14949 + Interview Questions in Maths in Class 11 Page 256 InterviewSolution

12751.	Statement-1: Let P(x) = (x+1) ( x+2) ( x+3) ... ( x+11), then coefficient of x^(10)= 64. Statement-2: Coefficient of x^(n-1) in the product of (x+1) (x+2) ... ( x+n) is (n (n+1))/( 2).
Answer» Statement-1 is TRUE, Staternent-2 is true, Statement-2 is not a CORRECT EXPLANATION for Statement-1 Statement-1 is true, Statement-2 is FALSE. Statement-1 is false, Statement-2 is true. Statement-1 is true, Statement-2 is true, Statement-2 is correct explanation for Statement-1. Answer :C

Discussion

12752.	Find the degree measures corresponding to the following radian measures (Use pi = (22)/(7) ). (i) 11/16 (ii) -4 (iii)(5pi)/(3) (iv) (7pi)/(6)
Answer» ANSWER :` (i) 39^(@) 22' 30''` (II) `-229^(@)5'27''` (iii)` 3000 ^(@)` (IV) `210^(@)`

Discussion

12753.	Assertion (A) : The radius of the circle inscribed in the triangle obtained by joining the middle points of the sides of DeltaABC is equal to half the radius of incircle of DeltaABC Reasons (R): In DeltaABC D, E, F be midpoints of the sides of DeltaABC, Delta 2ss denote area and perimeter of DeltaDEF then Delta=Delta//4= and s=s//2
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 true, R is false A is false, R is true Answer :A

Discussion

12754.	If fg = ch, the lines represented by hxy+ gx+ fy + c = 0 form a quadrilateral with the coordinate axes which is a
Answer» RHOMBUS PARALLELOGRAM but not rectangle Rectangle Trapezium ANSWER :C

Discussion

12755.	Let f:R rarr R be a continuous function such that f(x)-2 f(x/2) + f(x/4)=x^(2). Now answer the following f(0)=
Answer» 0 1 `F(0)` `-f(0)` ANSWER :A

Discussion

12756.	If n is a positive integer then find the number of terms in the expansion of (x+y-2z)^(n)
Answer» SOLUTION :N/a

Discussion

12757.	If (sin 3B)/(sinB)=((a^(2)-c^(2))/(2ac)) then a^(2),b^(2),c^(2) are in
Answer» <P>A.P G.P H.P A.G..P ANSWER :A

Discussion

12758.	If tan^(-1)(x+1)+tan^(-1)(x-1)="tan"^(-1)8/31 then x=
Answer» 1 `1//2` `-1//22` `1//4` ANSWER :D

Discussion

12759.	If cos(cot^(-1)(1/2))=cot(cos^(-1)x), then a value of x is
Answer» 1)`1/(sqrt(6))` 2)`(-1)/(sqrt(12))` 3)`2/(sqrt(6))` 4)`(-2)/(sqrt(6))` ANSWER :A

Discussion

12760.	Evaluate the following limits : Lt_(xto0)(log(1+x))/x
Answer» ANSWER :1

Discussion

12761.	cosh 3 theta = 99 if cosh theta =
Answer» 3 9 11 27 Answer :A

Discussion

12762.	The value of Sin^(-1)(cot(Sin^(-1)sqrt((2-sqrt(3))/4)+Cos^(-1)""sqrt(12)/4+Sec^(-1)sqrt(2))) is
Answer» 0 `PI/2` `pi/3` `pi` ANSWER :A

Discussion

12763.	Find the derivative of the function from first principle cos ax
Answer» ANSWER :`-a SIN AX`

Discussion

12764.	If 4-digit numbers greater than 5,000 are randomly formed from the digits 0,1, 3, 5, and 7, what is the probability of forming a number divided by 5 when, (i) the digits are repeated? (ii) the repeition of digits is not allowed?
Answer» ANSWER :(I) `33/83` (II) `3/8`

Discussion

12765.	solve tan 2x =-cot (x+ ( pi )/(3) )
Answer» ANSWER :`X = N pi + (5pi)/(5)`

Discussion

12766.	The minimum distance of the cruve x^(2)+2y^(2)=6 from the line x+y =7 is
Answer» `2sqrt(2)` `5sqrt(2)` `SQRT(8)` 6 Answer :A::C

Discussion

12767.	sin theta sin (60^(@) - theta) sin (60^(@)+ theta) in [-k,k] rArr k=
Answer» `(1)/(2)` `(1)/(3)` `(1)/(4)` `(3)/(4)` ANSWER :C

Discussion

12768.	Consider the system of equations cos^(-1)x+(sin^(-1)y)^(2)=(ppi^(2))/4 and (cos^(-1)x)(sin^(-1)y)^(2)=pi^(4)/16, p in Z. The value of p for which system has a solution is
Answer» 1 2 0 `-1` ANSWER :B::C::D

