14949 + Interview Questions in Maths in Class 11

1.	If y =cot^(-1) (1-x+x^2) , then (dy)/(dx) =
Answer» `1/(1+x^2)+1/(1+(x-1)^2)` `1/(1+(x-1)^2)+1/(1+x^2)` `1/(1+x^2)-1/(1+(x-1)^2)` `1/(""^(-)1+x^2)-1/(1+(x-1)^2)` ANSWER :C

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2.	Solve the inequality 3(1-x)
Answer» ANSWER :`X>(-1)`

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3.	AA n in N, 49^(n) + 16n -1 is divisible by
Answer» 64 49 132 32 Answer :A

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4.	Show that cos 35^(@) + cos 85^(@) + cos 155^(@) = 0
Answer» 0 1 -1 2 Answer :A

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5.	x = ct, y = c/t, then dy/dx is:
Answer» `-1/t^(2)` `1/t^(2)` `1/t` `c/t^(2)` ANSWER :A

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6.	The sequence (1)/(sqrt(3)),(1)/(sqrt(3)+sqrt(2)),(1)/(sqrt(3)+2sqrt(2)) ….. form an ………
Answer» AP GP HP AGP Answer :C

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7.	Find the value of cos^(2)52(1^@)/(2) - sin^(2)22 (1^@)/2
Answer» ANSWER :`-((SQRT(3)+1)/(4sqrt(2)))`

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8.	Find all the points of local maxima and local minima of the function f(x)=x^3-6x^2+12x-8
Answer» ANSWER :F'(2)=0

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9.	Sum of the coefficient in expansion (x+y+z)^n is 3^n .
Answer» ANSWER :TRUE STATEMENT

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10.	Express the equation 9x^2+16y^2=144 of an ellipse standard form
Answer» SOLUTION :`x^2/16+y^2/9=1`

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11.	(1^(2) )/( 1) + (1^(2) + 2^(2) )/(1+2) + (1^(2) + 2^(2)+ 3^(2) )/( 1+ 2+ 3)+ …. + n terms =
Answer» `(N (n+3))/(4)` `( n (n+3) )/(5)` `(n ( n+2))/( 3)` `(n ( n+5) )/(6)` Answer :C

Discussion

12.	e^(log_(e)(cos h^(-1)2)) =
Answer» `log_(E) (2 - sqrt(3))` `log_(e) (3 - sqrt(2))` `log_(e) (sqrt(3) + 2)` `log_(e) (sqrt(5) + 2)` Answer :C

Discussion

13.	describe the sample space for the indicated experiment. From a group of 2 boys and 3 girls, two children are selected.
Answer» ANSWER :`S={B_(1)B_(2),B_(1)G_(1),B_(1)G_(2),B_(1)G_(3),B_(2)G_(2),B_(2)G_(3),G_(1)G_(2),G_(1)G_(3),G_(2)G_(3)}`

Discussion

14.	A bag contains 4 white and 5 black balls. Another bag contains 9 white and 7 black balls. A ball is transferred from the first bag to the second and then a ball is drawn at random from the second bag. Find the probability that the ball drawn is white.
Answer» ANSWER :24

Discussion

15.	If veca, vecb, vecc are three coplanar vectors, barp, barq, barr are non-zero vectors then \|(barpbara,barpbarb,barpbarc),(barqbara,barqbarb,barqbarc),(barrbara,barrbarb,barr*barc)\|=
Answer» 0 1 2 3 Answer :A

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16.	If theta = - 400^(@) ,determine then the sign of sin theta + cos theta
Answer» ANSWER :POSITIVE `( GT 0)`

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17.	Three sides of a triangle are represented by the equation x+y -6 =0, 2x+ y-4 =0 and x+2y -5 =0. The co-ordinate of its orthocentre of
Answer» `(10,11)` `(2,3)` `(-2, -3)` `(-11, -10)` ANSWER :D

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18.	Express the following in the form a+ bi ((4i^(3)-i)^(2))/(2i+1)
Answer» ANSWER :`3-4i`

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19.	sin h^(-1)((x)/(sqrt(1-x^(2)))) =
Answer» `cos h^(-1)X` `cos h^(-1)(2x)` `tan h^(-1)x` `tan h^(-1)(2x)` ANSWER :C

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20.	A card is drawn from a deck of 2 cards. Find theprobability of getting an ace or a spade card.
Answer» ANSWER :`(4)/(13)`

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21.	Write the following intervals in set-builder form : (– 3, 0)
Answer» Answer :`={X : x in R, -3 LT x lt 0}`

