14949 + Interview Questions in Maths in Class 11 Page 60 InterviewSolution

2951.	Find the modulus and argument of the complex number (2 + i)/(4i + (1+ i)^(2))
Answer» Answer :Modulus `= (SQRT5)/(6)`, amplitude `=TAN^(-1) 2`

Discussion

2952.	A= {a, b ,{c, d}, e} which of the following statements are correct? a in A
Answer» ANSWER :CORRECT

Discussion

2953.	If f is a function defined by f(x)={{:((x-1)/(sqrt(x)-1),"if " xgt1),(5-3x,"if "-2ltxle1),((6)/(1-10),"if "xlt-2):} then disuss the continuity of f .
Answer» ANSWER :CONTINUOUS at x=1 and DISCONTINUOUS at x=-2

Discussion

2954.	If in a triangle ABC, the altitudes from the A,B,C on opposite sides are in H.P. then sinA, sin B, sin C are in
Answer» G.P. A.P. H.P. A.G.P Answer :B

Discussion

2955.	Find the area of the triangle bounded by the straight line 2x+3y=6 and the coordinate axis.
Answer»

Discussion

2956.	The variance of 15 observations is 8. If each observation is multiplied by 4, then the variance of new observation is……
Answer» 32 24 8 128 Answer :D

Discussion

2957.	If L= {1, 2, 3, 4}, M= {3, 4, 5, 6} and N= {1, 3, 5}, then verify that L - (M cup N)= (L - M) cap (L - N).
Answer» ANSWER :`= {2}`

Discussion

2958.	Write the following sets in the set builder form : E= {1, 2, 5, 10}
Answer» Answer :E= {X : x is a natural number x is FACTORS of 10}

Discussion

2959.	Let (c cos x)/( 2 cos 2 x - 1) = (b + sin x)/( (cos^(2) x - 3 sin^(2) x)tan x), b in R For any value of b for which the equation has a solutions, the number of solution when x in (0, 2 pi) are always
Answer» infinite depends UPON VALUE of B four two Answer :C

Discussion

2960.	In the permutations of n things r, taken together, the number of permutation in which m perticular things occur together is""^((n-m))P_((r-m))xx""^rP_m.
Answer» ANSWER :`""^((n-m))C_r-mxx (r-m+1)!XX m!`

Discussion

2961.	Statement I : The range of the function f(x)=(sin([x]pi))/(x^(2)+x+1) is {0} Statement II : The range of the function f(x)=(x-[x])/(1+x-[x]) is [0, 1/2).
Answer» only IIS true only II is true both I and II are true neither I nor II are true Answer :C

Discussion

2962.	Reduce the following equations in intercept form and find their intercepts on axis. (i) 3x+2y-12=0
Answer» ANSWER :`(X)/(4) + (y)/(6) =1`

Discussion

2963.	If ""^(n)C_(10) = ""^(n) C _ (14), find the value of""^(n) C_(20) and ""^(25)C_n.
Answer» ANSWER :` 10626, 25`

Discussion

2964.	If y = sin^(-1)((sqrtx-1)/(sqrtx+1))+sec^(-1)((sqrtx+1)/(sqrtx-1)), x gt 0then (dy)/(dx) =
Answer» 1 0 `pi/2` `-1` ANSWER :B

Discussion

2965.	If abs(bara+barb)lt abs (bara-barb) " then the angle between " bara and barb can lie in the interval
Answer» `(0,PI/2)` `(pi/2,pi)` `(0,pi/4)` `(pi/4,pi/2)` ANSWER :B

Discussion

2966.	If vec(r )= x vec(i) + y vec(j) + z vec(k) then (vec(r ) xx vec(i)).(vec(r ) xx vec(j)) + xy=
Answer» 2 0 3 4 Answer :B

Discussion

2967.	Evaluate the following limits : Lim_(x to 2) ((x^(8)-16)/(x^(4)-4) +(x^(2)-9)/(x-3))
Answer» ANSWER :25

Discussion

2968.	Showthat therangeof sin^(2)theta +cos^(4) thetasi [(3)/(4),1]
Answer» ANSWER :`(a+b)^(2)`

Discussion

2969.	Two dice are thrown and the sum of the numbers which come up on the dice is noted. Let us consider the following events associated with this experiment A : 'the sum is even' B : 'the sum is a multiple of 3'. C: 'the sum is less than 4' D: 'the sum is greater than 11'. Which pairs of these events are mutually exclusive ?
Answer» ANSWER :C and D are MUTUALLY EXCLUSIVE.