Discussion

12769.	If veca =2bari+3barj,vecb =bari+barj+bark and vecc=lamdabari+4barj+2bark are coterminous edges of a parallelopiped of volume 2 cu. units then value of lamda is
Answer» 1 2 3 4 Answer :D

Discussion

12770.	The roots of the equation \|(3x^(2),x^(2) + x cos theta + cos^(2) theta ,x^(2) + x sin theta + sin^(2) theta),(x^(2) + x cos theta + cos^(2) theta,3 cos^(2) theta,1 + (sin 2 theta)/(2)),(x^(2) + x sin theta + sin^(2) theta,1 + (sin 2 theta)/(2),3 sin^(2) theta)\| = 0
Answer» `SIN THETA, COS theta` `sin^(2) theta, cos^(2) theta` `sin theta, cos^(2) theta` `sin^(2) theta, cos theta` ANSWER :A

Discussion

12771.	The sum of five consecutive terms of G.P is 243. The sum of second and fourth is10. Find these numbers.
Answer» ANSWER :`48, 12, 3, (3)/(4)`,……

Discussion

12772.	If the graph of Y = (x) is symmetric about Y axis then …........
Answer» ANSWER :`F(-X)`

Discussion

12773.	Evaluate the following limits : Lim_(x to 0) (sin 3x)/(5x)
Answer» ANSWER :`3/5`

Discussion

12774.	Write down all the subsets of the following sets {a}
Answer» ANSWER :`φ, { a }`

Discussion

12775.	Given the function f(x)=(a^(x)+a^(-x))/(2)( where a gt 2 ). Then f(x+y)+f(x-y)=
Answer» `2F(X).F(y)` `f(x).f(y)` `(f(x))/(f(y))` `f(x)-f(y)` ANSWER :A

Discussion

12776.	M is the foot of perpendicular from point P of the parabola y^(2)= 4ax to its directrix. Then area of an equilateral triangle SPM is …….. Sq. unit. (Where S is focus of parabola)
Answer» `4sqrt(3)a^(2)` `(SQRT(3))/(4)a^(2)` `2sqrt(3)a^(2)` `(sqrt(3))/(2)a^(2)` ANSWER :A

Discussion

12777.	If ax^2+2hxy+by^2+2gx+2fy+c=0 represents a pair of parallel lines then sqrt([q^2-ac/f^2-bc])=
Answer» `a/B` `SQRT([a/b])` `sqrt([b/a])` `b/a` ANSWER :B

Discussion

12778.	InDelta ABC" if " 3 sin A = 6 sin B = 2 sqrt3 sin C ," then "angle A =
Answer» `30^(@)` `45^(@)` `60^(@)` `90^(@)` ANSWER :D

Discussion

12779.	Let a and b be thelength of the legs of a right triangle wth following properties All 3 sides of the triangle are integreers the perimeter of the triangle is numerically equal to area of the triangle it is given that altb Maximum passibel primeter of the triangle is
Answer» 27 28 29 30 Answer :D

Discussion

12780.	Let a and b be thelength of the legs of a right triangle wth following properties All 3 sides of the triangle are integreers the perimeter of the triangle is numerically equal to area of the triangle it is given that altb The number of ordred pairs (a,b) will be
Answer» 1 2 3 4 Answer :B

Discussion

12781.	Differentiate from first principles: 9. sqrt( 2x +3)
Answer» ANSWER :`(1)/( SQRT(2X +3))`

Discussion

12782.	If cos x - sin alpha cot beta sin x = cos alpha then the value of tan(x//2) is
Answer» `-TAN (alpha/2)COT(beta/2)` `tan (alpha/2)tan(beta/2)` `-cot (alpha/2)tan(beta/2)` `cot (alpha/2)cot (beta/2)` ANSWER :A::B

Discussion

12783.	If((n),(12))=((n),(8)) then n = ........ .
Answer» ANSWER :20

Discussion

12784.	Show that the straight lines (a-b)x+(b-c)y=c-a,(b-c)x+(c-a)y=a-b and (c-a)x+(a-b)y=b-c are concurrent.
Answer» ANSWER :p=2

Discussion

12785.	sin^(-1)(x^(2)+2x+2)+tan^(-1)(x^(2)-3x-k^(2)) gt pi/2" for "k in
Answer» (-1, 0) (0, 1) (-2, 2) (0, 2) Answer :A::B::C::D

Discussion

12786.	Find the sum to n terms of the series whose n^(th)" terms is n"(n+3).
Answer» ANSWER :`=(N(n+1)(n+5))/3`

Discussion

12787.	If (25)^(15) is divided by 13 , then the remainder is ………
Answer» ANSWER :12

Discussion

12788.	Out of the following statement which is false?
Answer» `SINTHETA=-(1)/(5)` `costheta=1` `sectheta=(1)/(2)` `tantheta=20` ANSWER :C

