14949 + Interview Questions in Maths in Class 11 Page 150 InterviewSolution

7451.	If y=e ^(-2x) sin ^(3) x, then (d^(2)y)/dx^(2)=
Answer» Answer :`e ^(-2x) ( SIN ^(3) X - 12 sin ^(2) x COS x + 6 sin x cos ^(2) x )`

Discussion

7452.	Let f (x-y) = f (x) g (y) - f (y) g (x) and g(x-y) =g (x) g (y) + f (x) f (y), AA x , y in R. If right derivative of f(x) exists at x=0, then show that g'(0) =0
Answer» ANSWER :`LT 2`

Discussion

7453.	Find the smallest positive number p for which the equation cos (p sinx) = sin ( p cos x) has a solution whenx in [0,2pi].
Answer» ANSWER :`(PI)/( 2 SQRT2)`

Discussion

7454.	If tan(alpha-beta)=(sin 2beta)/(3-cos2beta), then
Answer» `TAN ALPHA=2TAN beta` `tan beta=2 tan alpha` `2tan alpha = 3 tan beta` `3tan alpha = 2 tan beta` ANSWER :A

Discussion

7455.	If the sum of n terms of an A.P. is (pn + qn^2) , where p and q are constants, find the common difference.
Answer» ANSWER :2Q

Discussion

7456.	If the staight lines 2x+3y-1=0,x+2y-1=0, and ax+by-1=0 from a triangle with the origin as orthocenter, then (a,b) is given by
Answer» (6,4) (-3,3) (-8,8) (0,7) ANSWER :C

Discussion

7457.	Match the Column-I with the correct answer in Column-II
Answer» ANSWER :B

Discussion

7458.	Match the Column-I with the correct answer in Column-II
Answer» ANSWER :B

Discussion

7459.	Answer the equation: int(5x-2)/(x^(2)-x-2)dx
Answer» ANSWER :`(5)/(2)LOG(x^(2)-x-2)+(1)/(6)log\|(x-2)/(x+1)\|+c`

Discussion

7460.	Ifsin (alpha+beta ) =1 , sin (alpha-beta ) =1//2 " then " tan (alpha +2beta ) tan(2alpha+beta )=
Answer» 1 -1 0 `1/2` ANSWER :A

Discussion

7461.	cosA, sinA, cotA are in GP then tan^(6) A - tan^(2) A =
Answer» -1 0 1 2 Answer :C

Discussion

7462.	Expressthe following in the forma+bi, sqrt(-8)
Answer» ANSWER :`2 SQRT2I`

Discussion

7463.	A coin is tossed 5 times.Determine the number of ways in which 0 head (i.e. 0 head and 5 tails)can apear. Also find the number of ways in which 1 head (i.e. 1 head and 4 tails) can appear , and so on. Thencomplete the giventable:{:("No. of heads :",0,1,2,3,4,5),("No. of ways :",,,,,,):}
Answer» ANSWER :`{:("No. of HEADS :",0,1,2,3,4,5),("No. of WAYS :",1,5,10,10,5,1):}`

Discussion

7464.	Find the derivative of the following functions: 3cotx+5" cosec "x
Answer» ANSWER :`-"3cosec"^(2)x-5" COSEC "xcotx`

Discussion

7465.	Find the angle of roation of the axes so thatthe equation 2x + 3y =7 may be reduced to form X = K
Answer» ANSWER :`TAN^(-1) (3)/(2)`

Discussion

7466.	Write the following implications (p implies q) in the form(~p vv q) andwrite its negation. 'IfDelta ABC is isosceles then the base angles A and B are equal.'
Answer» <P> ANSWER :Let p :`Delta ABC`Is isosceles q: The base ANGLES A and B are equal . Then.`(~p vv q)` Either`Delta ABC`is not isosceles or the base angles A and B are equal. The negation of the given statement is (p ^^ ~q), given by`Delta ABC` is isosceles, and the base angles A and B are not equal.

