28278 + Interview Questions in Maths in Class 12 Page 116 InterviewSolution

5751.	If the determinant \|{:(x+a,p+u,l+f),(y+b,q+v,m+g),(z+c,r+w,n+h):}\| splits into exactly K determinants of order 3, each elements of which contains only one term, then the value of K is 8
Answer» ANSWER :TRUE

Discussion

5752.	It was time for celebrations in the Gryffindor common room. But as luck would have had it, Seamus miscued a spell setting the common room floor on fire. The students were evacuated quickly. Dumbledore was informed of this act and he thought of the perfect punishment for Seamus. He had to tile the common room without using magic (of course). The room was two units wide and N units long. Seamus was provided with two types of tiles: a rectangle that is one unit wide and two units long, and a L-shaped tile covering 3 square units. Pictures of the tiles are shown below. Seamus was allowed to rotate the tiles as he laid them. He had an unlimited supply of tiles. He however failed, and requested Harry to help. Harry said that he could only tell the number of different ways of tiling the room using these tiles. For instant, a2 xx 3 room could be tiled in 5 different ways as follows: Notice that the tiling could use both types of tiles. consider the tiling of a 2 xx 4 room below. Seamus then asks Harry for the number of different ways of tiling a room of dimension 2 xx 12. What would be Harry's answer?
Answer» 1055 1255 1455 1450 Solution :For a `2 XX 10` room, Total WAYS of TILLING : 1255

Discussion

5753.	State which of the following are positive ?sec 73^@
Answer» SOLUTION :`SEC 73^@` is +ve as sec +ve in the 1ST QUADRANT.

Discussion

5754.	Evaluate : int_(2)^(5)[\|x-2\|+\|x-3\|+\|x-4\|]dx
Answer» ANSWER :`1/2`

Discussion

5755.	The radical centre of the circles x^2+y^2=1,x^2+y^2-2x-3=0 and x^2+y^2-2y-3=0 is
Answer» (1,1) (1,-1) (-1,1) (-1,-1) ANSWER :D

Discussion

5756.	If the fociof the ellipse (x^(2))/(16)+(y^(2))/(b^(2))=1and thehyperbola coincide then b^(2) equals
Answer» 5 7 9 1 Answer :B

Discussion

5757.	int(x^(4)+1)/(1+x^(6))dx =
Answer» `TAN^(-1)(x^(3))+tan^(-1)x+c` `(1)/(3)tan^(-1)x+tan^(-1)x^(3)+c` `3TAN^(-1)x^(3)+tan^(-1)x+c` `tan^(-1)x+(1)/(3)tan^(-1)x^(3)+c` ANSWER :D

Discussion

5758.	Show that the four common tangents can be drawn for the circles given by x^(2) + y^(2) -14 x + 6y + 33 = 0"____(1)" and x^(2) + y^(2) + 30x-2y +1 =0"_____(2)" and find the internal and external centres of similitude.
Answer» ANSWER :` ((3)/(2),-2) , (18,5) `

Discussion

5759.	Statement-1 :If a le x_i le b where x_i denotes the value of x in the i^"th" case for i=1,2,….n, then (b-a)^2 le Variance (x) . Statement-2 : S.D. le range (b-a)
Answer» ANSWER :3

Discussion

5760.	Show that the line passing through (1, -1, 2) and (3, 4, -2) is perpendicular to the line passing through the points (0, 3, 2) and (3, 5, 6).
Answer» ANSWER :HENCE the LINES `L_1`, and `L_2` are PERPENDICULAR.

Discussion

5761.	Find order and value of given differential equation y"+(y')^(2) + 2y = 0
Answer» ANSWER :ORDER 2; DEGREE 1

Discussion

5762.	Vocal cords occur in :-
Answer» TRACHEA Larynx Glottis Bronchiai tube Answer :A

Discussion

5763.	Show that the line x + 2y - 4 = 0 touches the ellipse 3x^(2) + 4y^(2) = 12 also find the point of contact.
Answer» ANSWER :`1,3/2`

Discussion

5764.	{:(Lt),(n->oo):}[(1)/(n+1) + (1)/(n+2) + … "to n terms"] =
Answer» log 2 log 3 log `(1)/(2)` 2 log 2 Answer :A

