14949 + Interview Questions in Maths in Class 11 Page 23 InterviewSolution

1101.	If Delta ABC
Answer» `sin A sin B sin C le (3 sqrt3)/( 8)` `sin^(2) A + sin^(2) B + sin^(2) C le (9)/(4)` `sinA sinB sinC` is always positive `sin^(2) A + sin^(2) B le 1 + COS C` Answer :A::B::C::D

Discussion

1102.	Are the following pair of sets equal? Give reasons A= {p, q, r, s} B= {q, p, s, r}.
Answer» ANSWER :it is an EQUAL SET

Discussion

1103.	the sum of the first six terms of a GP is 9 times the sum of the first three terms. The common ratio is
Answer» ANSWER :`16/7;2;16/7(2^(N)-1)`

Discussion

1104.	Evaluate the following :(i)root(3)(1003) correct to 4 places of decimals (ii) (1)/(root(3)(128)) correct to 4 places of decimals.
Answer» ANSWER :(i) `= 10.0100` (II)`=0.1984256`

Discussion

1105.	What is meant by simple harmonic oscillation? Give examples and explain why every simple harmonic motion is a periodic motion whereas the converse need not be true.
Answer» Solution :(i) Simple harmonic motion is a special type of oscillatory motion in which the acceleration or force on the particle is directly proportional to its displacement from a fixed point and is always directed towards that fixed point. (ii) In one dimensional case, let X be the displacement of the particle and `a_x` be the acceleration of the particle, then ` a_x prop x` ` a_x = - bx` where b is a constant which measures acceleration per unit displacement and dimensionally it is equal to `T^(-2)` . (iii) By multiplying by mass of the particle on both sides of equation and from Newton's second law, the force is ` F_x =-k x` where k is a force constant which is defined as force per unit length. (iv) The negative sign indicates that displacement and force (or acceleration) are in opposite directions. (v) This means that when the displacement of the particle is taken towards right of equilibrium position (x TAKES positive value), the force (or acceleration) will point towards equilibrium (towards left) and similarly, when the displacement of the particle is taken towards left of equilibrium position (x takes negative value), the force (or acceleration) will point towards equilibrium (towards right). (vi) This type of force is known as restoring force because it always DIRECTS the particle executing simple harmonic motion to restore to its original (equilibrium or mean) position. This force (restoring force) is CENTRAL and attractive whose center of attraction is the equilibrium position. (vii) In order to represent in two or three dimensions, we can write using VECTOR notation ` vecF= - k vecr` (viii) where `vecr`is the displacement of the particle from the chosen origin. Note that the force and displacement have a linear relationship. This means that the exponent of force `vecF`and the exponent of displacement `vecr`are unity. (IX) The sketch between cause (magnitude of force) and effect(magnitude of displacement `\|vecr\|`) is a straight line passing through second and fourth quadrant by measuring slope `1/k` one can find the numerical value of force constant k.

Discussion

1106.	If vec(a) is a unit vector and vec(a) xx vec(i) = vec(j), then vec(a).vec(i)=
Answer» 0 1 2 3 Answer :A

Discussion

1107.	If l,m,n are in A.P then the liens represented by lx+my+n=0 are concurrent at the point
Answer» (1,2) (2,4) (-2,1) (1,-2) ANSWER :D

Discussion

1108.	Let P be the image of the point (3,1,7) with respect to the plane x - y + z =3. Then the equation of the plane passing through P and containing the straight line x/1 = y/2 = z/1
Answer» `x + y -3Z =0` `3x + z=0` `x + 4y + 7Z =0` `2x - y =0` Answer :C

Discussion

1109.	A(0,-1,-2), B(3,1,4) and C(5,7,1) are vertices of DeltaABD then find the measure of angleA.
Answer» Answer :Centroid `(-(16)/(3) , 10)`, In centre `(-1, 8)` Circum centre `(-8,(63)/(2))`, In centre `(-1,8)` Circum centre `(-8,(63)/(2))`, ORTHO centre `(0,-33)`

Discussion

1110.	Evaluate the following limits : Lim_(x to 0 ) (sin x^(@))/x
Answer» ANSWER :`pi/180`

Discussion

1111.	If the slope of one line of the pair 8x^(2)+2hxy+y^(2)=0 is twice the slope of the second line, then h=
Answer» -3 9 16 12 Answer :A

