14949 + Interview Questions in Maths in Class 11 Page 169 InterviewSolution

8401.	Express the following in the form a+bi (sqrt3 + 5i) (sqrt3 -5i)^(2) + (-4+ 5i)^(2)
Answer» ANSWER :`(28sqrt3-9)-180i`

Discussion

8402.	Ifsin 2 theta + cos theta = 0"then " theta =
Answer» `2 N pi - (pi)/(6), n in Z` `2 n pi + (pi)/(3), n in Z` `(2 n pi)/(3)- (pi)/(6) , n in Z` `(2 n pi)/(3)+ (pi)/(4) , n in Z` ANSWER :C

Discussion

8403.	The value of tan^(-1)((x cos theta)/(1-x sin theta))-cot^(-1)((cos theta)/(x-sin theta)) is
Answer» `2 THETA` `theta` `theta//2` INDEPENDENT of `theta` ANSWER :B

Discussion

8404.	d/(dx)(a^(log_asqrtx))=1/(2sqrtx) where a gt 1 inR^+
Answer» ANSWER :TRUE STATEMENT

Discussion

8405.	The orthocentre of triangle formed by lines xy+3x+3y+9 = 0 and the line 3x+4y-5=0 is
Answer» (3,3) (-3,3) (3,-3) (-3,-3) ANSWER :D

Discussion

8406.	If Lt_(xto0)(1+ax+bx^(2))^(2//x)=e^(3), find a and b.
Answer» ANSWER :`a=3/2,binR`

Discussion

8407.	Evaluate lim_(xrarrinfty)[(x^2 -3x -4 )/(x^2 +3x+2)]^x
Answer» ANSWER :`1/(e^6)`

Discussion

8408.	cos^(-1)("cos"(7pi)/6) is equal to
Answer» `(7pi)/6` `(5PI)/3` `(5pi)/6` `(13pi)/6` ANSWER :C

Discussion

8409.	Find the number of terms in the expansion of the following : (x+2a)^(10)+(x-2a)^(10)
Answer» ANSWER :6

Discussion

8410.	Differentiate x^(a) with respect to a^(x).
Answer» ANSWER :`X^(a-1)/(LOG a^(x-1))`

Discussion

8411.	Match the following
Answer» a,C,d,b b,a,d,c a,b,c,d d,c,b,a Answer :D

Discussion

8412.	Using binomial theorem, evaluate (101)^4
Answer» ANSWER :` 104060401`

Discussion

8413.	If (d)/(dx)((1+x^(4)+x^8)/(1+x^(2)+x^(4)))=ax^(3)+bx then …………….
Answer» a=4,B=2 a=4,b=-2 a=-2,b=4 None of these Answer :B

Discussion

8414.	A coin is tossed four times write the elements of sample space.
Answer» Answer :`={HHHH,HHTH,HTHH,THHH,T T TH,T THH,THTH,HT TH,HHHT,HHT T,HTHT,THHT,T T T T,T THT,THT T,HT T T}`

Discussion

8415.	If y= Tan^(-1)""(sqrt(1+x^2) -1)/x then (dy)/(dx)=
Answer» `1/(1+x^2)` `(-1)/(1+x^2)` `1/(2(1+x^2))` `2/((1+x^2))` ANSWER :C

Discussion

8416.	If x^(p) occurs in the expansion of (x^(2)+1/x)^(2n) then prove that its coefficient is (2n!)/((((4n-p)!)/(3!))(((2n+p)!)/(3!)))
Answer» ANSWER :`=((2N)!)/(((2n+p)!)/(3!)XX((4n-p)!)/(3!))`

Discussion

8417.	If f_(n)(x)=(sinx)/(cos3x)+(sin3^2x)/(cos3^2x)+(sin3^2x)/(cos3^(3)x)+....+(sin3^(n-1)x)/(cos3^(n)x) Then f_(2)(pi//4)+f_3(pi//4)=
Answer» 0 1 `-1` 2 Answer :C

Discussion

8418.	If bar(AB)=2bara+barb and bar(AD) = bara-2barb " where " absbara=1, absbarb =1, (bara,barb) = 60^(@) are the adjacent sides of a parallelogram, then the length of the diagonal "bar(BD) is
Answer» `SQRT13` `SQRT7` `sqrt12` `SQRT10` ANSWER :A

Discussion

8419.	If the lengths of the sides of triangle are 3, 5, and 7, then the largest angle of the triangle is
Answer» `pi/2` `(5pi)/6` `(2PI)/3` `(3PI)/4` ANSWER :C

