14949 + Interview Questions in Maths in Class 11 Page 260 InterviewSolution

12951.	If the roots of the equation(x_(1)^(2)-a^(2))m^(2)-2x_(1)y_(1)m+y_(1)^(2)+b^(2)=0 are the slopes of two perpendicular lines intersecting at P(x_(1), y_(1)) then the locus of P is
Answer» `X^(2)+y^(2)=a^(2)+B^(2)` `x^(2)+y^(2)=a^(2)-b^(2)` `x^(2)-y^(2)=a^(2)+b^(2)` `x^(2)-y^(2)=a^(2)-b^(2)` ANSWER :B

Discussion

12952.	Find the variance of the following data: 6, 8, 10, 12, 14, 16, 18, 20, 22, 24
Answer» ANSWER :5.74

Discussion

12953.	In Delta ABC, if a sin^2""C/2+c sin^2""A/2 in terms of s,a,b,c is
Answer» ANSWER :` s-b`

Discussion

12954.	If .^(22)P_(r+1) :.^(20)P_(r+2) = 11:52, find the value of r.
Answer» Solution :`.^(22)P_(r+1): .^(20)P_(r+1) = 11:52` `RARR (22!)/((22-r-1)!) : (20!)/((20-r-2)!) = 11:52` `rArr (22!)/((21-r)!): (20!)/((18-r)!) = 11:52` `rArr(22!)/((21-r)!) xx ((18-r)!)/(20!) = (11)/(52)` `rArr (22 xx 21 xx 20!)/((21-r) xx (20-r) xx (19-r) xx(18-r)!) xx ((18-r)!)/(20!) = (11)/(52)` `rArr (22 xx 21)/((21-r)(20-r)(19-r)) = (11)/(52)` `rArr (21-r) (20-r) (19-r) = (22 xx 21 xx 52)/(11)` `= 14 xx 13 xx 12` On comparing: `rArr 21 - r = 14` `rArr r = 7`.

Discussion

12955.	Solve 2cos^(2)x+3 sin x=0
Answer» ANSWER :`X = NPI + (-1) ^(N)`

Discussion

12956.	Find the sum of: n terms of 4, 7 , 10, ....
Answer» ANSWER :`(N)/(2) (3n+5)`

Discussion

12957.	Find the value of tan ""(13pi)/(12).
Answer» ANSWER :`2-sqrt3`

Discussion

12958.	Express each of the complex number given in the form of a+ib [(1/3 + i7/3) + (4+I 1/3)] -(-4/3 + i)
Answer» ANSWER :`17/3 + i(5/3)`

Discussion

12959.	If a and b are integers then abis a rational number Check the validity of the statement
Answer» <P> Answer :p: a and B are integers q : ab is a rational NUMBER Since , when a and b are integers , thentheir product is ALSO an integer and hence a rational number , thus the given statementis VALID.

Discussion

12960.	Write each of the following statements in the form if then: A quadrilateral is a parallelogram if its diagonals bisect each other.
Answer» ANSWER :If the DIAGONALS of QUADRILATERAL BISECTS each other, then it is PARALLELOGRAM.

Discussion

12961.	Rewrite each of the following statements in the form ''p if and only if q'' q: For you to get an A grade, it is necessary and sufficient that you do all the homework regularly.
Answer» ANSWER :You GET an A GRADE if and only if you do all the HOMEWORK REGULARLY

Discussion

12962.	Find the component statements of the following compound statements: sqrt(7) is a rational number or an irrational number.
Answer» <P> ANSWER :p: is a RATIONAL NUMBER q: is an IRRATIONAL number.