Discussion

7467.	Iff ""^(5)P_(r)=""^(6)P_(r-1) find r.
Answer» ANSWER :4

Discussion

7468.	If PV^(1//4)=C, then the volume is decreased by 1/2% then the percentage error in P is
Answer» `(1)/(4)` `(1)/(8)` `(1)/(2)` 1 Answer :B

Discussion

7469.	Find (a, b) if Lt_(xtooo){(x^(2)+1)/(x+1)-ax-b}=0
Answer» ANSWER :`(1,-1)`

Discussion

7470.	If sin "" (pi)/(18) sin "" (5pi)/(18) sin ""(7pi)/(18) =
Answer» 8 `1/8` `1//7` 6 Answer :B

Discussion

7471.	Match the following{:("Column -I","Column -II"),((A)((x-1)(x-2))/(x-3),"P Decreases when "xin(1-sqrt(2,1)+sqrt(2))),((B)((x-2)(x-3))/(x-3),"Q Decreases when "x in (3-sqrt(2),3+sqrt(2))),((C)((x-1)(x-3))/(x-3),"R Decreases when " X in R),((D)(x-2)/((x-1)(x-3)),"SIncreases when " x in R),(,"is monotonicfunction"):}
Answer» ANSWER :A-q;B-p;C-st;,D-rt

Discussion

7472.	Find the combined equation of two lines whose equations are ax + by + c = 0 and px + qy = 0. Find the equations to two lines represented by the equation.
Answer» Answer :` apx^(2) + (AQ + BP) xy + BAY^(2) + cpx + cqy = 0`

Discussion

7473.	Three dice are rolling simultaneously. Find the probability of getting same numbers on all dice.
Answer» ANSWER :`(1)/(36)`

Discussion

7474.	Solvesqrt(3)x^(2) - sqrt(2)x + 3sqrt(3)=0
Answer» ANSWER :`(SQRT(2) +- sqrt(34)i)/(2sqrt(3))`

Discussion

7475.	Assertion (A ) : The maximum value of2 cos^(2)theta + sqrt(5) cos theta sin theta +4 sin^(2) thetais (9)/(2)Reason (R ) : Themaximumvalueofacos^(2)theta +b cos theta sin theta+c sin^(2)thetais(1)/(2) [ (a+c)+ sqrt((a-c)^(2) + b^(2))]
Answer» A is TRUER istrueand R is CORRECTEXPLANATION of A A is trueR istrueand RIS not correctexplanatinof A A istrueR isfalse A isfalseR istrue . ANSWER :1

Discussion

7476.	If the point (x_(1) +t[x_(2)-x_(1)], y_(1)+t[y_(2)-y_(1)]) divides the join of (x_(1), y_(1)) and (x_(2), y_(2)) internally, then
Answer» `t lt 0` `0 lt t lt 1` `t GT 1` `t = 1` ANSWER :B

Discussion

7477.	If (1+x)^(n)=C_(0)+C_(1).x+C_(2).x^(2)+….+C_(n).x^(n). then prove that (i) C_(0)+2C_(1)+3C_(2)+…+(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

7478.	(a ) Find the sum of all 4 digit numbers that canbe formedusingthe digits 1,2,3,4 and 5 repetition not allowed ? (b ) Three vectorsvec (a) , vec(b) and vec(c )are such that\|vec (a)\| = 2 ,\|vec(b)\| = 3 ,\|vec (c )\| = 4 andvec(a)+vec(b ) + vec( c) = 0Find4vec (a ) .vec (b)+ 3vec(b) . vec(c ) +3 vec (c ) . vec(a)
Answer» ANSWER :399960 =-42

Discussion

7479.	Find the numbers of ways of arranging 6 players to throw the cricket ball so that the oldest players may not throw first.
Answer» ANSWER :` 600 `

Discussion

7480.	A die is thrown two times.
Answer» ANSWER :`{(X, Y) : X, Y = 1, 2, 3, 4, 5, 6}` or `{(1,1), (1,2), (1,3), … , (1,6), (2, 1), (2, 2), … , (2,6), …. (6, 1), (6, 2), … , (6, 6)}`

Discussion

7481.	If f:R rarr and g:R rarr R are defined by f(x)=3x-4 and g(x)=2+3x then (g^(-1)" of"^(-1))(5)=
Answer» 1 `1//2` `1//3` `1//5` ANSWER :C

