(-1)x), t_(4)=(cos^(-1)x)^(cos^(-1)x) Match the items of column I with the items Column II
Answer» ANSWER :A-q,B-s,C-r,D-p

Discussion

9563.	If bara and barb are unit vectors, then the vector ( bara + barb) xx ( bara xx barb) is parallel to the vector
Answer» `veca-vecb` `veca+vecb` `2veca-vecb` `2veca+vecb` ANSWER :A

Discussion

9564.	If 0 le x le (pi)/(3) then range of f(x) = sec((pi)/(6) - x) sec((pi)/(6) + x) is
Answer» `((4)/( SQRT3) , OO)` `[ (4)/( sqrt3) , oo)` `( 0, (4)/( sqrt3) ]` `( 0, (4)/( sqrt3))` ANSWER :B

Discussion

9565.	State whether the following sentences are statements are not:
Answer» The ANGLES OPPOSITE to equal sides of a TRIANGLE are equal. The moon is a SATELLITE of earth. May God bless you! Asia is a continent. Answer :A

Discussion

9566.	Find the vector equation of the plane passing through the points 2bar(i)+bar(j)-bar(k), bar(i)-bar(j)+2bar(k) and parallel to bar(i)-2bar(j)-2bar(k)
Answer» ANSWER :`BAR(R)=(1-s)(2bar(i)+bar(j)-bar(K))+s(bar(i)-bar(j)+2bar(k))+t(i-2j-2k)" where "s, t in R`

Discussion

9567.	Value of sec(-1680^(@)).sin330^(@)
Answer» `-1` 0 2 `-1` ANSWER :D

Discussion

9568.	Find the equation of tangents to the hyperbola x^(2)-2y^(2)=8 thatmake an angle of 45^(@) with the positive direction of x -axis .
Answer» ANSWER :`y=x+-2`

Discussion

9569.	If z_(1)=2 + 7i and z_(2)=1- 5i, then verify that \|z_(1)-z_(2)\| gt \|z_(1)\|-\|z_(2)\|
Answer» ANSWER :`12.04 GT 2.18`

Discussion

9570.	Find the variance and standard deviation of the following data:
Answer» ANSWER :VARIANCE = 29.09; S.D = 5.395

Discussion

9571.	If 5 parallel lines intersect another set of 4 , parallel lines (not parallel to the lines inthe first set) then the no. of parallelograms formed in this lattice structure is:
Answer» 15 20 9 60 Answer :D

Discussion

9572.	If y = SX and z = tX where all the letters denotes the functions of x and suffixes denotes the differentiation w.r.t x and \|(X,Y,Z),(X_1,Y_1,Z_1),(X_2,Y_2,Z_2)\|=X^(k) \|(S_1,t_1),(S_2,t_2)\| then K is
Answer» ANSWER :C

Discussion

9573.	Which of the following sentences are statement? Give reason for your answer: Who are you?
Answer» ANSWER :Not a STATEMENT

Discussion

9574.	If in two circles, arcs of same length subtend angles 60^(@) and75^(@) at the centre, find the ratio of their radii?
Answer» Answer :` rArr r_(1) : r_(2) = 5 : 4 `

Discussion

9575.	……..is the equation of hyperbola whose distance between two focii is 16 and eccentricity e = sqrt(2).
Answer» ANSWER :`X^(2) - y^(2) = 32`

Discussion

9576.	Match the following:
Answer» 1-d, 2-a, 3-b, 4-c 1-a, 2-b, 3-c, 4-d 1-c, 2-b, 3-d, 4-c 1-b,2-c,3-a, 4-d ANSWER :A

Discussion

9577.	Consider a triangle ABC with vertics A (2,5),B (-4,9) and C (-2,-1) Find the co-ordinates of the mid points of AB,BC and AC
Answer» SOLUTION :(-1,7), (-3,4)

Discussion

9578.	Which of the following sentences are statements? Justify 0 is a complex number.
Answer» ANSWER :It is STATEMENT.

Discussion

9579.	If a =5 ,b =4 and cos (A-B)= (31)/(32), then show that c= 6
Answer» ANSWER :` C = 6`

Discussion

9580.	The remainder when 5^(99) is divided by 13 is
Answer» `6` `8` `9` `10` ANSWER :B

Discussion

9581.	If in trianlge ABC, a,c and angle A are given and c sin A lt alt c , then b_(1) and b_(2), are values of
Answer» `b_(1)+b_(2)=2c COSA` `b_(1)+b_(2)=cosA` `b_(1)b_(2)=c^(2)-a^(2)` `b_(1)b_(2)=c^(2)+a^(2)` ANSWER :A::C

Discussion

9582.	Of all the closed cylindrical cans (right circular), which enclose a given volume of 100.cm., which one has the minimum surface area?
Answer» ANSWER :`2((50)/PI)^(1//3)`