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22.	Axx(BcupC)=....... .
Answer» ANSWER :`(AXXB) CUP (A XXC)`

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23.	Find the multiplicative inverse of each of the following complex numbers when it exists. -7+ 0i
Answer» ANSWER :`-(1)/(7) + 0I`

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24.	Differentiate x^(1/x) withrespect to xlogx.
Answer» ANSWER :`X^(1/x-2)`

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25.	IfA=6 sin20^(@) - 8 sin^(3) 20^@ , B= 8 cos^(3) 20^(@)-6 cos 20^(@) and C= ( sin 3 theta )/( sin theta ) - ( cos 3 theta )/( cos theta )then
Answer» `CgtAgtB` `AGTBGTC` `AgtCgtB` `CgtBgtA` ANSWER :A

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26.	......... is the minimum value of n such that (1+i)^(2n) = (1 - i)^(2n) .Where n in N.
Answer» ANSWER :2

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27.	Find the multiplicative inverse of each of the following complex numbers when it exists. (1+ i)^(2)
Answer» ANSWER :`0- (1)/(2)i`

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28.	The statement P(n) (1xx1!) + (2 xx2!) + (3 xx 3!) + … …. + (nxx n!) = (n+1)! - 1 is
Answer» True for all `n GT 1` Not true for any `n` True for all `n in N` True for all `n gt 10`. Answer :C

Discussion

29.	A straight line is equally inclined to all the three coordinate axes. Then an angle made by the line with the y - axis
Answer» `COS^(-1) "" (1/3)` `cos^(-1) "" (1/sqrt3)` `cos^(-1)"" (2/sqrt3)` `pi/4` ANSWER :B

Discussion

30.	Find (dy)/(dx) for the function (using logarithms). y = ((a - x ) ^(2)(b -x) ^(3))/( (c -2 x) ^(3))
Answer» ANSWER :`y [ (6)/( X - 2x) - (3)/( b -x) - (2)/(a -x) ]`

Discussion

31.	The owner of a milk store finds that, he can sell 980 litres of milk each week at Rs 14/litre and 1220 litres of milk each week at Rs 16/ litre. Assuming a linear relationship between selling price and demand, how many litres could he sell weekly at Rs 17/litre?
Answer» ANSWER :`1340` LITRES.

Discussion

32.	cos 20^(@) + cos 40^(@) + cos 60^(@) +...+cos160^(@)+cos 180^(@)=
Answer» 0 1 -1 2 Answer :C

Discussion

33.	The trigonometric equation sin2x+sin3x+sin4c+………….+sinnx=n-1 (n is a natural number greater than 2)
Answer» has unique solution for any N has no solution for any n has INFINITE solutions has no solution in `[2,n PI]` ANSWER :B::D

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34.	Prove that Sigma_(K=0)^(n)""^nC_(k)sin K x , cos (n-K)x =2^(n-1) sin x.
Answer»

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35.	alpha, beta,gamma, deltaare angles in I, II, III and IV quadrant respectively and no one of them is an integral multiple of pi//2- They form an increasing arithmetic progression. Which of the following holds:
Answer» `cos(alpha + DELTA) GT 0` `cos(alpha + delta)=0` `cos(alpha + delta) lt 0` DATA is sufficient ANSWER :A

Discussion

36.	alpha, beta,gamma, deltaare angles in I, II, III and IV quadrant respectively and no one of them is an integral multiple of pi//2- They form an increasing arithmetic progression. Which of the following does not hold:
Answer» `SIN(beta + GAMMA) =sin(alpha + beta)` `sin(beta - gamma)=sin(alpha -delta)` `tan2(alpha - beta) = TAN(beta - delta)` `cos(alpha + gamma)=COS2BETA` ANSWER :B

Discussion

37.	alpha, beta, gamma, delta are angles in I, II, III and IV quadrant respectively and no one of them is an integral multiple of pi//2. They form an increasing arithmetic progression.If alpha+beta+gamma+delta=theta and alpha=70^(@)
Answer» `400^(@) lt THETA lt 580^(@)` `470^(@) lt theta lt 650^(@)` `680^(@) lt theta lt 860^(@)` `540^(@) lt theta lt 900^(@)` Answer :C

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38.	Find equaiton of hyperbola satisfying given conditons Verticies (pm 6, 0) and one directrix is x = 4.
Answer» Answer :`(x^(2))/(36) - (y^(2))/(45) = 1`