Discussion

8420.	Find the equation of parabolawith itsaxis parallelto x - axisand passing through the points (-2,1) ,(1,2) and (-1,3) .
Answer» ANSWER :`y^(2)-y + 2X + 4 = 0 `

Discussion

8421.	Evaluate the following limits in lim_(xrarr1)(ax^(2)+bx+c)/(cx^(2)+bx+a), a+b+c ne0
Answer» ANSWER :1

Discussion

8422.	Differentiateby 1^(st) principalf(x) = tan (1-2x)
Answer» ANSWER :`-2 SEC^(2) (1-2x)`

Discussion

8423.	d/(dx)(sinh^(-1)(sqrtx)) =
Answer» `1/(SQRT(1+x)).1/sqrtx` `1/(sqrt(1+x)).1/(2sqrtx)` `-1/(sqrt(1+x)).1/(2sqrtx)` `-1/(sqrt(1+x)).1/sqrtx` ANSWER :B

Discussion

8424.	Find Lt_(xtoa)(log(x-a))/(log(e^(x)-e^(a)))
Answer» ANSWER :1

Discussion

8425.	The point on the parabola y =x^(2) + 7x + 2 which is elosest to the line y = 3x - 3 is
Answer» ANSWER :(2, -8)

Discussion

8426.	The locus of the point x=a+lamda^(2),y=b-lamda where lamda is a parameter is
Answer» `(x-a)^(2)=b-y` `x-a=(b-y)^(2)` `x+a=y^(2)` `x-a=y^(2)` ANSWER :2

Discussion

8427.	How many strings of length 6 can be formedusing the letter of the word FRIEND if (i) either starts with F or ends with D (ii) neither starts with F nor ends with D.
Answer» ANSWER :504

Discussion

8428.	If X={(1,2,3,4,5} and Y={1,3,5,7,9}, then find which of the following sets are functions from X to Y? (i) R_(1)={(x,y):y=x+2, x in X, y in Y} (ii) R_(2) ={(1,2),(2,1),(3,3),(4,3), (5,3)} (iii)R_(3)={(1,1),(1,3),(3,5),(3,7),(5,7)} (iv) R_(4)={(1,3),(2,5),(4,7),(5,9),(3,1)}
Answer» ANSWER :`R_(2) and R_(4)` are FUNCTIONS

Discussion

8429.	If z = x + yi, omega = (2-iz)/(2z-i) and \|omega\|=1, find the locus of z in the complex plane
Answer» ANSWER :`3X^(2) + 3y^(2)- 8y-3= 0`. This is a circle WHOSE centre is `(0, (4)/(3))` and radius is `(5)/(3)`

Discussion

8430.	sin^(2)pi/8+sin^(2)(3pi)/(8)+sin^(2)(5pi)/(8)+sin^(2)(7pi)/(8)=?
Answer» `-1` 1 `-2` 2 Solution :N//A

Discussion

8431.	If f: R rarr R, f(x)= x-2, g: R rarr R, g(x)= x + 2 then (f+ g) (x)= ……..
Answer» X `x^(2)-4` 2x 4 Answer :C

Discussion

8432.	If f and g are differentiable functions in [0,1] satifying f(0)=2=g(1),g(0)=0 and f(1) =6 , then for some c in (0,1)
Answer» G'(C ) `-g'(c )` `2G'(c )` `3G'(c )` ANSWER :C

Discussion

8433.	If xgt0 then the interval of monotonically increasing of f(x)=2x^(2)-logx is
Answer» `(-OO,(-1)/(2))` `((-1)/(2),0)` `(0,(1)/(2))` `((1)/(2),oo)` ANSWER :D

Discussion

8434.	The mean deviation about mean of the observation 3, 10, 10, 4, 7, 10, 5 is
Answer» 2 2.57 3 3.75 Answer :B

Discussion

8435.	Let barr be a vector perpendicular to bara + barb + barc . If barr=l(barbxxbarc)+m(barcxxbara)+n(baraxxbarb) then l+m+n is
Answer» 0 1 2 `3SQRT3` ANSWER :A

Discussion

8436.	The side of triangle ABC satisfy the relation a + b - c = 2 " and " 2ab - c^(2) = 4, then square of the area of triangle is :
Answer» 3 `SQRT3` 9 81 Answer :A

Discussion

8437.	log ( x )^(n) = n .log x is true for n.
Answer» `AA N in N` `AA n in Z` `n` is POSITIVE odd integer `n` is positive EVEN integer Answer :C