Discussion

1112.	Let f_k(x)=(1)/(k)(sin^k x+ cos^k x) " where " x in R and k ge 1 . Then f_4(x)-f_6(x) equals
Answer» `(1)/(6)` `(1)/(3)` `(1)/(4)` `(1)/(12)` ANSWER :D

Discussion

1113.	The probability that a person will win a game is (2)/(3) andthe probability that he willnot win a horse race is (5)/(9) . If the probability of getting in at least one of the events is (4)/(5) ,what is the probability that he will be successful in both the events ?
Answer» ANSWER :`=(14)/(45)`.

Discussion

1114.	For the given data, the calculation corresponding to all values of varsities (x, y) isfollowing: Sigma (x - barx)^(2) = 36, Sigma(y-bary)^(2)=25, Sigma(x-barx), (y-bary)=20 Karl Pearson's correlation coefficient is
Answer» 0.66 `-0.66` `-0.5` `1.66` SOLUTION :N/A

Discussion

1115.	Ifcos 4 x = a_(0) + a_(1) cos ^(2) x + a_(2) cos ^(4) xis truefor all values of x in R . Then the value of 5 a_(0) + a_(1) + a_(2) is _____
Answer» ANSWER :5

Discussion

1116.	The maximum value of y=tan^(-1)((1-x)/(1+x)) on [0,1] is
Answer» `(PI)/(2)` `(2)/(pi)` `(4)/(pi)` `(pi)/(4)` ANSWER :D

Discussion

1117.	If the domain of the function f(x)=x^(2)-6x+7 is (-oo, oo), then the range of function is
Answer» `(-OO, oo)` `[-2, oo)` `(-2, 3)` `(-oo, -2)` ANSWER :B

Discussion

1118.	The vector bara,barb,barc are equal in length and pair wise make equal angles. Ifbara=bari+barj, barb=barj+bark " , then " barc=
Answer» (1,0,1) (1,1,1) (0,1,1) (1,1,0) ANSWER :A

Discussion

1119.	If (z-1)/(z+1) is purely imaginary number (zne-1) then find the value of \|z\|.
Answer» ANSWER :`[ :. \|z\|=sqrt(X^(2)+y^(2))]`

Discussion

1120.	Express the following in the form a+ bi sqrt((5(2+i))/(2-i))
Answer» ANSWER :`2+i`

Discussion

1121.	(i) If y= (x-1)/( 2x^(2) - 7x +5), find (dy)/( dx) at x=2.
Answer» ANSWER :(i) `-2`

Discussion

1122.	Find the transformed equation of x^(2)+y^(2)+2x-4y+1=0 when the origin is shifted to the point (-1, 2).
Answer» ANSWER :`X^(2)+Y^(2)-4 =0`

Discussion

1123.	Find the valuesof the trigonometric functions sin(-(11pi)/(3))
Answer» ANSWER :`(SQRT3)/(2)`

Discussion

1124.	Write out the expansions of the following: (e ) (1+2x)^(7)
Answer» Answer :`1+ 14x 84x^(2) + 280x^(3) + 560 x^(4) + 672x^(5)+ 448x^(6) + 128 x^(7)`

Discussion

1125.	The range off: R to R,f(x)= ((sqrt(( x^(2)+ 1 ))- 3x))/( sqrt( x^(2) +1)+x)is
Answer» `(0, OO)` `(-1, oo)` `(-oo, -1)` `[1, oo)` ANSWER :B

Discussion

1126.	If theta = - 1590^(@), then tan theta is
Answer» `SQRT(3)` 1 `PROP` `(1)/(sqrt(3))` ANSWER :D

Discussion

1127.	If the orthocentre and the circucentre of a triangle are (-3,5,1),(3,3,-1) then the centroid is
Answer» (3, 3, 4) `((3)/(2), (7)/(2), (9)/(2))` `(9, 9, 12) ` `((9)/(2), (-3)/(2), (3)/(2))` Answer :a