Discussion

12963.	Mention the different ways of increasing the number of molecular collision? Per unit time in a gas.
Answer» Solution :The number of collision. Per unit time can be increased by (i) increasing the TEMPERATURE of the gas (II) increasing the number of MOLECULES and (III) DECREASING the volume of the gas

Discussion

12964.	Find Lt_(xto0)(sqrt(1+x)-sqrt(1+x^(2)))/(sqrt(1-x^(2))-sqrt(1-x))
Answer» ANSWER :1

Discussion

12965.	Consider the system of liner equations in x, y andz ( sin 3 theta ) x - y + x = 0 ( cos2 theta ) x + 4 y + 3 z = 02 x + 7 y + 7 z = 0which of the followingcan be the values of thetafor whichthe systemhas a non-trivial solution
Answer» `n pi + ( - 1)^(n) pi // 6 , AA n in Z` ` n pi + ( - )^(n) pi// 3, AA n in Z` ` n pi + ( - 1)^(n) pi // 9, AA n in Z` ` n pi + ( - 1)^(n) (pi)/( 12) , AA n in Z` Answer :A

Discussion

12966.	CotA + CotB + CotC + (Cos(A+B+C))/(SinASinBSinC)=
Answer» COTA CotB CotC TanA TanB TanC CosA COSB CosC SinA SINB SinC ANSWER :A

Discussion

12967.	The value of cot(7pi)/16 + 2cot(3pi)/8 + cot(15pi)/16 is:
Answer» 4 2 `-2` `-4` ANSWER :B

Discussion

12968.	If the coefficients of x^2 and x^3 in the expansion of (3 + ax)^(9) are the same, find the value of a.
Answer» ANSWER :`(9)/(7)`

Discussion

12969.	If alpha , betaare supplementary angles , thencos^(2)alpha + sin^(2) beta =
Answer» 1 -1 2 0 Answer :A

Discussion

12970.	If the matrix A=((1,-1),(-1,1)) then A^(n+1)=
Answer» `2((1,-1),(-1,1))` `2N((1,-1),(-1,1))` `2^(n)((1,-1),(-1,1))` `2^(n+1)((1,-1),(-1,1))` ANSWER :C

Discussion

12971.	Find sum_(n=1)^n 1/((4n^(2) -1))
Answer» ANSWER :`N/(2n+1)`

Discussion

12972.	If (4,2sqrt(3))is the transformed form of (2 sqrt(3),5) by rotating the axes then the angle of rotation is
Answer» `(pi)/(12)` `(pi)/(6)` `(pi)/(4)` `(pi)/(3)` ANSWER :B

Discussion

12973.	A tower of height h standing at the centre of a square with sides of length 'a' makes the same angle aat each of the four corners, then a^(2)=
Answer» `H^(2)cot^(2)ALPHA` `h^(2) tan^(2) alpha` `2h^(2)cot^(2) alpha` `2h^(2) tan^(2) alpha` ANSWER :C

Discussion

12974.	sinh3 - cosh3 =
Answer» `E^(-3)` `-e^(-3)` `e^(3)` `-e^(3)` ANSWER :B

Discussion

12975.	Find the transformed equation of 2x^(2)+y^(2)-4x+4y=0 when the origin is shifted to the point (-1,2).
Answer» ANSWER :`2X^(2)+Y^(2)-8X+8Y+18=0`

Discussion

12976.	Find (a) the coefficient of x^7in theepansion of(ax^2+1/(bx))^11 (b)The coefficient of x^(-7) in the expansion of (ax^2+1/(bx))^11 Also , find the relation between a and b, so that these coefficients are equal .
Answer» Solution :In the expansion of `(ax^2+(1)/(BX))^11`, the general term is :, `T_(r+1)=^(11)C_(r)(ax^2)^(11-r)(1/(bx))^r=11C_(r).(a^(11-r))/(b^r).x^(22-3r)` PUTTING 22-3r = 7 `therefore3r= 15rArr r= 5 ` `therefore T_(6)=^(11)C_(5)(a^6)/(b^(5)).X^7` Hence the cofficient of `x^7 in (ax^2+(1)/(bx))^11is ""^11 C_(5)a^6 b^(-5)` NOTE that BINOMIAL coefficient of sixth term is `""^(11)C_(5)` In the expansion of `(ax^2+(1)/(bx^2)^11` general term is `T_(r+1)=""^11C_r(ax)^(11-r)((-1)/(bx^2))^r=(-1)^(r 11) C_(r)(a^(11-r))/(b^(r)).X^(11-3r)` putting 11-3r = -7 `therefore T_(6)=^(11)C_(5)(a^6)/(b^(5)).X^7` Hence the coffieceint of `x^7 "in" (ax^2+(1)/(bx))^11 is ""^(11)C_(6)a^5b^(-6)` Also given : Coefficient of `x^7 "in" (ax -(1)/(bx^2))^11=" coeffiecient of " x-7 "in" (ax-(1)/(bx^2))^11` `rArr""C_(5)a^(6)b^(-5)=""11C_(6)a^5b^(-6)` `rArrab=1 ""(therefore""^C_(5)=""^(11)C_(6))` which is the required relation between a and b .