Discussion

9583.	If the vectros (cosx)bari +(sinx)barj and xbari+(sinx)barj are collinear vectors, then find the range of 'x'.
Answer» ANSWER :`{npi//N INZ,n NE0}uu{x_(0)} " where "pi/6ltx_(0)ltpi/3 and cosx_(0) = x_(0)`

Discussion

9584.	In the triangle ABC with verticesA (2, 3) , B (4, -1) " and " C (1, 2), find the equation and length of altitude from the vertex A.
Answer» ANSWER :`y - X = 1, SQRT2`

Discussion

9585.	Third term of arithmetic sequence is 9 and tenth term is 21. Then sum of its 12 term is ........... .
Answer» ANSWER :180

Discussion

9586.	If b lt 1. sin t lt0.cos t lt 0 and log_(b) (sin t)=x, then log_(b) (cost) is equal to
Answer» `(1)/(2)log_(b)(1-b^(2^(X)))` `2log(1-b^(x//2))` `log_(b)SQRT(1-b^(2X))` `sqrt(1-x^(2))` Answer :A::C

Discussion

9587.	If the equation sin^(-1)(x^(2)+x+1)+cos^(-1)(lambdax+1)=pi/2 has exactly two solutions for lambda in [a, b), then the value of a + b is
Answer» ANSWER :1

Discussion

9588.	Equation of a straight line passing through the point (4,5) and equally inclined to the lines 3x=4y+ 7 and 5y=12x+6 is
Answer» 9x-7y=1 9x+7y=71 7x+9y=73 7x-9y+17=0 Answer :A::C

Discussion

9589.	A person has 2 parents, 4 grandparents, 8 great grandparents, and so on.Find the number of his ancestors during the ten generations preceding his own.
Answer» ANSWER :2046

Discussion

9590.	Equation of a line is 3x-4y+ 10 =0. Find its (i) slope,
Answer» ANSWER :(i) `m = (3)/(4)`

Discussion

9591.	Four points A(+1, -1, 1) , B(1, 3, 1), C(4, 3, 1), and D(4, -1, 1), taken in order are the vertices of
Answer» a parallelogram which is NEITHER a RECTANGLE nor a rhombus rhombus an isosceles TRAPEZIUM a cyclic quadrilateral Answer :d

Discussion

9592.	Find 'a' such that Rank (A)=2 where A=[(2,1,1,2),(3,0,-1,4),(7,2,a,8)]
Answer» ANSWER :`a=1`

Discussion

9593.	Solve the equation: (2x-7)(x^(2)-9)(2x+5)=91.
Answer» ANSWER :`4,(-7)/(2),(1pmsqrt(65))/(4)`.

Discussion

9594.	[(baraxxbarb)xx(barbxxbarc)(barbxxbarc)xx(barcxxbara)(barcxxbara)xx(baraxxbarb)]=
Answer» `[BARA BARB BARC]` `[bara barb barc]^(2)` `[BARABARB barc]^(3)` `[bara barb barc]^(4)` Answer :D

Discussion

9595.	Angle between the ........... intersecting lines 2x-y+3=0 and x+2y+3=0.
Answer» `90^(@)` `60^(@)` `45^(@)` `30^(@)` ANSWER :A

Discussion

9596.	In which ratio line x+y=4 divides line segment joining points (-1,1) and (5,7) ?
Answer» ANSWER :`1:2`

Discussion

9597.	bar(AB) joining A(1,k) and B(3,5) is diameter of circle with centre C(h,3) then h and k = ............
Answer» ANSWER :`H = 2 and K = 1`

Discussion

9598.	If z=x + yi and omega= (1-zi)/(z-i) show that \|omega\|=1 rArr z is purely real
Answer» ANSWER :`X + 0I`

Discussion

9599.	Find the value of tan ""pi/8.
Answer» ANSWER :`TAN "" (PI)/(8) = sqrt2-1`

Discussion

9600.	Consider the first 10 positive integers . If we multiple each number by -1 and then add 1 toeach number , the variance of the numbers so obtained is…..
Answer» 8.25 6.5 3.87 2.87 Answer :A

Discussion

Explore topic-wise InterviewSolutions in .

Four cards are drawn from a full pack of cards . Find the probability thatall are diamonds ,

If (x)/(y) = (cos A)/( cos B) then (x tan A +y tan B)/(x +y) =

Two unbiased dice are thrown . Find the probability that the total of the numbers on the dice is any number from 2 to 12 , both inclusive.

The value of x which satisfies sin(cot^(-1)x)=cos(tan^(-1)(1+x)) is

Find the distance between parallel lines (i) 15x + 8y - 34 = 0 " and " 15x + 8y + 31 = 0(ii) l (x + y) + p = 0 " and " l (x + y) - r = 0 .

2 (x-1) lt x + 5, 3 (x+2) gt 2-x

Aray of light passing through the point (1, 2) reflects on the x-axis at point and the reflected ray passes through the point (5,3). Find the coordinates of A.