Discussion

1128.	For all n in N, x in R, tan^(-1) [ ( x)/( 1.2+ x^2) ] + tan^(-1) [ (x)/( 2.3+ x^2) ] + …. + tan^(-1) [ ( x)/( n(n+1) +x^2) ] =
Answer» `tan^(-1) [ (X)/( N) ] - tan^(-1) [ (x)/( n+1) ]` `tan^(-1) [x] - tan^(-1) [ (x)/( n+1) ]` `tan^(-1) [n+1] - tan^(-1) [x]` `tan^(-1) [x]` Answer :B

Discussion

1129.	ABC is a right angled triangle with AB = 4, BC = 3, AC = 5. P is mid point of AB. Q is a point on AC such that lfloor PQA = 90^(@) . Then BA.
Answer» `4/3 SQRT13` `5/4 sqrt13` `3/4 sqrt12` NONE ANSWER :a

Discussion

1130.	Let the vectors bara, barb, barc, bard be such that (bara xx barb) xx (barc xx bard) = bar0. Let pi_(1), pi_(2) be planes determined by the pairs of vectors bara, barb and barc, bard respectively, then angle betwen pi_(1) and pi_(2) is
Answer» `0^(@)` `30^(@)` `45^(@)` `60^(@)` ANSWER :A

Discussion

1131.	Find the 5th term from the end of : ((x^3)/(2) - (2)/(x^2) )^12 , x ne 0
Answer» ANSWER :`(7920)/(x^4)`

Discussion

1132.	If theta=-1000^(@), determine the sign of theta-cos theta.
Answer» ANSWER :`COS10^(@)-SIN10^(@)`

Discussion

1133.	If the angle theta between the vectors bara = 2x^(2)bari +4xbarj+bark and barb= 7bari -2barj + xbark " is such that " 90^(@)lt theta lt180^(@) then x lie in the interval
Answer» `(0,1/2)` `(1/2,1)` `(1,3/2)` `(1/2,3/2)` ANSWER :A

Discussion

1134.	A function g(x) is defined as g(x)=(1)/(4)f(2x^(2)-1)+(1)/(2)f(1-x^(2))andf(x) is an increasing function Then g(x) is increasing in the interal
Answer» `(-1,1)` `(-SQRT((2)/(3)),0)uu(sqrt((2)/(3)),oo)` `(-sqrt((2)/(3)),sqrt((2)/(3)))` `(-2,2)` ANSWER :B

Discussion

1135.	During a certain period the cost of living index number goes from 150 to 180 and salary of a worker is also raised from Rs.13000 to Rs.18000 . The real wage of the employee in the current year is
Answer» (a) `Rs.10000` (B) `Rs.15000` (C) `Rs.18000` (d) NONE of these Answer :A

Discussion

1136.	(sinx)/(sin(x/8))=
Answer» `8 COS (x//8) sin(x//4)cos(x//2)` `8 cos (x//8) cos(x//4)sin(x//2)` `8 cos (x//8) cos(x//4)cos(x//2)` `8sin(x//8)sin(x//4)sin(x//2)` ANSWER :C

Discussion

1137.	Write the equation of the circle having radius 5 and tangent as the line 3x-4y+5=0 at (1,2)
Answer» ANSWER :`(x+2)^(2)+(y-6)^(2)=25` and `(x-4)^(2)+(y+2)^(2)=25`

Discussion

1138.	Write the negation of " All triangles are not equilateral triangle "
Answer» ANSWER :All TRIANGLES are EQUILATERAL triangles.

Discussion

1139.	Find the rank of the following matrices using elementary transformations (i) [(0,1,2),(1,2,3),(3,2,1)] (ii) [(1,2,0,-1),(3,4,1,2),(-2,3,2,5)] (iii) [(-1,-2,-3),(3,4,5),(4,5,6)]
Answer» ANSWER :(i) 2 (II) 3 (III) 2

Discussion

1140.	One of the lines of3x^(2)+4xy+y^(2)=0 is perpendicular to lx+y+4=0 then l=
Answer» `-1` `-2` `-3` 0 Answer :A

Discussion

1141.	A bag contains 30 tickets numbered from 1 to 30 . Fivetickets are drawn at random and arranged in ascending order . Find the probability that the third number is 20. (ii)a bag contains 50 tickets numbered 1,2,3 ……, 50 of which five are drawn at random and arranged in ascending order of magnitude (x_(1)ltx_(2)ltx_(3)ltx_(4)ltx_(5)) . What is the probability that x_(3)=30.?
Answer» ANSWER :(i)`=(285)/(5278)` (II)`=(551)/(15134)`.