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39.	In the binomial expansion of (1+ x)^(m+n), prove that the coefficients of x^(m) and x^(n) are equal.
Answer» ANSWER :`105101.00501`

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40.	Construct index numbers by the simple average of relative method for 1990 and.1991 with 1989 as the base year.
Answer» ANSWER :`1990 to 115.83, 1991 to 143.0`

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41.	Find the component statements of the following compound statements: Two lines in a plane either intersect at one point or they are parallel.
Answer» ANSWER :EXCLUSIVE SENCE

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42.	A(6, 3), B(-3, 5), C(4, -2) and D(x, 3x) are given points. Find x if ("Area at" Delta DBC )/( "Area at" Delta ABC)= (1)/(2).
Answer» ANSWER :`11/8`

Discussion

43.	Find the square roots of the following : -15-8i
Answer» ANSWER :`I+4i`

Discussion

44.	The sequence (1)/(sqrt(3)), (1)/(sqrt(3)+sqrt(2)), (1)/(sqrt(3) + 2 sqrt(2)) form an ........ .
Answer» AP GP HP AGP Answer :C

Discussion

45.	d/(dx)[(cosx)^(logx)+(logx)^(x)] =
Answer» `(logx)^X[1/(logx)+LOG(logx)]+(COSX)^(logx)[1/xlog(cosx)-logx.tanx]` `(cosx)^(logx)[log(cosx)-cotx.logx]+(logx)^(logx)[1+log(logx)]` `((cos x)^("log" x) + ("log x")^(x))["log" x."cos " x + x " log" x]` `(logx)^(x)[logx+log(logx)](cosx)^(logx)` ANSWER :A

Discussion

46.	P(m,n)(where m,n are natural numbers) is any point in the interior of the quadrilateral formed by the pair of lines xy =0 and the lines 2x+y-2=0 and 4x+5y =20. The possible number of positions of point P is
Answer» 7 5 4 6 Answer :B

Discussion

47.	Let P(n) :a^(n) + b^(n)such that a,b are even, then P(n) will be divisible by a+b if
Answer» `N gt 1` `AA n` is odd `AA n` is even `n gt 2` Answer :B

Discussion

48.	Let R be the universal relation on a set X with more than one element. Then R is
Answer» not REFLEXIVE notsymmetric transitive none of the above ANSWER :C

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49.	Evaluate the following limits. Lt_(xtoa)(sin(x-a))/(x^(3)-a^(3))
Answer» ANSWER :`1/(3A^(2))`

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50.	If sin^(2)xgtsqrt(2)sin^(2)x+(2-sqrtS(2))cos^(2)x then
Answer» `x in (N pi +(pi)/6, n pi +(pi)/4), n in Z` `x in (n pi +(pi)/8, n pi +(pi)/4), n in Z` `x in (npi+(pi)/4, n pi+(pi)/3), n inZ` `x in (npi+(pi)/3, n pi+(pi)/2), n in Z` Answer :B

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If y =cot^(-1) (1-x+x^2) , then (dy)/(dx) =

Solve the inequality 3(1-x)

AA n in N, 49^(n) + 16n -1 is divisible by

Show that cos 35^(@) + cos 85^(@) + cos 155^(@) = 0

x = ct, y = c/t, then dy/dx is:

The sequence (1)/(sqrt(3)),(1)/(sqrt(3)+sqrt(2)),(1)/(sqrt(3)+2sqrt(2)) ….. form an ………

Find the value of cos^(2)52(1^@)/(2) - sin^(2)22 (1^@)/2

Find all the points of local maxima and local minima of the function f(x)=x^3-6x^2+12x-8

Sum of the coefficient in expansion (x+y+z)^n is 3^n .

Express the equation 9x^2+16y^2=144 of an ellipse standard form

(1^(2) )/( 1) + (1^(2) + 2^(2) )/(1+2) + (1^(2) + 2^(2)+ 3^(2) )/( 1+ 2+ 3)+ …. + n terms =

e^(log_(e)(cos h^(-1)2)) =

describe the sample space for the indicated experiment. From a group of 2 boys and 3 girls, two children are selected.

A bag contains 4 white and 5 black balls. Another bag contains 9 white and 7 black balls. A ball is transferred from the first bag to the second and then a ball is drawn at random from the second bag. Find the probability that the ball drawn is white.