Discussion

8438.	A straight line L with negative slope passes through the point (8,2) and cuts the positive coordinate axes at points P and Q. Then the absolute minimum value of OP+OQ as L varies, [where O is the origin ] is 6n, then n=
Answer» ANSWER :3

Discussion

8439.	If f: R to [0, infty) defined by f(x) = 10^(x) then f^(-1)(x)=
Answer» `log_(X)10` `x^(10)` `log_(10)x` `10^(x)` ANSWER :C

Discussion

8440.	Lt_(ntooo)((n+2)!+(n+1)!)/((n+2)!-(n+1)!)
Answer» ANSWER :1

Discussion

8441.	If ""^(n)C_(9)=""^(n)C_(8), find ""^(n)C_(17).
Answer» ANSWER :1

Discussion

8442.	If sin((picottheta)/(4))=cos((pitantheta)/(4)) and theta is in the first quadrant, then theta =
Answer» `pi//3` `pi//2` `pi//4` `pi//6` ANSWER :C

Discussion

8443.	If (sqrt(8)+i)^(50)=3^(49)(a+ib) then a^(2)+b^(2)=....
Answer» 3 8 9 `SQRT(8)` ANSWER :C

Discussion

8444.	Evaluate C(31,26)-C(30,26)
Answer» ANSWER :` 142506`

Discussion

8445.	If the vectors 2bar(i) + lambda bar(j) - bar(k) and 4bar(i)-2bar(j)+2bar(k) are perpendicular to each other than find lambda.
Answer» ANSWER :3

Discussion

8446.	If the equation of the pair of straight lines passing through the point (1,1) one making an angle theta with the positive dirction of the x-axis and the other making the same angle with the positive direction of the y-axis is x^2-(a+2)xyy^2+a(x+y-1)=0, ane-2 then the value of sin2theta is
Answer» a-2 a+b `2//(a+2)` `2//a` ANSWER :C

Discussion

8447.	Let A = { a, e, i, o, u } and B = { a, i, u }. Show that A ∪ B= A
Answer» ANSWER :`B SUB A," then "A CUP B = A`

Discussion

8448.	f:R rarr R, function f(x) is defined as f(x)= 2x +\|x\| then f(2x)+f(-x)-f(x) = ...........
Answer» ANSWER :`2\|x\|`

Discussion

8449.	Prove thatsum (r+r_1)tan ((B-C)/( 2))=0
Answer» ` ( ABC)/( Delta ^(3)) ` `0` ` 4Rr^(2) ` ` (1)/ ( r ) ` Answer :B

Discussion

8450.	A(-1,1)B(5,3) are the opposite vertices of a square. Perpendicular distance from (1,2) to the other diagonal (which is not passing through A,B) of the square is
Answer» `1/(SQRT(10))` `2/(sqrt(10))` `3/(sqrt(10))` `4/(sqrt(10))` Answer :C

Discussion

Explore topic-wise InterviewSolutions in .

Express the following in the form a+bi (sqrt3 + 5i) (sqrt3 -5i)^(2) + (-4+ 5i)^(2)

Ifsin 2 theta + cos theta = 0"then " theta =

The value of tan^(-1)((x cos theta)/(1-x sin theta))-cot^(-1)((cos theta)/(x-sin theta)) is

d/(dx)(a^(log_asqrtx))=1/(2sqrtx) where a gt 1 inR^+

The orthocentre of triangle formed by lines xy+3x+3y+9 = 0 and the line 3x+4y-5=0 is

If Lt_(xto0)(1+ax+bx^(2))^(2//x)=e^(3), find a and b.

Evaluate lim_(xrarrinfty)[(x^2 -3x -4 )/(x^2 +3x+2)]^x

cos^(-1)("cos"(7pi)/6) is equal to

Find the number of terms in the expansion of the following : (x+2a)^(10)+(x-2a)^(10)

Differentiate x^(a) with respect to a^(x).

Match the following

Using binomial theorem, evaluate (101)^4

If (d)/(dx)((1+x^(4)+x^8)/(1+x^(2)+x^(4)))=ax^(3)+bx then …………….

A coin is tossed four times write the elements of sample space.

If y= Tan^(-1)""(sqrt(1+x^2) -1)/x then (dy)/(dx)=

If x^(p) occurs in the expansion of (x^(2)+1/x)^(2n) then prove that its coefficient is (2n!)/((((4n-p)!)/(3!))(((2n+p)!)/(3!)))