Discussion

1142.	Find the number ofpermutations of the letter of the words 'ALLAHABAD '
Answer» ANSWER :` 7560`

Discussion

1143.	Find the value of Tan10^(@) + Tan35^(@) + Tan10^(@).Tan35^(@).
Answer» ANSWER :1

Discussion

1144.	The maximum value of -x^(2)-8x+17 is
Answer» 17 `-1` 33 2 Answer :C

Discussion

1145.	Statement-1: If a, b, c are the sides of a triangle, then the minimum value of (2a)/(b+c-a)+(2b)/(c+a-b)+(2c)/(a+b-c) is 9. Statement-2 : A M ge G.M. ge H.M
Answer» Statement-1 is TRUE, Statement-2 is True, Statement-2 is a CORRECT EXPLANATION for Statement-1 Statement-1 is True, Statement-2 is True, Statement-2 NOT a correct explanation for Statement-1 Statement-1 is True, Statement-2 is FALSE Statement-1 is False, Statement-2 is True. Answer :D

Discussion

1146.	Evaluate 4x^2+8x+35, when x=2+sqrt-3
Answer» ANSWER :`55+34isqrt3`

Discussion

1147.	Evaluate the following limits : Lim_(x to 0) (sin x )/x
Answer» ANSWER :` Lim_(xto0) (COS X)/1 = 1 `

Discussion

1148.	If cot theta=(4)/(3), find the values of other t-ratios of theta.
Answer» ANSWER :`sintheta=pm3/5,costheta=pm4/5,tantheta=3/4,sectheta=pm"COSEC"theta=pm5/3`.

Discussion

1149.	ABC is an equilateral triangle of side 4cm. If R,r, and h are the circumradius, inradius, and altitude, respectively, then (R+r)/(h) is equal to
Answer» 4 2 1 3 Answer :C

Discussion

1150.	(i) For any three set A, B, and C, prove that : A-(B-C)=(A-B)cup(AcapC) (ii) Using Venn diagram, prove that : A-(B capC)=(A-B)cup(A-C)
Answer»

Discussion

Explore topic-wise InterviewSolutions in .

If Delta ABC

Are the following pair of sets equal? Give reasons A= {p, q, r, s} B= {q, p, s, r}.

the sum of the first six terms of a GP is 9 times the sum of the first three terms. The common ratio is

Evaluate the following :(i)root(3)(1003) correct to 4 places of decimals (ii) (1)/(root(3)(128)) correct to 4 places of decimals.

What is meant by simple harmonic oscillation? Give examples and explain why every simple harmonic motion is a periodic motion whereas the converse need not be true.

If vec(a) is a unit vector and vec(a) xx vec(i) = vec(j), then vec(a).vec(i)=

If l,m,n are in A.P then the liens represented by lx+my+n=0 are concurrent at the point

Let P be the image of the point (3,1,7) with respect to the plane x - y + z =3. Then the equation of the plane passing through P and containing the straight line x/1 = y/2 = z/1

A(0,-1,-2), B(3,1,4) and C(5,7,1) are vertices of DeltaABD then find the measure of angleA.

Evaluate the following limits : Lim_(x to 0 ) (sin x^(@))/x

If the slope of one line of the pair 8x^(2)+2hxy+y^(2)=0 is twice the slope of the second line, then h=

Let f_k(x)=(1)/(k)(sin^k x+ cos^k x) " where " x in R and k ge 1 . Then f_4(x)-f_6(x) equals

The probability that a person will win a game is (2)/(3) andthe probability that he willnot win a horse race is (5)/(9) . If the probability of getting in at least one of the events is (4)/(5) ,what is the probability that he will be successful in both the events ?

