28278 + Interview Questions in Maths in Class 12 Page 71 InterviewSolution

3501.	Find the coordinates of the foot of the perpendicular drawn from the point (-1,2,3) to the straight line vec(r)=(veci-4hatj+3hatk)+t(2hati+3hatj+hatk) . Also , find the shortest distance from the given point to the straight line.
Answer» ANSWER :`sqrt26` UNITS

Discussion

3502.	Corner points of the feasible region for an LPP are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5). Let F = 4x + 6y be the objective function. (Maximum of F)-(Minimum of F) =
Answer» 60 48 42 18 Answer :A

Discussion

3503.	If x^(3) + x^(2)y + xy^(2) + y^(3) = 81 find (dy)/(dx).
Answer» ANSWER :`-((3X^(2)+2xy+y^(2)))/((X^(2)+2xy+3y^(2)))`

Discussion

3504.	Find (dy)/(dx)," if "y=sec^(-1) ((1)/(2x^(2)-1)), 0 lt x lt (1)/(sqrt2)
Answer» ANSWER :`-(2)/(SQRT(1-x^(2)))`

Discussion

3505.	If the circle x^(2)+y^(2)=r^(2) intersects the hyperbola xy=c^(2) in four points (x_(i),y_(i)) for i=1,2,3 and 4 then y_(1)+y_(2)+y_(3)+y_(4)=
Answer» 0 c a `c^4` ANSWER :A

Discussion

3506.	Find the maximum bumber of electron inCr havin m=0?
Answer» ANSWER :`12.00`

Discussion

3507.	A and B are two square matrices such that A^(2)B=BA and if (AB)^(10)=A^(k)B^(10) then the value of k-1020 is.
Answer» ANSWER :3

Discussion

3508.	If the angle between the lines whose direction cosines are -(2)/(sqrt(21)),( C)/(sqrt(21)),(1)/(sqrt(21)) and (3)/(sqrt(54)),(3)/(sqrt(54)),(6)/(sqrt(54)) is (pi)/(2), then the value of C is
Answer» 6 4 -4 2 Answer :B

Discussion

3509.	If area bounded by the curve x^(2)y+y^(2)x=alpha y is 2 units, then possible values of alpha is/are
Answer» `+2` 2 `PM4` 4 Answer :A

Discussion

3510.	Find all the values of (8i)^(1//3) and hence find sum and product of their values.
Answer» Answer :SUM of the VALUES=`(sqrt3+i)+(-sqrt3+i)+(-2I)=0` Product of the values `=(sqrt3+i)(-sqrt3+i)(-2i)=8i`

Discussion

3511.	If A+B+C=270^(@) then sin 2A+sin2B+sin2C=
Answer» `4sinA SIN B sin C` `4 COS A cos B cos C` `-4sinA sin B sin C` `-4cos A cos B cos C` ANSWER :D

Discussion

3512.	Contra-positive of p rarr ( q rarr r ) is logically equivalent to
Answer» `p RARR ( q rarr R ) ` `(q rarr r ) rarr ~ p ` `p vee q rarr r ` `( q rarr r) rarr p ` ANSWER :A

Discussion

3513.	f is a differentiable function defined on an interval I with positive derivative . Then f is ...........
Answer» INCREASING on I DECREASING on I strictly increasing on I strictly decreasing on I Answer :C

Discussion

3514.	log5-(log25)/(2^(2))+(log125)/(3^(2))-(log625)/(4^(2))+ ……
Answer» LOG 2 log5 log`2**(log5)` log 10 ANSWER :C

Discussion

3515.	A plane whose normal has direction ratios lt 3, -2, k gt is parallel to the line joining (-1,1,- 4) and (5,6,-2). Then the value of k =........[6,-4,-1,0]
Answer» 6 -4 -1 0 Answer :D

Discussion

3516.	Choose the incorrect statementfrom thefollowing :
Answer» `tan^(-1) (tanx) = X` if and only if `(-PI)/2 LT x lt (pi)/2` The principal value of `tan^(-1) sqrt(3) ` is `pi/3` `tan^(-1) tan. (5pi)/4 = pi/4` `cos^(-1) (1/2) = sin^(-1) (5/4)` ANSWER :d

Discussion

3517.	Construct a 3xx4 matrix A=[a_(ij)] whose elements are given by a_(ij)={{:(3i-2j",""where "i nej,),(0",""where"i=j,):}
Answer» ANSWER :`A=[{:(0,-1,-3,-5),(4,0,0,-2),(7,5,0,1):}]`

Discussion

3518.	In the expansionof (y^3+a^7/y^5)^10,Does there exist a term independent of y in the above expansion?
Answer» SOLUTION :LET (r+1)th term is independent of y. THEREFORE `y^(30-8r)` = 1 = `y^0` or, 30-8r = 0 or, r = 30/8 = 15/4 which is not possible as `RIN N` or zero. therefore There is no term in the expansion of `(y^3+a^7/y^5)^10` which is independent of y.