Discussion

12789.	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 – D
Answer» ANSWER :`{2, 4, 6, 8, 12, 14, 16}`

Discussion

12790.	Find the volume of the parallelopiped having coterminus edges 2bari-3barj,bari+barj-bark,3bari-bark
Answer» ANSWER :4

Discussion

12791.	Show that the line x + y sqrt(3) = 4 touches the circles x^(2) + y^(2) - 4x - 4 sqrt( 3) y +12 = 0and x^(2) y^(2)= 4at the same point . Also find the coordinate of the point
Answer» ANSWER :`(1 , SQRT(3))`

Discussion

12792.	Statement I : If m cos(theta+alpha)=n cos (theta-alpha) then tan theta.tan alpha=(m+n)/(m-n)Statement II : If (sin(alpha+beta))/(sin(alpha-beta))=(a+b)/(a-b) then tan alpha.cot beta=(a)/(b) Which of the above statements is correct ?
Answer» Only I Only II Both I and II Neither I not II Answer :B

Discussion

12793.	A straight line through Q(2,3) makes anangle (3pi)/4 with the negative direction of the x-axis. If the straight line intersects the line x+y-7=0 at P, find PQ.
Answer» ANSWER :`SQRT(2)`

Discussion

12794.	The minimum value of 3^([(x^2-2)^2+8]) is
Answer» `3^8` 3 1 5 Answer :A

Discussion

12795.	Find intervals in which the function given by f(x) = (3)/(10)x^(4) - (4)/(5)x^(3) - 3x^(2) + (36)/(5)x + 11 is (a) strictly increasing (b) strictly decreasing
Answer» ANSWER :`3, OO`

Discussion

12796.	There are four machines and it is known thatexactly two of them are faulty. They aretested , one by one , in a random order till both the faulty machines areidentified. Then theprobability that only two tests are needed is
Answer» `(1)/(3)` `(1)/(6)` `(1)/(2)` `(1)/(4)` Answer :B

Discussion

12797.	If x(3-x) ge 2" then "Sin^(-1)(x)+Sin^(-1)(x^(2))+……..+Sin^(-1)(x^(10))=
Answer» `(pi)/2` `2PI` `5PI` `10p` Answer :C

Discussion

12798.	Write the truth value of the following statement: 1 and 2 are roots of the equation x^(2)-3x+2=0.
Answer» ANSWER :1

Discussion

12799.	Find argument of the complex numbersz = sqrt3 + i
Answer» ANSWER :`pi/6`

Discussion

12800.	( cos^(3) A + sin^(3) A )/( cos A + sin A ) + (cos^(3) A - sin^(3)A)/( cos A- sin A) =
Answer» 0 -1 1 2 Answer :D

Discussion

Explore topic-wise InterviewSolutions in .

Statement-1: Let P(x) = (x+1) ( x+2) ( x+3) ... ( x+11), then coefficient of x^(10)= 64. Statement-2: Coefficient of x^(n-1) in the product of (x+1) (x+2) ... ( x+n) is (n (n+1))/( 2).

Find the degree measures corresponding to the following radian measures (Use pi = (22)/(7) ). (i) 11/16 (ii) -4 (iii)(5pi)/(3) (iv) (7pi)/(6)

If fg = ch, the lines represented by hxy+ gx+ fy + c = 0 form a quadrilateral with the coordinate axes which is a

Let f:R rarr R be a continuous function such that f(x)-2 f(x/2) + f(x/4)=x^(2). Now answer the following f(0)=

If n is a positive integer then find the number of terms in the expansion of (x+y-2z)^(n)

If (sin 3B)/(sinB)=((a^(2)-c^(2))/(2ac)) then a^(2),b^(2),c^(2) are in

If tan^(-1)(x+1)+tan^(-1)(x-1)="tan"^(-1)8/31 then x=

If cos(cot^(-1)(1/2))=cot(cos^(-1)x), then a value of x is

Evaluate the following limits : Lt_(xto0)(log(1+x))/x

cosh 3 theta = 99 if cosh theta =

The value of Sin^(-1)(cot(Sin^(-1)sqrt((2-sqrt(3))/4)+Cos^(-1)""sqrt(12)/4+Sec^(-1)sqrt(2))) is

Find the derivative of the function from first principle cos ax

If 4-digit numbers greater than 5,000 are randomly formed from the digits 0,1, 3, 5, and 7, what is the probability of forming a number divided by 5 when, (i) the digits are repeated? (ii) the repeition of digits is not allowed?

solve tan 2x =-cot (x+ ( pi )/(3) )