For the given data, the calculation corresponding to all values of varsities (x, y) isfollowing: Sigma (x - barx)^(2) = 36, Sigma(y-bary)^(2)=25, Sigma(x-barx), (y-bary)=20 Karl Pearson's correlation coefficient is

Ifcos 4 x = a_(0) + a_(1) cos ^(2) x + a_(2) cos ^(4) xis truefor all values of x in R . Then the value of 5 a_(0) + a_(1) + a_(2) is _____

The maximum value of y=tan^(-1)((1-x)/(1+x)) on [0,1] is

If the domain of the function f(x)=x^(2)-6x+7 is (-oo, oo), then the range of function is

The vector bara,barb,barc are equal in length and pair wise make equal angles. Ifbara=bari+barj, barb=barj+bark " , then " barc=

If (z-1)/(z+1) is purely imaginary number (zne-1) then find the value of |z|.

Express the following in the form a+ bi sqrt((5(2+i))/(2-i))

(i) If y= (x-1)/( 2x^(2) - 7x +5), find (dy)/( dx) at x=2.

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

Find the valuesof the trigonometric functions sin(-(11pi)/(3))

Write out the expansions of the following: (e ) (1+2x)^(7)

The range off: R to R,f(x)= ((sqrt(( x^(2)+ 1 ))- 3x))/( sqrt( x^(2) +1)+x)is

If theta = - 1590^(@), then tan theta is

If the orthocentre and the circucentre of a triangle are (-3,5,1),(3,3,-1) then the centroid is

For all n in N, x in R, tan^(-1) [ ( x)/( 1.2+ x^2) ] + tan^(-1) [ (x)/( 2.3+ x^2) ] + …. + tan^(-1) [ ( x)/( n(n+1) +x^2) ] =

ABC is a right angled triangle with AB = 4, BC = 3, AC = 5. P is mid point of AB. Q is a point on AC such that lfloor PQA = 90^(@) . Then BA.

Let the vectors bara, barb, barc, bard be such that (bara xx barb) xx (barc xx bard) = bar0. Let pi_(1), pi_(2) be planes determined by the pairs of vectors bara, barb and barc, bard respectively, then angle betwen pi_(1) and pi_(2) is

Find the 5th term from the end of : ((x^3)/(2) - (2)/(x^2) )^12 , x ne 0

If theta=-1000^(@), determine the sign of theta-cos theta.

If the angle theta between the vectors bara = 2x^(2)bari +4xbarj+bark and barb= 7bari -2barj + xbark " is such that " 90^(@)lt theta lt180^(@) then x lie in the interval

A function g(x) is defined as g(x)=(1)/(4)f(2x^(2)-1)+(1)/(2)f(1-x^(2))andf(x) is an increasing function Then g(x) is increasing in the interal

During a certain period the cost of living index number goes from 150 to 180 and salary of a worker is also raised from Rs.13000 to Rs.18000 . The real wage of the employee in the current year is

(sinx)/(sin(x/8))=

Write the equation of the circle having radius 5 and tangent as the line 3x-4y+5=0 at (1,2)

Write the negation of " All triangles are not equilateral triangle "

Find the rank of the following matrices using elementary transformations (i) [(0,1,2),(1,2,3),(3,2,1)] (ii) [(1,2,0,-1),(3,4,1,2),(-2,3,2,5)] (iii) [(-1,-2,-3),(3,4,5),(4,5,6)]

One of the lines of3x^(2)+4xy+y^(2)=0 is perpendicular to lx+y+4=0 then l=

Find the number ofpermutations of the letter of the words 'ALLAHABAD '

Find the value of Tan10^(@) + Tan35^(@) + Tan10^(@).Tan35^(@).

The maximum value of -x^(2)-8x+17 is

Statement-1: If a, b, c are the sides of a triangle, then the minimum value of (2a)/(b+c-a)+(2b)/(c+a-b)+(2c)/(a+b-c) is 9. Statement-2 : A M ge G.M. ge H.M

Evaluate 4x^2+8x+35, when x=2+sqrt-3

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

If cot theta=(4)/(3), find the values of other t-ratios of theta.

ABC is an equilateral triangle of side 4cm. If R,r, and h are the circumradius, inradius, and altitude, respectively, then (R+r)/(h) is equal to

(i) For any three set A, B, and C, prove that : A-(B-C)=(A-B)cup(AcapC) (ii) Using Venn diagram, prove that : A-(B capC)=(A-B)cup(A-C)