Discussion

5765.	In the figure, triangle ABC and ABD are right triangle , what is the value of x?
Answer» 20 30 50 70 Answer :D

Discussion

5766.	The standard deviation of the observations 22, 26, 28, 20, 24, 30 is
Answer» 2 2.4 3 3.42 Answer :D

Discussion

5767.	int (1)/(sqrt(1-e^(2x)))dx=...
Answer» `x-LOG[1+sqrt(1-e^(2X))]+C` `x+log[1+sqrt(1-e^(2x))]+c` `log[1+sqrt(1-e^(2x))]+c` NONE of these Answer :A

Discussion

5768.	Find the area bounded by the curve x^(2) = 4y and the line x = 4y -2.
Answer» ANSWER :`9/8`

Discussion

5769.	Let x,y be real members such that x ne y and xy ne1. If ax + b sec (tan^(-1)x)=c and ay+ b sec (tan^(-1)y) =c," then "(x+y)/(1-xy)=
Answer» `(2ab)/(a^(2)-B^(2))` `(2AC)/(a^(2)+c^(2))` `(2ab)/(a^(2)+b^(2))` `(2ac)/(a^(2)-c^(2))` ANSWER :D

Discussion

5770.	If a line makes angles tan^(-1) sqrt7, tan^(-1) (sqrt5)/(sqrt3) with x-axis, Y-axis respectively, then the angle made by it with Z-axis is
Answer» `(pi)/(2)` `(pi)/(6) or (5pi)/(6)` `(pi)/(3) or (2PI)/(3)` `(pi)/(4) or (3pi)/(4)` ANSWER :D

Discussion

5771.	The table below shows the percents of U.S. citizens who had ever consumed Bob's soda , out of all soda consumers , for each year form 1986 through 2006. Which of the following years had the LEAST increase in the percent of U.S. citizens who had consumed Bob'ssoda from the previous year ?
Answer» 1990 1998 2001 2004 Answer :B

Discussion

5772.	The plane 2x-(1+lambda)y+3lambdaz=0 passes through the intersection of the plane
Answer» 2x-y=0 and y+3z=0 2x-y=0 and y-3z=0 2x+3x=0 and y=0 None of these Answer :B

Discussion

5773.	The table below shows the percents of U.S. citizens who had ever consumed Bob's soda , out of all soda consumers , for each year form 1986 through 2006. The figure below shows a scatterplot of the data in the table and solid lines that are possible modals for the data. Which of the 5 lines appears to be the best representation of the data ?
Answer» A B C D Answer :D

Discussion

5774.	The table below shows the percents of U.S. citizens who had ever consumed Bob's soda , out of all soda consumers , for each year form 1986 through 2006. By 2002 there were 74,672,120 U.S. citizens who had consumed Bob's soda. According to this information , approximately how many people were soda consumers , of Bob's soda or other sodas, in 2002 ?
Answer» 4700000000 150000000 119000000 47000000 Answer :C

Discussion

5775.	Find the coefficient of x^(6) in the expansion of (1-3x)^((-2)/(5))
Answer» SOLUTION :N/A

Discussion

5776.	If f(x)=((8^(x)-1)^(2))/(sin x log (1+ x/4)) in [-1, 1] - {0}, thenforremovable discontinuity of f at x=0, f(0)=
Answer» 4 log 8 8 log 2 `4 (log 8)^(2)` `8 (log 2)^(2)` Answer :C

Discussion

5777.	The points A, B and C with position vectors 3hat(i)-yhat(j)+2hat(k),5hat(i)-hat(j)+hat(k)and3xhat(i)+3hat(j)-hat(k) are collinear, then the values of x and y respectively are
Answer» 2, 3 4, 5 3, 3 `-1, 4` Answer :C

Discussion

5778.	Let ABC to be an acute triangle with BC=a,CA =b and AB=c,where a ne b ne c. From any point 'p' inside Delta ABClet B,E,F denot foot of perpendiculars form 'p' noto the sides, BC, CA and AB, respectively. Now, answer the following equations. Let (A (7,0), B(4,4) and C(0,0)and Delta DEF is isosceles with DE = DF. Then, the curve on which 'P' may lie
Answer» `X=4 or x+y y=7 or 4x=3y` `x=4 or x^(2)+y^(2) =4x+4y` `3(x^(2)+y^(2))+196=49 (x+y)` NONE of the above Answer :C