The minimum distance of the cruve x^(2)+2y^(2)=6 from the line x+y =7 is

sin theta sin (60^(@) - theta) sin (60^(@)+ theta) in [-k,k] rArr k=

Consider the system of equations cos^(-1)x+(sin^(-1)y)^(2)=(ppi^(2))/4 and (cos^(-1)x)(sin^(-1)y)^(2)=pi^(4)/16, p in Z. The value of p for which system has a solution is

If veca =2bari+3barj,vecb =bari+barj+bark and vecc=lamdabari+4barj+2bark are coterminous edges of a parallelopiped of volume 2 cu. units then value of lamda is

The roots of the equation |(3x^(2),x^(2) + x cos theta + cos^(2) theta ,x^(2) + x sin theta + sin^(2) theta),(x^(2) + x cos theta + cos^(2) theta,3 cos^(2) theta,1 + (sin 2 theta)/(2)),(x^(2) + x sin theta + sin^(2) theta,1 + (sin 2 theta)/(2),3 sin^(2) theta)| = 0

The sum of five consecutive terms of G.P is 243. The sum of second and fourth is10. Find these numbers.

If the graph of Y = (x) is symmetric about Y axis then …........

Evaluate the following limits : Lim_(x to 0) (sin 3x)/(5x)

Write down all the subsets of the following sets {a}

Given the function f(x)=(a^(x)+a^(-x))/(2)( where a gt 2 ). Then f(x+y)+f(x-y)=

M is the foot of perpendicular from point P of the parabola y^(2)= 4ax to its directrix. Then area of an equilateral triangle SPM is …….. Sq. unit. (Where S is focus of parabola)

If ax^2+2hxy+by^2+2gx+2fy+c=0 represents a pair of parallel lines then sqrt([q^2-ac/f^2-bc])=

InDelta ABC" if " 3 sin A = 6 sin B = 2 sqrt3 sin C ," then "angle A =

Let a and b be thelength of the legs of a right triangle wth following properties All 3 sides of the triangle are integreers the perimeter of the triangle is numerically equal to area of the triangle it is given that altb Maximum passibel primeter of the triangle is

Let a and b be thelength of the legs of a right triangle wth following properties All 3 sides of the triangle are integreers the perimeter of the triangle is numerically equal to area of the triangle it is given that altb The number of ordred pairs (a,b) will be

Differentiate from first principles: 9. sqrt( 2x +3)

If cos x - sin alpha cot beta sin x = cos alpha then the value of tan(x//2) is

If((n),(12))=((n),(8)) then n = ........ .

Show that the straight lines (a-b)x+(b-c)y=c-a,(b-c)x+(c-a)y=a-b and (c-a)x+(a-b)y=b-c are concurrent.

sin^(-1)(x^(2)+2x+2)+tan^(-1)(x^(2)-3x-k^(2)) gt pi/2" for "k in

Find the sum to n terms of the series whose n^(th)" terms is n"(n+3).

If (25)^(15) is divided by 13 , then the remainder is ………

Out of the following statement which is false?

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 – D

Find the volume of the parallelopiped having coterminus edges 2bari-3barj,bari+barj-bark,3bari-bark

Show that the line x + y sqrt(3) = 4 touches the circles x^(2) + y^(2) - 4x - 4 sqrt( 3) y +12 = 0and x^(2) y^(2)= 4at the same point . Also find the coordinate of the point

Statement I : If m cos(theta+alpha)=n cos (theta-alpha) then tan theta.tan alpha=(m+n)/(m-n)Statement II : If (sin(alpha+beta))/(sin(alpha-beta))=(a+b)/(a-b) then tan alpha.cot beta=(a)/(b) Which of the above statements is correct ?

A straight line through Q(2,3) makes anangle (3pi)/4 with the negative direction of the x-axis. If the straight line intersects the line x+y-7=0 at P, find PQ.

The minimum value of 3^([(x^2-2)^2+8]) is

Find intervals in which the function given by f(x) = (3)/(10)x^(4) - (4)/(5)x^(3) - 3x^(2) + (36)/(5)x + 11 is (a) strictly increasing (b) strictly decreasing

There are four machines and it is known thatexactly two of them are faulty. They aretested , one by one , in a random order till both the faulty machines areidentified. Then theprobability that only two tests are needed is

If x(3-x) ge 2" then "Sin^(-1)(x)+Sin^(-1)(x^(2))+……..+Sin^(-1)(x^(10))=

Write the truth value of the following statement: 1 and 2 are roots of the equation x^(2)-3x+2=0.

Find argument of the complex numbersz = sqrt3 + i

( cos^(3) A + sin^(3) A )/( cos A + sin A ) + (cos^(3) A - sin^(3)A)/( cos A- sin A) =