Discussion

12977.	f (x) =(e^(1//x^(2)))/(e^(1//x^(2))-1) , x ne 0, f (0) = 1then f at x = 0 is
Answer» discontinuous continuous not DETERMINED NONE ANSWER :B

Discussion

12978.	If 2 tan""(alpha)/2= tan""(beta)/2 then (3+5cos beta)/(5+3cos beta)=
Answer» `cos ALPHA` `SIN alpha` `TAN alpha ` `COT alpha` Answer :A

Discussion

12979.	Prove that \|{:((b+c)^(2),a^(2),a^(2)),(b^(2),(c+a)^(2),b^(2)),(c^(2),c^(2),(a+b)^(2)):}\|=2abc(a+b+c)^(3)
Answer» ANSWER :`2ABC(a+b+c)^(2)`

Discussion

12980.	16 sin x cosx cos 2x cos 4x cos 8x in
Answer» `[-1,1]` `[-(1)/(4), (1)/(4)]` `[-(3)/(4), (3)/(4)]` `[-(SQRT(3))/(2), (sqrt(3))/(2)]` ANSWER :A

Discussion

12981.	A(0,2,3), B(2,-1,5),C(3,0, -3) are vertices of DeltaABC. If a,b,c are HG, GS, SH then their increasing order is (H,G, S are orthocentre, centroid and circumcentre)
Answer» a, B, C c, b, a b, a, c b, c, a ANSWER :c

Discussion

12982.	Focal distances of a pointP : x = 13 on13 on81x^(2) - 144 y^(2) = 11664are
Answer» `(38)/(3) , (92)/(3)` 13, 117 71 , 311 `(17)/(4) , (113)/(4)` Solution :N/A

Discussion

12983.	The total number of ways in which six '+' and four '_' signs can be arranged in a line such that no two '_'signs occur together , is …….
Answer» ANSWER :35

Discussion

12984.	If 2a+3b+6c=0 , then at least one root of the eqution ax^2+bx+c=0 lies in the interval
Answer» (0,1) (1,2) (2,3) (0,4) ANSWER :A

Discussion

12985.	Compute the derivative of sin x.
Answer» ANSWER :`COSX`

Discussion

12986.	The periodof tan x tan ((2pi)/(3)-x )tan ((2pi)/(3) + x) is
Answer» `(PI)/(2)` `(pi)/(3)` `(2PI)/(3)` `pi` ANSWER :2

Discussion

12987.	Write the converse, inverse and contrapositive of the following statements. If you drink milk, you will be strong.
Answer» ANSWER :Converse: If you are STRONG, then you drink your milk. Inverse : If you do not drink your milk, then you are notstrong. CONTRAPOSITIVE : If you are not strong, then you do not drink your milk.

Discussion

12988.	Which of the following sentences are statements? Give reasons for your answer The square of a number is an even number.
Answer» Answer :This sentence is sometimes true and sometimes not true. For example the SQUARE of 2 is even number and the square of 3 is an ODD number. Therefore, it is not a STATEMENT.