Discussion

5779.	Let ABC to be an acute triangle with BC=a,CA =b and AB=c,where a ne b ne c. From any point 'p' inside Delta ABClet B,E,F denot foot of perpendiculars form 'p' noto the sides, BC, CA and AB, respectively. Now, answer the following equations. If DeltaDEF is equilateral, then 'P'
Answer» COINCIDES with INCENTRE of `Delta ABC` coincides with orthocentre of `Delta ABC` lies on padal `Delta` of `Delta ABC` NONE of the above Answer :D

Discussion

5780.	int(x-11C_(1)x^(2)+11C_(2)x^(3)-11C_(3)x^(4)+....-11C_(11)x^(12))dx=....
Answer» `((1-x)^(12))/(12)-((1-x)^(11))/(11)+C` `((1-x)^(13))/(12)-((1-x)^(12))/(12)+c` `((1-x)^(11))/(11)-((1-x)^(12))/(12)+c` `((1-x)^(12))/(12)-((1-x)^(13))/(12)+c` ANSWER :B

Discussion

5781.	Let ABC to be an acute triangle with BC=a,CA =b and AB=c,where a ne b ne c. From any point 'p' inside Delta ABClet B,E,F denot foot of perpendiculars form 'p' noto the sides, BC, CA and AB, respectively. Now, answer the following equations. All positions of point 'p' for which Delta BEF is isosceles lie on
Answer» the incircle of `Delta ABC` line of intternal angle BISECTORS from A, B and C ARCS of 3 CIRCLES None of the above ANSWER :C

Discussion

5782.	If sin^(-1)x+sin^(-1)y=(pi)/(2), then x^(2) is equal to
Answer» 1)`1-y^(2)` 2)`y^(2)` 3)0 4)`SQRT(1-y)` ANSWER :A

Discussion

5783.	If 7c -2b=15 and 3b-6c=2, what is the value of b +c ?
Answer» `-27` `-3` 8 17 Solution :If you're not asked to find the value of an INDIVIDUAL variable, the question may lead itself to combination. This EQUATION ASKA for ` b + c,` so don't waste your time finding the VARIABLES individually if yu can avoid it. After rearranging the equations so that variables and constants are aligned, you an add the equations together : `-2b+7c =15` `(+ 3B -6c =2)/(b +c=17)`

Discussion

5784.	If A=[[0,5],[1,0]] , B= [[1,1],[1,0]] ,then find AB .
Answer»

Discussion

5785.	Each question given below has four possible answers out of which only one is correct. Choose the correct one. veca.vecbxxveca =
Answer» `VEC0` 0 1 `veca^2vecb` ANSWER :B

Discussion

5786.	If the joining A(1,3,4)and B is dividedby the point (-2,3,5) in the ratio1:3 then, B is
Answer» `(-11,3,8)` `(-11,3,-8)` `(-8,12,20)` `(13,6,-13)` ANSWER :A

Discussion

5787.	int (dx)/(sqrt(1-x))=..
Answer» `sin^(-1) SQRT(x)+c` `-2 sqrt(1-x)+c` `-sin^(-1) sqrt(x)+c` `2sqrt(1-x)+c` Answer :B

Discussion

5788.	Integrate the function in Exercise. (xe^(4))/((1+x)^(2))
Answer» ANSWER :`E^(X)F(x)+C`

Discussion

5789.	Evaluate the following integrals int(tan^2theta+1)/(tan^2theta-1)d theta
Answer» Solution :`int(tan^2theta+1)/(tan^2theta-1)d THETA` PUT `TANTHETA=t` `sec^2theta d theta=DT` `int(sec^2thetad theta )/(tan^2theta-1)` `int(dt)/(t^2-1)=(1/2)Inabs(t-1)/(t+1)+C` `(1/2)Inabs((tantheta-)/(tantheta+1)) +C`