If veca, vecb, vecc are three coplanar vectors, barp, barq, barr are non-zero vectors then |(barp*bara,barp*barb,barp*barc),(barq*bara,barq*barb,barq*barc),(barr*bara,barr*barb,barr*barc)|=

If theta = - 400^(@) ,determine then the sign of sin theta + cos theta

Three sides of a triangle are represented by the equation x+y -6 =0, 2x+ y-4 =0 and x+2y -5 =0. The co-ordinate of its orthocentre of

Express the following in the form a+ bi ((4i^(3)-i)^(2))/(2i+1)

sin h^(-1)((x)/(sqrt(1-x^(2)))) =

A card is drawn from a deck of 2 cards. Find theprobability of getting an ace or a spade card.

Write the following intervals in set-builder form : (– 3, 0)

Axx(BcupC)=....... .

Find the multiplicative inverse of each of the following complex numbers when it exists. -7+ 0i

Differentiate x^(1/x) withrespect to xlogx.

IfA=6 sin20^(@) - 8 sin^(3) 20^@ , B= 8 cos^(3) 20^(@)-6 cos 20^(@) and C= ( sin 3 theta )/( sin theta ) - ( cos 3 theta )/( cos theta )then

......... is the minimum value of n such that (1+i)^(2n) = (1 - i)^(2n) .Where n in N.

Find the multiplicative inverse of each of the following complex numbers when it exists. (1+ i)^(2)

The statement P(n) (1xx1!) + (2 xx2!) + (3 xx 3!) + … …. + (nxx n!) = (n+1)! - 1 is

A straight line is equally inclined to all the three coordinate axes. Then an angle made by the line with the y - axis

Find (dy)/(dx) for the function (using logarithms). y = ((a - x ) ^(2)(b -x) ^(3))/( (c -2 x) ^(3))

The owner of a milk store finds that, he can sell 980 litres of milk each week at Rs 14/litre and 1220 litres of milk each week at Rs 16/ litre. Assuming a linear relationship between selling price and demand, how many litres could he sell weekly at Rs 17/litre?

cos 20^(@) + cos 40^(@) + cos 60^(@) +...+cos160^(@)+cos 180^(@)=

The trigonometric equation sin2x+sin3x+sin4c+………….+sinnx=n-1 (n is a natural number greater than 2)

Prove that Sigma_(K=0)^(n)""^nC_(k)sin K x , cos (n-K)x =2^(n-1) sin x.

alpha, beta,gamma, deltaare angles in I, II, III and IV quadrant respectively and no one of them is an integral multiple of pi//2- They form an increasing arithmetic progression. Which of the following holds:

alpha, beta,gamma, deltaare angles in I, II, III and IV quadrant respectively and no one of them is an integral multiple of pi//2- They form an increasing arithmetic progression. Which of the following does not hold:

alpha, beta, gamma, delta are angles in I, II, III and IV quadrant respectively and no one of them is an integral multiple of pi//2. They form an increasing arithmetic progression.If alpha+beta+gamma+delta=theta and alpha=70^(@)

Find equaiton of hyperbola satisfying given conditons Verticies (pm 6, 0) and one directrix is x = 4.

In the binomial expansion of (1+ x)^(m+n), prove that the coefficients of x^(m) and x^(n) are equal.

Construct index numbers by the simple average of relative method for 1990 and.1991 with 1989 as the base year.

Find the component statements of the following compound statements: Two lines in a plane either intersect at one point or they are parallel.

A(6, 3), B(-3, 5), C(4, -2) and D(x, 3x) are given points. Find x if ("Area at" Delta DBC )/( "Area at" Delta ABC)= (1)/(2).

Find the square roots of the following : -15-8i

The sequence (1)/(sqrt(3)), (1)/(sqrt(3)+sqrt(2)), (1)/(sqrt(3) + 2 sqrt(2)) form an ........ .

d/(dx)[(cosx)^(logx)+(logx)^(x)] =

P(m,n)(where m,n are natural numbers) is any point in the interior of the quadrilateral formed by the pair of lines xy =0 and the lines 2x+y-2=0 and 4x+5y =20. The possible number of positions of point P is

Let P(n) :a^(n) + b^(n)such that a,b are even, then P(n) will be divisible by a+b if

Let R be the universal relation on a set X with more than one element. Then R is

Evaluate the following limits. Lt_(xtoa)(sin(x-a))/(x^(3)-a^(3))

If sin^(2)xgtsqrt(2)sin^(2)x+(2-sqrtS(2))cos^(2)x then

If veca, vecb, vecc are three coplanar vectors, barp, barq, barr are non-zero vectors then |(barpbara,barpbarb,barpbarc),(barqbara,barqbarb,barqbarc),(barrbara,barrbarb,barr*barc)|=