Discussion

2970.	A die has two faces each with number '1', three faces each number '2' and one face with number '3'. If die is rolled once, determine (i) P(2), (ii) P(1 or 3), (iii) P(not 3).
Answer» ANSWER :(i) `1/2`, (II) `1/2`, (III) `5/6`

Discussion

2971.	What is the resulting sample space if Two coins are tossed simultaneously ,
Answer» ANSWER :S={HH,HT,TH,TT}

Discussion

2972.	Find the middle term in expansion of : (1-2x+x^(2))^(n)
Answer» Answer :`((2N)!)/((N!)^(2))(-1)^(n)x^(n)`

Discussion

2973.	A triangle has sides 6,7 and 8. The line through its incentre parallel to the shortest side is drawn to meet the other two sides at P and Q. Then find the length of the segment [PQ] (where [.] isg.i.f
Answer» 1 2 3 4 Answer :D

Discussion

2974.	n is any integer then arg(((sqrt(3)+i)^(4n+1))/((1-sqrt(3)i)^(4n)))=....
Answer» `(PI)/(3)` `(pi)/(6)` `(2pi)/(3)` `(5PI)/(6)` ANSWER :B

Discussion

2975.	InDelta ABC , 2ac sin ""( 1)/(2)(A-B+C)=
Answer» `a^(2) + B^(2) - C^(2)` `c^(2) + a^(2) - b^(2)` `c^(2) - a^(2) - b^(2)` `b^(2) - c^(2) - a^(2)` ANSWER :B

Discussion

2976.	Write the negation of the following statement. sqrt(7) is rational.
Answer» ANSWER :NEGATION : `SQRT(7)` is not RATIONAL.

Discussion

2977.	If sin theta sec theta =-1 and theta lies in the second quadrant, find sin theta and sec theta.
Answer» Answer :`sin THETA=(1)/(sqrt(2)),SEC theta=-sqrt(2)`

Discussion

2978.	If 18x=pi, then prove that tan 2x.tan3x.tan4x.tan8x=1
Answer» ANSWER :125

Discussion

2979.	Find lambda so that lambdax^(2)+5xy+4y^(2)+3x+2y+2=0 may represents a pair of straight lines. Find also the angle between them for this value of lambda.
Answer» Answer :`LAMBDA=(-10)/(9) tan^(-1)((3)/(5))`

Discussion

2980.	If sintheta=12/13 and 450^(@)ltthetalt540^(@) then "sin"theta/2=
Answer» `2/sqrt13` `3/sqrt13` `-3/sqrt13` `-2/sqrt13` ANSWER :C

Discussion

2981.	For all values of the a and b the lie (a+2b)x+(a-b)y+(a+5b)=0 passes through the point
Answer» `(-1,2)` `(2,-1)` `(-2,1)` `(1,-2)` ANSWER :C

Discussion

2982.	If acos theta -bsin theta =c, then show thatasine theta + bcos =pm sqrt (a^(2)+b^(2)-c^(2))
Answer» Answer :`K= pm sqrt(a^(2)+B^(2)-C^(2))`

Discussion

2983.	Integrate x^2 (2- x)^(15)
Answer» Answer :`-1/18(2 - X)^(18) + 4/17 (2 - x)^(17) - 1/4(2 - x)^(16) + c`.

Discussion

2984.	Arrange the following in the descending order of magnitude(A) [I xx j j xx k k xx i] (B) [I + jj + k k + i] (C ) (I xx j) (j xx k) (D) (K xx j) (k xx j)
Answer» B, A, C, D B, D, A, C D, C, B, A B,C,A,D Answer :A

Discussion

2985.	Find a vector of length sqrt6 and perpendicular to both vec(a)= 2vec(i) -vec(k), vec(b)= 3vec(i)-vec(j)-vec(k)
Answer» ANSWER :`+- (VEC(i) + vec(J) + 2vec(K))`

Discussion

2986.	The spherical ballon is being inflated so that its volume increases uniformly at the rate of 40 cubic cm per minute. The rate of increase in the surface as when the radius is 8 cm is
Answer» 5 sq.cm/min 6 sq.cm/min 10s sq.cm/min 15 sq.cm/min Answer :C

Discussion

2987.	Find the angle between the lines represented by 2x^(2) + xy- 6y ^(2)+ 7y - 2 = 0.
Answer» ANSWER :`cos^(-1)((4)/(sqrt(65)))`

Discussion

2988.	Let l_(1), l_(2), l_(3) be the lengths of the internal bisectors of angles A,B,C respectively of a Delta ABC Statement -1 : (cos. A/2)/l_(1) + (cos. B/2)/l_(2) + (cos. C/2)/l_(3) = 2 (1/a + 1/b + 1/c) Statement-2 : l_(1)^(2) = bc[1 -(a/(b+c))^(2)] ,l_(2)^(2)=ca[1 -(b/(c+a))^(2)], l_(3)^(2) = ab [1 - (c/(a+b))^(2)]
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