Discussion

5790.	Which of the following bonds forms via 2-lobe interaction ?
Answer» 2p-2p `(SIGMA)` 2s-2p `(sigma)` `3d_pi - 3d_pi` NONE of these

Discussion

5791.	Find the value of int (x^2 dx)/(1+x^6)
Answer»

Discussion

5792.	Find the value of int (dx)/sqrt(25-9x^2)
Answer»

Discussion

5793.	An ellipse passing through (4sqrt2, 2sqrt6) has foci at (-4,0) and (4,0). Then, its eccentricity is
Answer» `SQRT2` `1/2` `1/sqrt2` `1/sqrt3` ANSWER :B

Discussion

5794.	A tangent to the parabola y^2 + 4bx = 0 meets the parabola y^2 = 4ax in P and Q. The locus of the middle points of PQ is:
Answer» `x^2(2a+B)=4a^2y` `y^2(2a+b)=4a^2x` `y^2(a+b)=a^2x` `x^2(a+b)=a^2y` ANSWER :B

Discussion

5795.	The points - 6a + 3b + 2c, 3a - 2b + 4c, 5a + 7b + 3c, - 13a + 17b - c are
Answer» COLLINEAR COPLANAR but not collinear noncoplanar none Answer :D

Discussion

5796.	{{:(21x-6y=54),(9+y=3.5x):} The system of equations shown above has how many solutions ?
Answer» Zero ONE Two infinitely many Solution :Get the two equations into the same format so that you can distinguish among these POSSIBILITIES: ` 21X -6y=54` `3.5-y=9` Now it's easier to see that the FIRST equation is equivalent to MULTIPLYING every term in the second equation by 6. Both equations describe the same line, so there are infinitely many solutions, (D) is correct.

Discussion

5797.	Using integration find the area of region bounded by the triangle whose vertices are (-1,0), (1, 3) and (3, 2).
Answer» ANSWER :4

Discussion

5798.	If f(x) = (sin [x])/([x]), [x] ne 0 = 0, [x] = 0, where [x] denotes the greatest integer less than or equal to x, than lim_(x rarr 0) f(x) equals :
Answer» 1 0 -1 None of these ANSWER :D

Discussion

5799.	If the normals at three points A, B, C on the rectangular hyperbola xy = c^(2) intersect at a . Point D on the hyperbola, then
Answer» circumcircle of `Delta ABC` passes through D centroidof triangle ABC LIES at the CENTRE of hyperbola `XY = c^(2)` orthocentre of `Delta ABC`is the point D centre of the circumcircle of `Delta ABC` lies at another hyperbola Solution :N/A

Discussion

5800.	Fill in the blanks in each of the following, using the answers given against each of them : The lines 2x - 3y + 1 = 0 and 3x+ ky - 1 = 0 are perpendicular to each other if k = _____ .
Answer» 2 3 `-2` `-3` ANSWER :A

Discussion

Explore topic-wise InterviewSolutions in .

If the determinant |{:(x+a,p+u,l+f),(y+b,q+v,m+g),(z+c,r+w,n+h):}| splits into exactly K determinants of order 3, each elements of which contains only one term, then the value of K is 8

State which of the following are positive ?sec 73^@

Evaluate : int_(2)^(5)[|x-2|+|x-3|+|x-4|]dx

The radical centre of the circles x^2+y^2=1,x^2+y^2-2x-3=0 and x^2+y^2-2y-3=0 is

If the fociof the ellipse (x^(2))/(16)+(y^(2))/(b^(2))=1and thehyperbola coincide then b^(2) equals

int(x^(4)+1)/(1+x^(6))dx =

Show that the four common tangents can be drawn for the circles given by x^(2) + y^(2) -14 x + 6y + 33 = 0"____(1)" and x^(2) + y^(2) + 30x-2y +1 =0"_____(2)" and find the internal and external centres of similitude.

Statement-1 :If a le x_i le b where x_i denotes the value of x in the i^"th" case for i=1,2,….n, then (b-a)^2 le Variance (x) . Statement-2 : S.D. le range (b-a)

Show that the line passing through (1, -1, 2) and (3, 4, -2) is perpendicular to the line passing through the points (0, 3, 2) and (3, 5, 6).