Discussion

12989.	sqrt(2)x^(2) +x + sqrt(2)=0
Answer» ANSWER :`(1)/(2sqrt(2))-(SQRT(7))/(2sqrt(2))i`

Discussion

12990.	Solve the following systems of homogeneous equations. 3x+y-2z=0 x+y+z=0 x-2y+z=0
Answer» ANSWER :`x=y=z=0`

Discussion

12991.	Let A={x : x is a positive prime number less than 10} and B={x : x in N and 0 lt x-2 le 6}. Find P(A-B).
Answer» ANSWER :`{PHI, {2}}`

Discussion

12992.	. Find the angle between the x-axis and the line joining the points (3, -1) " and " (4, -2) .
Answer» ANSWER :`135^(@)`

Discussion

12993.	sin[cot^(-1)((2x)/(1-x^(2)))+cos^(-1)((1-x^(2))/(1+x^(2)))]=
Answer» `0` `1` `(x-y)/(1+xy)` `(2X)/(1-x^(2))` Answer :B

Discussion

12994.	lim_(xto0^(+))(\|sinx\|)/(x)=……….
Answer» 1 -1 0 Does not exists Answer :A

Discussion

12995.	Statement 1: If a+b=0,a!=0 then sin^(-1)ax+cos^(-1)bx=(3pi)/2 has no solution Statement 2: sin^(-1)x+cos^(-1)x=(pi)/2,-1lexle1
Answer» Both I and II are INDIVIDUALLY true and II is the correct EXPLANATION of I Both I and II are individually true but II is not the correct explanation of I I is true but II is FALSE I is false but II is true Answer :A

Discussion

12996.	Find the value of tan""(pi)/(8).
Answer» ANSWER :`TAN "" (PI)/(8) = sqrt2-1`

Discussion

12997.	Find the value of e^(2), rounded off to one decimal place.
Answer» ANSWER :7.4

Discussion

12998.	((6.45)^(3) xx (0.00034)^(1/3) xx (981.4))/((9.37)^(2) xx (8.93)^(1/4) xx (0.0617))
Answer» ANSWER :1963

Discussion

12999.	Find the value of x for which the points (x, -1)(2,1) and (4, 5) are collinear.
Answer» ANSWER :`X = 1`

Discussion

13000.	A die is thrown repeatedly until a six comes up. What is the sample space for this experiment ?
Answer» ANSWER :{(6, (1, 6), (2, 6), (3, 6), (4, 6), (5, 6), (1, 1, 6), (1, 2, 6), … , (1, 5, 6), (2, 1, 6), (2, 2, 6), … , (2, 5, 6), … , (5, 1, 6), (5, 2, 6), … }

Discussion

Explore topic-wise InterviewSolutions in .

If the roots of the equation(x_(1)^(2)-a^(2))m^(2)-2x_(1)y_(1)m+y_(1)^(2)+b^(2)=0 are the slopes of two perpendicular lines intersecting at P(x_(1), y_(1)) then the locus of P is

Find the variance of the following data: 6, 8, 10, 12, 14, 16, 18, 20, 22, 24

In Delta ABC, if a sin^2""C/2+c sin^2""A/2 in terms of s,a,b,c is

If .^(22)P_(r+1) :.^(20)P_(r+2) = 11:52, find the value of r.

Solve 2cos^(2)x+3 sin x=0

Find the sum of: n terms of 4, 7 , 10, ....

Find the value of tan ""(13pi)/(12).

Express each of the complex number given in the form of a+ib [(1/3 + i7/3) + (4+I 1/3)] -(-4/3 + i)

If a and b are integers then abis a rational number Check the validity of the statement

Write each of the following statements in the form if then: A quadrilateral is a parallelogram if its diagonals bisect each other.

Rewrite each of the following statements in the form ''p if and only if q'' q: For you to get an A grade, it is necessary and sufficient that you do all the homework regularly.

Find the component statements of the following compound statements: sqrt(7) is a rational number or an irrational number.

Mention the different ways of increasing the number of molecular collision? Per unit time in a gas.