2989.	Match Column - I and Column - II. {:("Column - I","Column- II"),("(i) The coordinates of the points P and Q on the line" x+5y =13 " which are at a distance of 2 units from the line" 12x - 5y + 26=0 "are","(a) (3, 1), (-7, 11)"),("(ii) The coordinates of the point on the line" x+y=4",which are at a unit distance"4x + 3y - 10 =0 "are","(b)" (- (1)/(3)","(11)/(3) )","((4)/(3)","(7)/(3))),("(iii) The coordinates of the point on the line joining A(-2, 5) and B(3, 1) such that AP = PQ = QB are","(c ) " (1","(12)/(5) ) "," (-3"," (16)/(5) )):}
Answer» ANSWER :(i) `to` (C ), (II) `to` (a) , (III) `to` (B)

Discussion

2990.	(x-a)/(x-b)
Answer» ANSWER :`(a-b)/((x-b)^(2))`

Discussion

2991.	The maximum value of (sqrt(-3+4x-x^(2))+4)^(2)+(x-5)^(2). (where 1lexle3) is
Answer» 34 36 32 20 Answer :B

Discussion

2992.	Find the sum of all those 4 digits numbers which can be formed with the digits 1,2,3,4.
Answer» ANSWER :66660

Discussion

2993.	Let f(x)=\|x^(2)-3x-4\|,-1lexle4.Then
Answer» F(x)is monotonically INCREASING in `[-1,3//2]` f(x) is monotonically DECREASING in (3/2 ,4] the maximum value of `f(x) ` is `(25)/(4)` theminimum value of f(x) =0 Answer :A::B::C::D

Discussion

2994.	The value of sin50^(@)-sin70^(@)+sin10^(@) is
Answer» 1 0 `(1)/(2)` 2 Answer :B

Discussion

2995.	Find the domain and range of the following function f(x)= (1)/(1-x^(2))
Answer» ANSWER :DOMAIN `R- (-1, 1)` Range `(-oo, 0)uu [1, oo)`

Discussion

2996.	The sides of a triangle are 3x+2y-6=0, 2x-3y+6=0, x+2y+2=0. P(0,b) is a point on y-axis. If P lies on the triangle or inside the triangle then the range of b is
Answer» [-1,3] [2,3] [-1,2] [-2,2] ANSWER :A

Discussion

2997.	Find the circumcentre of the triangle whose sides are 3x-y-5=0, x+2y-4=0 and 5x+3y+1=0.
Answer» ANSWER :`DELTAABC`

Discussion

2998.	Find the roots of the equations. Q. x^(2)+3x-3=0, giving your answer correct to two decimal places.
Answer» ANSWER :`-3.79,0.79`.

Discussion

2999.	Find the unit vectors perpendicular to both the vectors 2vec(i)- 3vec(j) + 5vec(k) and -vec(i) + 4vec(j) + 2vec(k)
Answer» ANSWER :`+- ((-26 VEC(i) -9vec(J) + 5vec(K)))/(sqrt782)`

Discussion

3000.	If tan A=-sqrt(3), find all the possible values of A between 0^(@) and 360^(@).
Answer» ANSWER :`120^(@)` and `300^(@)`

Discussion

Explore topic-wise InterviewSolutions in .

Find the modulus and argument of the complex number (2 + i)/(4i + (1+ i)^(2))

A= {a, b ,{c, d}, e} which of the following statements are correct? a in A

If f is a function defined by f(x)={{:((x-1)/(sqrt(x)-1),"if " xgt1),(5-3x,"if "-2ltxle1),((6)/(1-10),"if "xlt-2):} then disuss the continuity of f .

If in a triangle ABC, the altitudes from the A,B,C on opposite sides are in H.P. then sinA, sin B, sin C are in

Find the area of the triangle bounded by the straight line 2x+3y=6 and the coordinate axis.

The variance of 15 observations is 8. If each observation is multiplied by 4, then the variance of new observation is……

If L= {1, 2, 3, 4}, M= {3, 4, 5, 6} and N= {1, 3, 5}, then verify that L - (M cup N)= (L - M) cap (L - N).

Write the following sets in the set builder form : E= {1, 2, 5, 10}

Let (c cos x)/( 2 cos 2 x - 1) = (b + sin x)/( (cos^(2) x - 3 sin^(2) x)tan x), b in R For any value of b for which the equation has a solutions, the number of solution when x in (0, 2 pi) are always

In the permutations of n things r, taken together, the number of permutation in which m perticular things occur together is""^((n-m))P_((r-m))xx""^rP_m.