Which of the following sets are empty sets ? {x : x in N, x^(2)= 9}

If sin ^(2) x + (1)/(4) sin^(2) 3x = sin x sin^(2) 3 xthenx =

Let A be a square matrix. Then A+A^(T) will be

The points A91,3) and C (5,1) are the opposite vertices of a rectange. The equation of line passing through other two vertices and of gradient 2, is

Lett_(1)=(sin^(-1)x)^(sin^(-1)x),t_(2)=(sin^(-1)X)(cos^(-1)x),t_(3)=(cos^(-1)x)^(sin^(-1)x), t_(4)=(cos^(-1)x)^(cos^(-1)x) Match the items of column I with the items Column II

If bara and barb are unit vectors, then the vector ( bara + barb) xx ( bara xx barb) is parallel to the vector

If 0 le x le (pi)/(3) then range of f(x) = sec((pi)/(6) - x) sec((pi)/(6) + x) is

State whether the following sentences are statements are not:

Find the vector equation of the plane passing through the points 2bar(i)+bar(j)-bar(k), bar(i)-bar(j)+2bar(k) and parallel to bar(i)-2bar(j)-2bar(k)

Value of sec(-1680^(@)).sin330^(@)

Find the equation of tangents to the hyperbola x^(2)-2y^(2)=8 thatmake an angle of 45^(@) with the positive direction of x -axis .

If z_(1)=2 + 7i and z_(2)=1- 5i, then verify that |z_(1)-z_(2)| gt |z_(1)|-|z_(2)|

Find the variance and standard deviation of the following data:

If 5 parallel lines intersect another set of 4 , parallel lines (not parallel to the lines inthe first set) then the no. of parallelograms formed in this lattice structure is:

If y = SX and z = tX where all the letters denotes the functions of x and suffixes denotes the differentiation w.r.t x and |(X,Y,Z),(X_1,Y_1,Z_1),(X_2,Y_2,Z_2)|=X^(k) |(S_1,t_1),(S_2,t_2)| then K is

Which of the following sentences are statement? Give reason for your answer: Who are you?

If in two circles, arcs of same length subtend angles 60^(@) and75^(@) at the centre, find the ratio of their radii?

……..is the equation of hyperbola whose distance between two focii is 16 and eccentricity e = sqrt(2).

Match the following:

Consider a triangle ABC with vertics A (2,5),B (-4,9) and C (-2,-1) Find the co-ordinates of the mid points of AB,BC and AC

Which of the following sentences are statements? Justify 0 is a complex number.

If a =5 ,b =4 and cos (A-B)= (31)/(32), then show that c= 6

The remainder when 5^(99) is divided by 13 is

If in trianlge ABC, a,c and angle A are given and c sin A lt alt c , then b_(1) and b_(2), are values of

Of all the closed cylindrical cans (right circular), which enclose a given volume of 100.cm., which one has the minimum surface area?

If the vectros (cosx)bari +(sinx)barj and xbari+(sinx)barj are collinear vectors, then find the range of 'x'.

In the triangle ABC with verticesA (2, 3) , B (4, -1) " and " C (1, 2), find the equation and length of altitude from the vertex A.

Third term of arithmetic sequence is 9 and tenth term is 21. Then sum of its 12 term is ........... .

If b lt 1. sin t lt0.cos t lt 0 and log_(b) (sin t)=x, then log_(b) (cost) is equal to

If the equation sin^(-1)(x^(2)+x+1)+cos^(-1)(lambdax+1)=pi/2 has exactly two solutions for lambda in [a, b), then the value of a + b is

Equation of a straight line passing through the point (4,5) and equally inclined to the lines 3x=4y+ 7 and 5y=12x+6 is

A person has 2 parents, 4 grandparents, 8 great grandparents, and so on.Find the number of his ancestors during the ten generations preceding his own.

Equation of a line is 3x-4y+ 10 =0. Find its (i) slope,

Four points A(+1, -1, 1) , B(1, 3, 1), C(4, 3, 1), and D(4, -1, 1), taken in order are the vertices of

Find 'a' such that Rank (A)=2 where A=[(2,1,1,2),(3,0,-1,4),(7,2,a,8)]

Solve the equation: (2x-7)(x^(2)-9)(2x+5)=91.

[(baraxxbarb)xx(barbxxbarc)(barbxxbarc)xx(barcxxbara)(barcxxbara)xx(baraxxbarb)]=

Angle between the ........... intersecting lines 2x-y+3=0 and x+2y+3=0.

In which ratio line x+y=4 divides line segment joining points (-1,1) and (5,7) ?

bar(AB) joining A(1,k) and B(3,5) is diameter of circle with centre C(h,3) then h and k = ............

If z=x + yi and omega= (1-zi)/(z-i) show that |omega|=1 rArr z is purely real

Find the value of tan ""pi/8.

Consider the first 10 positive integers . If we multiple each number by -1 and then add 1 toeach number , the variance of the numbers so obtained is…..