Find Lt_(xto0)(sqrt(1+x)-sqrt(1+x^(2)))/(sqrt(1-x^(2))-sqrt(1-x))

Consider the system of liner equations in x, y andz ( sin 3 theta ) x - y + x = 0 ( cos2 theta ) x + 4 y + 3 z = 02 x + 7 y + 7 z = 0which of the followingcan be the values of thetafor whichthe systemhas a non-trivial solution

CotA + CotB + CotC + (Cos(A+B+C))/(SinASinBSinC)=

The value of cot(7pi)/16 + 2cot(3pi)/8 + cot(15pi)/16 is:

If the coefficients of x^2 and x^3 in the expansion of (3 + ax)^(9) are the same, find the value of a.

If alpha , betaare supplementary angles , thencos^(2)alpha + sin^(2) beta =

If the matrix A=((1,-1),(-1,1)) then A^(n+1)=

Find sum_(n=1)^n 1/((4n^(2) -1))

If (4,2sqrt(3))is the transformed form of (2 sqrt(3),5) by rotating the axes then the angle of rotation is

A tower of height h standing at the centre of a square with sides of length 'a' makes the same angle aat each of the four corners, then a^(2)=

sinh3 - cosh3 =

Find the transformed equation of 2x^(2)+y^(2)-4x+4y=0 when the origin is shifted to the point (-1,2).

Find (a) the coefficient of x^7in theepansion of(ax^2+1/(bx))^11 (b)The coefficient of x^(-7) in the expansion of (ax^2+1/(bx))^11 Also , find the relation between a and b, so that these coefficients are equal .

f (x) =(e^(1//x^(2)))/(e^(1//x^(2))-1) , x ne 0, f (0) = 1then f at x = 0 is

If 2 tan""(alpha)/2= tan""(beta)/2 then (3+5cos beta)/(5+3cos beta)=

Prove that |{:((b+c)^(2),a^(2),a^(2)),(b^(2),(c+a)^(2),b^(2)),(c^(2),c^(2),(a+b)^(2)):}|=2abc(a+b+c)^(3)

16 sin x cosx cos 2x cos 4x cos 8x in

A(0,2,3), B(2,-1,5),C(3,0, -3) are vertices of DeltaABC. If a,b,c are HG, GS, SH then their increasing order is (H,G, S are orthocentre, centroid and circumcentre)

Focal distances of a pointP : x = 13 on13 on81x^(2) - 144 y^(2) = 11664are

The total number of ways in which six '+' and four '_' signs can be arranged in a line such that no two '_'signs occur together , is …….

If 2a+3b+6c=0 , then at least one root of the eqution ax^2+bx+c=0 lies in the interval

Compute the derivative of sin x.

The periodof tan x tan ((2pi)/(3)-x )tan ((2pi)/(3) + x) is

Write the converse, inverse and contrapositive of the following statements. If you drink milk, you will be strong.

Which of the following sentences are statements? Give reasons for your answer The square of a number is an even number.

sqrt(2)x^(2) +x + sqrt(2)=0

Solve the following systems of homogeneous equations. 3x+y-2z=0 x+y+z=0 x-2y+z=0

Let A={x : x is a positive prime number less than 10} and B={x : x in N and 0 lt x-2 le 6}. Find P(A-B).

. Find the angle between the x-axis and the line joining the points (3, -1) " and " (4, -2) .

sin[cot^(-1)((2x)/(1-x^(2)))+cos^(-1)((1-x^(2))/(1+x^(2)))]=

lim_(xto0^(+))(|sinx|)/(x)=……….

Statement 1: If a+b=0,a!=0 then sin^(-1)ax+cos^(-1)bx=(3pi)/2 has no solution Statement 2: sin^(-1)x+cos^(-1)x=(pi)/2,-1lexle1

Find the value of tan""(pi)/(8).

Find the value of e^(2), rounded off to one decimal place.

((6.45)^(3) xx (0.00034)^(1/3) xx (981.4))/((9.37)^(2) xx (8.93)^(1/4) xx (0.0617))

Find the value of x for which the points (x, -1)(2,1) and (4, 5) are collinear.

A die is thrown repeatedly until a six comes up. What is the sample space for this experiment ?