Discussion

7482.	The value of underset(x to 0)"Lt" ((a_(1)^(1//x)+a_(2)^(1//x)+.....+a_(n)^(1//x))/(n))^(nx)) is
Answer» ANSWER :`a_(1)a_(2)a_(3)...a_(N)`

Discussion

7483.	Expand (i) (2x^(2)-(3)/(x))^(3)(ii)(2x^(2)-3sqrt(1-x^(2)))^(4)+(2x^(2)+3sqrt(1-x^(2)))^(4)
Answer» ANSWER :(i) `= 8x^(6)-36x^(3)+54-(27)/(x^(3))` (II)`=32X^(8)-432x^(6)+59x^(4)-324x^(2)+162`

Discussion

7484.	Consider the line L : (x-1)/(2) = (y)/(1) = (z+1)/(-2) and a point A (1,1,1). Let P be the foot of the perpendicular from A on L and Q be the image of the point A in the line L, 'O' being the origin. The distance of the origin from the plane passing through the point A and containing the line L is
Answer» `1/3` `(1)/(SQRT3)` `2/3` `1/2` ANSWER :A

Discussion

7485.	Find the specified term of the expression in each of the following binomials: (i) Fifth term of (2 a + 3b)^(12). Evaluate it when a = (1)/(3), b = (1)/(4).
Answer» ANSWER :`(55)/(9)`

Discussion

7486.	The point to which the axes should be translated to eliminate first degree terms in the equation 2x^2-2y^2+z^2-4x+8y-5=0 is
Answer» ANSWER :A-s;B-p;C-p;D-r

Discussion

7487.	The range of f(x)=(x-[x])/(1-[x]+x) ( where [.] is G.I.F) is
Answer» `[0, 1/2]` `[0, 1]` `(0, 1/2]` `[0, 1/2)` ANSWER :D

Discussion

7488.	Consider the line L : (x-1)/(2) = (y)/(1) = (z+1)/(-2) and a point A (1,1,1). Let P be the foot of the perpendicular from A on L and Q be the image of the point A in the line L, 'O' being the origin. The distance of the origin from the point Q is
Answer» `sqrt3` `sqrt ((17)/(6))` `sqrt ((17)/(3))` `(1)/(sqrt3)` Answer :C

Discussion

7489.	Let R be the set of real numbers. Define the real function f: R to R by f(x)=x+10 and sketch the graph of this function.
Answer» ANSWER :20 and 0

Discussion

7490.	Consider the line L : (x-1)/(2) = (y)/(1) = (z+1)/(-2) and a point A (1,1,1). Let P be the foot of the perpendicular from A on L and Q be the image of the point A in the line L, 'O' being the origin. The distance of the point A from the line L is
Answer» 1 2 `SQRT3` `4/3` ANSWER :B

Discussion

7491.	If alpha=3sin^(-1)(6/11) and beta=3cos^(-1)(4/9), where the inverse trigonometric functions take only the principal values, then the correct option(s) is(are)
Answer» `cosbeta GT 0` `sinbeta LT 0` `cos(alpha+beta) gt 0` `COSALPHA lt 0` Answer :B::C::D

Discussion

7492.	Let PQR be a right angle isosceles triangle, right angle at P(2, 1). If the equation of the line QR is 2x+y=3, then the equation representing the pair of lines PQ and PR is
Answer» `3X^(2)-3Y^(2)+8xy-20x-10y+25=0` `3x^(2)-3y^(2)-8xy-20x-10y+25=0` `3x^(2)-3y^(2)+8xy+20x-10y+25=0` `3x^(2)-3y^(2)+8xy-20x+10y+25=0` ANSWER :A

Discussion

7493.	Find a vector vec( c) such that \|vec(c )\| = sqrt6 and vec(c ).vec(a)= 0= vec(c ).vec(b) where vec(a) = 2vec(i) -vec(k), vec(b)= 3vec(j)- vec(i)-vec(k).
Answer» ANSWER :`+- (VEC(i) + vec(J) + 2vec(K))`

Discussion

7494.	In Delta ABC, if cos A+cos B+ cos C=3//2, then the triangle is
Answer» Answer :` THEREFORE DELTA ABC ` is an equilateral TRIANGLE.