Discussion

3519.	Let f(x)=sin ^(4)x] then( where[.]represents thegreatest integer function ).
Answer» F(X)is continuous at x=0 f(x)is differentiableat x=0 f(x)is non-differnentiableatx=0 `f'(0) =1` Answer :A::B

Discussion

3520.	Statement -1: f(x) = x^(3)-3x+1 =0 has one root in the interval [-2,2]. Statement-2: f(-2) and f(2) are of opposite sign.
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 is NOT a correct EXPLANANTION for Statement-1 Statement-1 is True, Statement-2 is FALSE Statement -1 is False, Statement-2 is False Answer :D

Discussion

3521.	Evaluate the following determinants.[[0.2,0.1,3],[0.4,0.2,7],[0.6,0.3,2]]
Answer» SOLUTION :`[[0.2,0.1,3],[0.4,0.2,7],[0.6,0.3,2]]` `2[[0.1,0.1,3],[0.2,0.2,7],[0.3,0.3,2]]=0(because C_1=C_2)`

Discussion

3522.	IF(x^2 )/(a^2)+(y^2)/(b^2)=1, then(d^2y)/(dx^2)=
Answer» `-(b^4)/(a^2y^3)` `(b^2)/(ay^2)` `(-b^3)/(a^2y^3)` `(b^3 )/(a^2y^2)` ANSWER :A

Discussion

3523.	Find (dy)/(dx) when x and y are connected by the relation given: tan^(-1) (x^(2) + y^(2))=a
Answer» ANSWER :`-(X)/(y)`

Discussion

3524.	The value of determinant \|{:(a-b,b+c,a),(b-a,c+a,b),(c-a,a+b,c):}\|
Answer» `a^3+b^3+c^3` 3 ABC `a^3+b^3+c^3-3abc` NONE of these ANSWER :D

Discussion

3525.	Using differentials, find the approximate values of the following: 1/(2.002)^(2)
Answer» ANSWER :`0.2495`

Discussion

3526.	If each of the observation x_(1), x_(2), ...,x_(n) is increased by 'a', where a is a negative or positive number, show that the variance remains unchanged.
Answer» ANSWER :`=SIGMA^(2)`

Discussion

3527.	What is the total number of different diagonals of a given pentagon?
Answer» Solution :The TOTAL number of DIFFERENT diagonals of given pentagon is `(""^5P_2)/(2!)-5=10-5=5.`

Discussion

3528.	A variable point P is chosen on the straight line x + y = 4 and tangents PA and PB are drawn from it to circle x^(2) + y^(2) = 1 . Then the position of P for the smallest length of chord of contact AB is
Answer» (3,1) (0,4) (2,2) (4,0) ANSWER :C

Discussion

3529.	Find the equation of louse of a point which is equidistant from the coordinate axes.
Answer» ANSWER :`X^(2)-y^(2)=0`

Discussion

3530.	Let O be a point inside DeltaABC such that angleOAB = angleOBC = angle OCA = theta cosec^(2) A + cosec^(2)B + cosec^(2)C is equal to
Answer» `cot^(2) theta` `cosec^(2) theta` `tan^(2) theta` `sec^(2) theta` Solution : Applying sine rule in `DeltaAOB`, we have `(OA)/(sin angleABO) = (AB)/(sin angle AOB)` or `OA = (c sin angleABO)/(sin angleAOB) = (c sin (B - theta))/(sin B)`...(i) `[ :' angle ABO = B - theta, angle AOB = 180^(@) - theta - angleABO = 180^(@) -B]` Again in `DeltaAOC`, we have `(OA)/(sin angleACO) = (AC)/(sin angleAOC)` `RARR OA = (b sin angleACO)/(sin angleAOC) = (b sin theta)/(sin A)` `[ :' ANGLEOAC = A - theta, angleAOC = 180^(@) - theta - angleOAC = 180^(@)]` From Eqs. (i) and (ii), we have `(c sin (B - theta))/(sin B) = (b sin theta)/(sin A)` or `c sin A (B - theta) = b sin theta sin B` `= b sin theta sin (A +C)` or `2R sin C sin A (sin B cos theta - cos B sin theta)` `= 2R sin B sin theta (sin A cos C + cos A sin C)` Dividing both sides by `2R sin theta sin A sin B sin C`, we get `cot theta - cot B = cot C + cot A` or `cot theta = cot A + cot B + cot C` Squaring both sides, we have `cot^(2) theta = cot^(2) A + cot^(2) B + cot^(2)C + 2(cotA cot B + cot B cot C + cot C cot A)` or `cosec^(2) theta - 1 = (cosec^(2) A -1) + (cosec^(2) B -1) + (cosec^(2) C -1) + 2` [since in `DeltaABC, cot A cot B + cot B cot C + cot C cot A = 1`] or `cosec^(2) theta = cosec^(2) A + cosec^(2) B + cosec^(2)C` Area of triangle ABC, `Delta = Delta_(1) + Delta_(2) + Delta_(3)` `=(1)/(2) [a OB + b OC + c OA] sin theta` `=(1)/(4) tan theta [2 a OB cos theta + 2b OC cos theta+ 2c OA cos theta]` `=(1)/(4) tan theta [(a^(2) + X^(2) -y^(2)) + (b^(2) + y^(2) - z^(2)) + (c^(2) + z^(2) - x^(2)]` `= (1)/(4) tan theta [a^(2) + b^(2) + c^(2)]`