If f_(n)(x)=(sinx)/(cos3x)+(sin3^2x)/(cos3^2x)+(sin3^2x)/(cos3^(3)x)+....+(sin3^(n-1)x)/(cos3^(n)x) Then f_(2)(pi//4)+f_3(pi//4)=

If bar(AB)=2bara+barb and bar(AD) = bara-2barb " where " absbara=1, absbarb =1, (bara,barb) = 60^(@) are the adjacent sides of a parallelogram, then the length of the diagonal "bar(BD) is

If the lengths of the sides of triangle are 3, 5, and 7, then the largest angle of the triangle is

Find the equation of parabolawith itsaxis parallelto x - axisand passing through the points (-2,1) ,(1,2) and (-1,3) .

Evaluate the following limits in lim_(xrarr1)(ax^(2)+bx+c)/(cx^(2)+bx+a), a+b+c ne0

Differentiateby 1^(st) principalf(x) = tan (1-2x)

d/(dx)(sinh^(-1)(sqrtx)) =

Find Lt_(xtoa)(log(x-a))/(log(e^(x)-e^(a)))

The point on the parabola y =x^(2) + 7x + 2 which is elosest to the line y = 3x - 3 is

The locus of the point x=a+lamda^(2),y=b-lamda where lamda is a parameter is

How many strings of length 6 can be formedusing the letter of the word FRIEND if (i) either starts with F or ends with D (ii) neither starts with F nor ends with D.

If X={(1,2,3,4,5} and Y={1,3,5,7,9}, then find which of the following sets are functions from X to Y? (i) R_(1)={(x,y):y=x+2, x in X, y in Y} (ii) R_(2) ={(1,2),(2,1),(3,3),(4,3), (5,3)} (iii)R_(3)={(1,1),(1,3),(3,5),(3,7),(5,7)} (iv) R_(4)={(1,3),(2,5),(4,7),(5,9),(3,1)}

If z = x + yi, omega = (2-iz)/(2z-i) and |omega|=1, find the locus of z in the complex plane

sin^(2)pi/8+sin^(2)(3pi)/(8)+sin^(2)(5pi)/(8)+sin^(2)(7pi)/(8)=?

If f: R rarr R, f(x)= x-2, g: R rarr R, g(x)= x + 2 then (f+ g) (x)= ……..

If f and g are differentiable functions in [0,1] satifying f(0)=2=g(1),g(0)=0 and f(1) =6 , then for some c in (0,1)

If xgt0 then the interval of monotonically increasing of f(x)=2x^(2)-logx is

The mean deviation about mean of the observation 3, 10, 10, 4, 7, 10, 5 is

Let barr be a vector perpendicular to bara + barb + barc . If barr=l(barbxxbarc)+m(barcxxbara)+n(baraxxbarb) then l+m+n is

The side of triangle ABC satisfy the relation a + b - c = 2 " and " 2ab - c^(2) = 4, then square of the area of triangle is :

log ( x )^(n) = n .log x is true for n.

A straight line L with negative slope passes through the point (8,2) and cuts the positive coordinate axes at points P and Q. Then the absolute minimum value of OP+OQ as L varies, [where O is the origin ] is 6n, then n=

If f: R to [0, infty) defined by f(x) = 10^(x) then f^(-1)(x)=

Lt_(ntooo)((n+2)!+(n+1)!)/((n+2)!-(n+1)!)

If ""^(n)C_(9)=""^(n)C_(8), find ""^(n)C_(17).

If sin((picottheta)/(4))=cos((pitantheta)/(4)) and theta is in the first quadrant, then theta =

If (sqrt(8)+i)^(50)=3^(49)(a+ib) then a^(2)+b^(2)=....

Evaluate C(31,26)-C(30,26)

If the vectors 2bar(i) + lambda bar(j) - bar(k) and 4bar(i)-2bar(j)+2bar(k) are perpendicular to each other than find lambda.

If the equation of the pair of straight lines passing through the point (1,1) one making an angle theta with the positive dirction of the x-axis and the other making the same angle with the positive direction of the y-axis is x^2-(a+2)xyy^2+a(x+y-1)=0, ane-2 then the value of sin2theta is

Let A = { a, e, i, o, u } and B = { a, i, u }. Show that A ∪ B= A

f:R rarr R, function f(x) is defined as f(x)= 2x +|x| then f(2x)+f(-x)-f(x) = ...........

Prove thatsum (r+r_1)tan ((B-C)/( 2))=0

A(-1,1)B(5,3) are the opposite vertices of a square. Perpendicular distance from (1,2) to the other diagonal (which is not passing through A,B) of the square is