Discussion

7495.	Given that alpha and beta are the roots of the equation x^(2)=7x+4, (i) show that alpha^(3)=53alpha+28 (ii) find the value of (alpha)/(beta)+(beta)/(alpha).
Answer» ANSWER :(II) `(-57)/(4)`

Discussion

7496.	Find the distance from the origin to each of the point: (-4,-3,-2)
Answer» ANSWER :`sqrt38`

Discussion

7497.	For a positive integer n , find the value of (1-i)^(n) (1 - 1/i)^(n)
Answer» ANSWER :`2^(N)`

Discussion

7498.	If a + b = 2h , then the area of the triangle formed by the lines ax^(2) + 2hxy + by^(2) = 0 and the line x-y+2=0, in sq. units, is
Answer» `\|(a+B)/(a-b)\|` `(a^(2)+b^(2))/(a-b)` `\|(a-b)/(a+b)\|` `(a^(2)+b^(2))/(a+b)` ANSWER :C

Discussion

7499.	An ellipseof eccentricity(2sqrt(2))/(3) is inscribed ina circle . A pointis choseninsidethe cirlceat random.Theprobaboilitythatthe pointliesoutsidethe ellipseis
Answer» `(1)/(2)` `(2)/(3)` `(1)/(9)` `(2)/(9)` ANSWER :B

Discussion

7500.	The third term of an arithmetical progression is 7, and the seventh term is 2 more than 3 times the third term. Find the first term, the common difference and the sum of the first 20 terms.
Answer» ANSWER :`-1,4,740`

Discussion

Explore topic-wise InterviewSolutions in .

If y=e ^(-2x) sin ^(3) x, then (d^(2)y)/dx^(2)=

Let f (x-y) = f (x) g (y) - f (y) g (x) and g(x-y) =g (x) g (y) + f (x) f (y), AA x , y in R. If right derivative of f(x) exists at x=0, then show that g'(0) =0

Find the smallest positive number p for which the equation cos (p sinx) = sin ( p cos x) has a solution whenx in [0,2pi].

If tan(alpha-beta)=(sin 2beta)/(3-cos2beta), then

If the sum of n terms of an A.P. is (pn + qn^2) , where p and q are constants, find the common difference.

If the staight lines 2x+3y-1=0,x+2y-1=0, and ax+by-1=0 from a triangle with the origin as orthocenter, then (a,b) is given by

Match the Column-I with the correct answer in Column-II

Match the Column-I with the correct answer in Column-II

Answer the equation: int(5x-2)/(x^(2)-x-2)dx

Ifsin (alpha+beta ) =1 , sin (alpha-beta ) =1//2 " then " tan (alpha +2beta ) tan(2alpha+beta )=

cosA, sinA, cotA are in GP then tan^(6) A - tan^(2) A =

Expressthe following in the forma+bi, sqrt(-8)

A coin is tossed 5 times.Determine the number of ways in which 0 head (i.e. 0 head and 5 tails)can apear. Also find the number of ways in which 1 head (i.e. 1 head and 4 tails) can appear , and so on. Thencomplete the giventable:{:("No. of heads :",0,1,2,3,4,5),("No. of ways :",,,,,,):}

Find the derivative of the following functions: 3cotx+5" cosec "x

Find the angle of roation of the axes so thatthe equation 2x + 3y =7 may be reduced to form X = K

Write the following implications (p implies q) in the form(~p vv q) andwrite its negation. 'IfDelta ABC is isosceles then the base angles A and B are equal.'

Iff ""^(5)P_(r)=""^(6)P_(r-1) find r.

If PV^(1//4)=C, then the volume is decreased by 1/2% then the percentage error in P is

Find (a, b) if Lt_(xtooo){(x^(2)+1)/(x+1)-ax-b}=0

If sin "" (pi)/(18) sin "" (5pi)/(18) sin ""(7pi)/(18) =

Find the combined equation of two lines whose equations are ax + by + c = 0 and px + qy = 0. Find the equations to two lines represented by the equation.

Three dice are rolling simultaneously. Find the probability of getting same numbers on all dice.