Discussion

3531.	If S(p,q,r)=(~p)vv[~(q^^r)] is a compound statement, then S(~p,~q,~r) is
Answer» <P>`~S(p,Q,R)` `S(p,q,r)` `PVV(q^^r)` `pvv(qvvr)` ANSWER :D

Discussion

3532.	Some standard forms of integration : intsinxsqrt(4-cos^(2)x)dx=..........+c
Answer» `-(cosx)/(2)SQRT(4-cos^(2)x)+2log\|x+sqrt(4-cos^(2)x)\|` `-(cosx)/(2)sqrt(4-cos^(2)x)+2sin^(-1)((cosx)/(2))` `-(cosx)/(2)sqrt(4-cos^(2)x)-2sin^(-1)((cosx)/(2))` `(cosx)/(2)sqrt(4-cos^(2)x)+2sin^(-1)((cosx)/(2))` Answer :C

Discussion

3533.	A tower stands at the foot of a hill whose inclination to the horizon is 9^(@), at a point 40 m up the hill the tower subtends an angle of 54^(@). The height of the tower is
Answer» 17.56 m 45.76 m 54.76 m None of these ANSWER :B

Discussion

3534.	If x^(2)+bx+x=0 has no real roots and a+b+c lt 0 then
Answer» `4a+2b+x GT 0` `a-b+C=0` `c LT 0` `a+b+c=0` ANSWER :C

Discussion

3535.	Let a function is defined as f:RtoR such that f(x)=(6)/(1+3"le"^(x)). Find the number of different integral values which function f(x) can take ?
Answer» SOLUTION :f(x) can TAKE 1,2,3,4,5 as f(x) is continous function. `:.` Using IVT we can say that f(x) can take 5 INTEGRAL VALUE

Discussion

3536.	If A and B are two events such that P(A)=3/4 and P(B)=5/8, then
Answer» `P(A uu B) ge 3/4` `P(A' NN B) LE 1/4` ` 3/8 le P(A nn B) le 5/8` NONE of these Answer :A::B::C

Discussion

3537.	A line makes angles of 45^@ and 60^@ with the z-axis and the x-axis respectively. The angle made byit with y-axis is
Answer» `30^@` or `150^@` `60^@` or `120^@` `45^@` or `135^@` `90^@` Answer :B

Discussion

3538.	Findthe areaofthetrianglewhoseverticesare (2,7 ) (1,1),(10 ,8)
Answer» ANSWER :`=(47)/(2) ` SQ UNITS

Discussion

3539.	Find the magnitude of the vector vec(a)=(3hati+4hatj)xx(hati+hatj-hatk).
Answer» ANSWER :`SQRT(74)`

Discussion

3540.	Statement -1 :if A = [a_(ij) ]_(nxxn)and a_(ij) =( i^(2) +j^(2) -ij) (I -i) ,T _r (A)= 0. T_r stands for trace ofthe matrix ) Statement -2 A skew symmetric matrix is always non-invertible
Answer» Statement -1 is True ,Statement -2 is True ,Statement -2 is CORECT explanation for Statement -1 Statement-1 is True .Statement -2 is true Statement -2 is Not a CORRECT explanation for Statement -1 Statement-1 is true Statement-2 is False Statement-1 is False , Statement-2 is True Answer :C