Statement I : The range of the function f(x)=(sin([x]pi))/(x^(2)+x+1) is {0} Statement II : The range of the function f(x)=(x-[x])/(1+x-[x]) is [0, 1/2).

Reduce the following equations in intercept form and find their intercepts on axis. (i) 3x+2y-12=0

If ""^(n)C_(10) = ""^(n) C _ (14), find the value of""^(n) C_(20) and ""^(25)C_n.

If y = sin^(-1)((sqrtx-1)/(sqrtx+1))+sec^(-1)((sqrtx+1)/(sqrtx-1)), x gt 0then (dy)/(dx) =

If abs(bara+barb)lt abs (bara-barb) " then the angle between " bara and barb can lie in the interval

If vec(r )= x vec(i) + y vec(j) + z vec(k) then (vec(r ) xx vec(i)).(vec(r ) xx vec(j)) + xy=

Evaluate the following limits : Lim_(x to 2) ((x^(8)-16)/(x^(4)-4) +(x^(2)-9)/(x-3))

Showthat therangeof sin^(2)theta +cos^(4) thetasi [(3)/(4),1]

A die has two faces each with number '1', three faces each number '2' and one face with number '3'. If die is rolled once, determine (i) P(2), (ii) P(1 or 3), (iii) P(not 3).

What is the resulting sample space if Two coins are tossed simultaneously ,

Find the middle term in expansion of : (1-2x+x^(2))^(n)

A triangle has sides 6,7 and 8. The line through its incentre parallel to the shortest side is drawn to meet the other two sides at P and Q. Then find the length of the segment [PQ] (where [.] isg.i.f

n is any integer then arg(((sqrt(3)+i)^(4n+1))/((1-sqrt(3)i)^(4n)))=....

InDelta ABC , 2ac sin ""( 1)/(2)(A-B+C)=

Write the negation of the following statement. sqrt(7) is rational.

If sin theta sec theta =-1 and theta lies in the second quadrant, find sin theta and sec theta.

If 18x=pi, then prove that tan 2x.tan3x.tan4x.tan8x=1

Find lambda so that lambdax^(2)+5xy+4y^(2)+3x+2y+2=0 may represents a pair of straight lines. Find also the angle between them for this value of lambda.

If sintheta=12/13 and 450^(@)ltthetalt540^(@) then "sin"theta/2=

For all values of the a and b the lie (a+2b)x+(a-b)y+(a+5b)=0 passes through the point

If acos theta -bsin theta =c, then show thatasine theta + bcos =pm sqrt (a^(2)+b^(2)-c^(2))

Integrate x^2 (2- x)^(15)

Arrange the following in the descending order of magnitude(A) [I xx j j xx k k xx i] (B) [I + jj + k k + i] (C ) (I xx j) (j xx k) (D) (K xx j) (k xx j)

Find a vector of length sqrt6 and perpendicular to both vec(a)= 2vec(i) -vec(k), vec(b)= 3vec(i)-vec(j)-vec(k)

The spherical ballon is being inflated so that its volume increases uniformly at the rate of 40 cubic cm per minute. The rate of increase in the surface as when the radius is 8 cm is

Find the angle between the lines represented by 2x^(2) + xy- 6y ^(2)+ 7y - 2 = 0.

(x-a)/(x-b)

The maximum value of (sqrt(-3+4x-x^(2))+4)^(2)+(x-5)^(2). (where 1lexle3) is

Find the sum of all those 4 digits numbers which can be formed with the digits 1,2,3,4.

Let f(x)=|x^(2)-3x-4|,-1lexle4.Then

The value of sin50^(@)-sin70^(@)+sin10^(@) is

Find the domain and range of the following function f(x)= (1)/(1-x^(2))

The sides of a triangle are 3x+2y-6=0, 2x-3y+6=0, x+2y+2=0. P(0,b) is a point on y-axis. If P lies on the triangle or inside the triangle then the range of b is

Find the circumcentre of the triangle whose sides are 3x-y-5=0, x+2y-4=0 and 5x+3y+1=0.

Find the roots of the equations. Q. x^(2)+3x-3=0, giving your answer correct to two decimal places.

Find the unit vectors perpendicular to both the vectors 2vec(i)- 3vec(j) + 5vec(k) and -vec(i) + 4vec(j) + 2vec(k)

If tan A=-sqrt(3), find all the possible values of A between 0^(@) and 360^(@).