Solvesqrt(3)x^(2) - sqrt(2)x + 3sqrt(3)=0

Assertion (A ) : The maximum value of2 cos^(2)theta + sqrt(5) cos theta sin theta +4 sin^(2) thetais (9)/(2)Reason (R ) : Themaximumvalueofacos^(2)theta +b cos theta sin theta+c sin^(2)thetais(1)/(2) [ (a+c)+ sqrt((a-c)^(2) + b^(2))]

If the point (x_(1) +t[x_(2)-x_(1)], y_(1)+t[y_(2)-y_(1)]) divides the join of (x_(1), y_(1)) and (x_(2), y_(2)) internally, then

Find the numbers of ways of arranging 6 players to throw the cricket ball so that the oldest players may not throw first.

A die is thrown two times.

If f:R rarr and g:R rarr R are defined by f(x)=3x-4 and g(x)=2+3x then (g^(-1)" of"^(-1))(5)=

The value of underset(x to 0)"Lt" ((a_(1)^(1//x)+a_(2)^(1//x)+.....+a_(n)^(1//x))/(n))^(nx)) is

Expand (i) (2x^(2)-(3)/(x))^(3)(ii)(2x^(2)-3sqrt(1-x^(2)))^(4)+(2x^(2)+3sqrt(1-x^(2)))^(4)

Consider the line L : (x-1)/(2) = (y)/(1) = (z+1)/(-2) and a point A (1,1,1). Let P be the foot of the perpendicular from A on L and Q be the image of the point A in the line L, 'O' being the origin. The distance of the origin from the plane passing through the point A and containing the line L is

Find the specified term of the expression in each of the following binomials: (i) Fifth term of (2 a + 3b)^(12). Evaluate it when a = (1)/(3), b = (1)/(4).

The point to which the axes should be translated to eliminate first degree terms in the equation 2x^2-2y^2+z^2-4x+8y-5=0 is

The range of f(x)=(x-[x])/(1-[x]+x) ( where [.] is G.I.F) is

Consider the line L : (x-1)/(2) = (y)/(1) = (z+1)/(-2) and a point A (1,1,1). Let P be the foot of the perpendicular from A on L and Q be the image of the point A in the line L, 'O' being the origin. The distance of the origin from the point Q is

Let R be the set of real numbers. Define the real function f: R to R by f(x)=x+10 and sketch the graph of this function.

Consider the line L : (x-1)/(2) = (y)/(1) = (z+1)/(-2) and a point A (1,1,1). Let P be the foot of the perpendicular from A on L and Q be the image of the point A in the line L, 'O' being the origin. The distance of the point A from the line L is

If alpha=3sin^(-1)(6/11) and beta=3cos^(-1)(4/9), where the inverse trigonometric functions take only the principal values, then the correct option(s) is(are)

Let PQR be a right angle isosceles triangle, right angle at P(2, 1). If the equation of the line QR is 2x+y=3, then the equation representing the pair of lines PQ and PR is

Find a vector vec( c) such that |vec(c )| = sqrt6 and vec(c ).vec(a)= 0= vec(c ).vec(b) where vec(a) = 2vec(i) -vec(k), vec(b)= 3vec(j)- vec(i)-vec(k).

In Delta ABC, if cos A+cos B+ cos C=3//2, then the triangle is

Given that alpha and beta are the roots of the equation x^(2)=7x+4, (i) show that alpha^(3)=53alpha+28 (ii) find the value of (alpha)/(beta)+(beta)/(alpha).

Find the distance from the origin to each of the point: (-4,-3,-2)

For a positive integer n , find the value of (1-i)^(n) (1 - 1/i)^(n)

If a + b = 2h , then the area of the triangle formed by the lines ax^(2) + 2hxy + by^(2) = 0 and the line x-y+2=0, in sq. units, is

An ellipseof eccentricity(2sqrt(2))/(3) is inscribed ina circle . A pointis choseninsidethe cirlceat random.Theprobaboilitythatthe pointliesoutsidethe ellipseis

The third term of an arithmetical progression is 7, and the seventh term is 2 more than 3 times the third term. Find the first term, the common difference and the sum of the first 20 terms.