Discussion

3541.	If the roots of ax^(2) + bx + c = 0 are both positive and b lt 0, then
Answer» `a LT 0, C lt 0` `a lt 0, c lt 0` `a GT 0, c lt 0` `a gt 0, c gt 0` ANSWER :D

Discussion

3542.	A particle moves along the curve y=x^2 + 2x . At what point(s) on the curve are x and ycoordinates of the particle changing at the same rate?
Answer» ANSWER :`(-1/2,-3/4)`

Discussion

3543.	If veca=2hati-hatj+hatk,vecb=3hati+2hatj-3hatk and vecc=hati+2hatj+hatk then 2veca+vecb-vecc=
Answer» `6hati-2hatj-2hatk` `6hati+2hatj-2hatk` `6hati-2hatj+2hatk` `6hati+2hatj+2hatk` ANSWER :A

Discussion

3544.	Study the velocity-time graph pictured below and match each segment of the graph given in list-II with position-time graph given in list-I of this motion at that time.
Answer» P`to`3, Q`to`2,4 , R`to`1 , S`to`6 P`to`3, Q`to`5 , R`to`1,2 , S`to`4,6 P`to`5, Q`to`2 , R`to`1 , S`to`2,4 P`to`3, Q`to`5 , R`to`4,6 , S`to`4,6 Answer :B

Discussion

3545.	From a point on the ground 100 m away from the base of a building, the angle of elevation of the top of the building is 60^(@). Which of the following is the best approximation for the height of the building ?
Answer» 172 m 173 m 174 m 175 m ANSWER :B

Discussion

3546.	Let alpha and beta be the roots of equation x^(2) -6x-2=0 if a_(n)=alpha^(n)-beta^(n), for n ge 1, then the value of (a_(10) -2a_(8))/(2a_(9))is equal to
Answer» 3 `-3` 6 `-6` ANSWER :a

Discussion

3547.	If D=[(0,i-100, i-500 ),(100 -i,0,1000-i),(500 -i,i-1000 ,0)]then\|D\| =……
Answer» 100 500 1000 0 Answer :D

Discussion

3548.	A bag contains 5 red balls, 6 green balls and 7 white balls. If three balls are drawn at random, one after another with replacement, then find the probability that these are green, red and white in order.
Answer» ANSWER :`(210)/((18)^(3))`

Discussion

3549.	A lot of 100 watches is known to have 10 defective watches. If 8 watches are selected (one by one with replacement) at random, then what is the probability that there will be atleast one defective watch ?
Answer» ANSWER :`1- ((9)/(10))^(8)`

Discussion

3550.	If A is a square matrix of order 3 such that abs(A)=5, then what is the value of abs(adj(adjA)?
Answer» S. griseus S. aureofacienns S. noursil saccharomyces cerevisiae Answer :A

Discussion

Explore topic-wise InterviewSolutions in .

Find the coordinates of the foot of the perpendicular drawn from the point (-1,2,3) to the straight line vec(r)=(veci-4hatj+3hatk)+t(2hati+3hatj+hatk) . Also , find the shortest distance from the given point to the straight line.

Corner points of the feasible region for an LPP are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5). Let F = 4x + 6y be the objective function. (Maximum of F)-(Minimum of F) =

If x^(3) + x^(2)y + xy^(2) + y^(3) = 81 find (dy)/(dx).

Find (dy)/(dx)," if "y=sec^(-1) ((1)/(2x^(2)-1)), 0 lt x lt (1)/(sqrt2)

If the circle x^(2)+y^(2)=r^(2) intersects the hyperbola xy=c^(2) in four points (x_(i),y_(i)) for i=1,2,3 and 4 then y_(1)+y_(2)+y_(3)+y_(4)=

Find the maximum bumber of electron inCr havin m=0?

A and B are two square matrices such that A^(2)B=BA and if (AB)^(10)=A^(k)B^(10) then the value of k-1020 is.

If the angle between the lines whose direction cosines are -(2)/(sqrt(21)),( C)/(sqrt(21)),(1)/(sqrt(21)) and (3)/(sqrt(54)),(3)/(sqrt(54)),(6)/(sqrt(54)) is (pi)/(2), then the value of C is

If area bounded by the curve x^(2)y+y^(2)x=alpha y is 2 units, then possible values of alpha is/are

Find all the values of (8i)^(1//3) and hence find sum and product of their values.

If A+B+C=270^(@) then sin 2A+sin2B+sin2C=

Contra-positive of p rarr ( q rarr r ) is logically equivalent to

f is a differentiable function defined on an interval I with positive derivative . Then f is ...........

log5-(log25)/(2^(2))+(log125)/(3^(2))-(log625)/(4^(2))+ ……

A plane whose normal has direction ratios lt 3, -2, k gt is parallel to the line joining (-1,1,- 4) and (5,6,-2). Then the value of k =........[6,-4,-1,0]

Choose the incorrect statementfrom thefollowing :

Construct a 3xx4 matrix A=[a_(ij)] whose elements are given by a_(ij)={{:(3i-2j",""where "i nej,),(0",""where"i=j,):}

In the expansionof (y^3+a^7/y^5)^10,Does there exist a term independent of y in the above expansion?

Let f(x)=sin ^(4)x] then( where[.]represents thegreatest integer function ).

Statement -1: f(x) = x^(3)-3x+1 =0 has one root in the interval [-2,2]. Statement-2: f(-2) and f(2) are of opposite sign.

Evaluate the following determinants.[[0.2,0.1,3],[0.4,0.2,7],[0.6,0.3,2]]

IF(x^2 )/(a^2)+(y^2)/(b^2)=1, then(d^2y)/(dx^2)=

Find (dy)/(dx) when x and y are connected by the relation given: tan^(-1) (x^(2) + y^(2))=a

The value of determinant |{:(a-b,b+c,a),(b-a,c+a,b),(c-a,a+b,c):}|

Using differentials, find the approximate values of the following: 1/(2.002)^(2)

If each of the observation x_(1), x_(2), ...,x_(n) is increased by 'a', where a is a negative or positive number, show that the variance remains unchanged.

What is the total number of different diagonals of a given pentagon?

A variable point P is chosen on the straight line x + y = 4 and tangents PA and PB are drawn from it to circle x^(2) + y^(2) = 1 . Then the position of P for the smallest length of chord of contact AB is

Find the equation of louse of a point which is equidistant from the coordinate axes.

Let O be a point inside DeltaABC such that angleOAB = angleOBC = angle OCA = theta cosec^(2) A + cosec^(2)B + cosec^(2)C is equal to

If S(p,q,r)=(~p)vv[~(q^^r)] is a compound statement, then S(~p,~q,~r) is

Some standard forms of integration : intsinxsqrt(4-cos^(2)x)dx=..........+c

A tower stands at the foot of a hill whose inclination to the horizon is 9^(@), at a point 40 m up the hill the tower subtends an angle of 54^(@). The height of the tower is

If x^(2)+bx+x=0 has no real roots and a+b+c lt 0 then

Let a function is defined as f:RtoR such that f(x)=(6)/(1+3"le"^(x)). Find the number of different integral values which function f(x) can take ?

If A and B are two events such that P(A)=3/4 and P(B)=5/8, then

A line makes angles of 45^@ and 60^@ with the z-axis and the x-axis respectively. The angle made byit with y-axis is

Findthe areaofthetrianglewhoseverticesare (2,7 ) (1,1),(10 ,8)

Find the magnitude of the vector vec(a)=(3hati+4hatj)xx(hati+hatj-hatk).

Statement -1 :if A = [a_(ij) ]_(nxxn)and a_(ij) =( i^(2) +j^(2) -ij) (I -i) ,T _r (A)= 0. T_r stands for trace ofthe matrix ) Statement -2 A skew symmetric matrix is always non-invertible

If the roots of ax^(2) + bx + c = 0 are both positive and b lt 0, then

A particle moves along the curve y=x^2 + 2x . At what point(s) on the curve are x and ycoordinates of the particle changing at the same rate?

If veca=2hati-hatj+hatk,vecb=3hati+2hatj-3hatk and vecc=hati+2hatj+hatk then 2veca+vecb-vecc=

Study the velocity-time graph pictured below and match each segment of the graph given in list-II with position-time graph given in list-I of this motion at that time.

From a point on the ground 100 m away from the base of a building, the angle of elevation of the top of the building is 60^(@). Which of the following is the best approximation for the height of the building ?

Let alpha and beta be the roots of equation x^(2) -6x-2=0 if a_(n)=alpha^(n)-beta^(n), for n ge 1, then the value of (a_(10) -2a_(8))/(2a_(9))is equal to

If D=[(0,i-100, i-500 ),(100 -i,0,1000-i),(500 -i,i-1000 ,0)]then|D| =……

A bag contains 5 red balls, 6 green balls and 7 white balls. If three balls are drawn at random, one after another with replacement, then find the probability that these are green, red and white in order.

A lot of 100 watches is known to have 10 defective watches. If 8 watches are selected (one by one with replacement) at random, then what is the probability that there will be atleast one defective watch ?

If A is a square matrix of order 3 such that abs(A)=5, then what is the value of abs(adj(adjA)?