Find order and value of given differential equation y"+(y')^(2) + 2y = 0

Vocal cords occur in :-

Show that the line x + 2y - 4 = 0 touches the ellipse 3x^(2) + 4y^(2) = 12 also find the point of contact.

{:(Lt),(n->oo):}[(1)/(n+1) + (1)/(n+2) + … "to n terms"] =

In the figure, triangle ABC and ABD are right triangle , what is the value of x?

The standard deviation of the observations 22, 26, 28, 20, 24, 30 is

int (1)/(sqrt(1-e^(2x)))dx=...

Find the area bounded by the curve x^(2) = 4y and the line x = 4y -2.

Let x,y be real members such that x ne y and xy ne1. If ax + b sec (tan^(-1)x)=c and ay+ b sec (tan^(-1)y) =c," then "(x+y)/(1-xy)=

If a line makes angles tan^(-1) sqrt7, tan^(-1) (sqrt5)/(sqrt3) with x-axis, Y-axis respectively, then the angle made by it with Z-axis is

The table below shows the percents of U.S. citizens who had ever consumed Bob's soda , out of all soda consumers , for each year form 1986 through 2006. Which of the following years had the LEAST increase in the percent of U.S. citizens who had consumed Bob'ssoda from the previous year ?

The plane 2x-(1+lambda)y+3lambdaz=0 passes through the intersection of the plane

Find the coefficient of x^(6) in the expansion of (1-3x)^((-2)/(5))

If f(x)=((8^(x)-1)^(2))/(sin x log (1+ x/4)) in [-1, 1] - {0}, thenforremovable discontinuity of f at x=0, f(0)=

The points A, B and C with position vectors 3hat(i)-yhat(j)+2hat(k),5hat(i)-hat(j)+hat(k)and3xhat(i)+3hat(j)-hat(k) are collinear, then the values of x and y respectively are

Let ABC to be an acute triangle with BC=a,CA =b and AB=c,where a ne b ne c. From any point 'p' inside Delta ABClet B,E,F denot foot of perpendiculars form 'p' noto the sides, BC, CA and AB, respectively. Now, answer the following equations. If DeltaDEF is equilateral, then 'P'

int(x-11C_(1)x^(2)+11C_(2)x^(3)-11C_(3)x^(4)+....-11C_(11)x^(12))dx=....

If sin^(-1)x+sin^(-1)y=(pi)/(2), then x^(2) is equal to

If 7c -2b=15 and 3b-6c=2, what is the value of b +c ?

If A=[[0,5],[1,0]] , B= [[1,1],[1,0]] ,then find AB .

Each question given below has four possible answers out of which only one is correct. Choose the correct one. veca.vecbxxveca =

If the joining A(1,3,4)and B is dividedby the point (-2,3,5) in the ratio1:3 then, B is

int (dx)/(sqrt(1-x))=..

Integrate the function in Exercise. (xe^(4))/((1+x)^(2))

Evaluate the following integrals int(tan^2theta+1)/(tan^2theta-1)d theta

Which of the following bonds forms via 2-lobe interaction ?

Find the value of int (x^2 dx)/(1+x^6)

Find the value of int (dx)/sqrt(25-9x^2)

An ellipse passing through (4sqrt2, 2sqrt6) has foci at (-4,0) and (4,0). Then, its eccentricity is

A tangent to the parabola y^2 + 4bx = 0 meets the parabola y^2 = 4ax in P and Q. The locus of the middle points of PQ is:

The points - 6a + 3b + 2c, 3a - 2b + 4c, 5a + 7b + 3c, - 13a + 17b - c are

{{:(21x-6y=54),(9+y=3.5x):} The system of equations shown above has how many solutions ?

Using integration find the area of region bounded by the triangle whose vertices are (-1,0), (1, 3) and (3, 2).

If f(x) = (sin [x])/([x]), [x] ne 0 = 0, [x] = 0, where [x] denotes the greatest integer less than or equal to x, than lim_(x rarr 0) f(x) equals :

If the normals at three points A, B, C on the rectangular hyperbola xy = c^(2) intersect at a . Point D on the hyperbola, then

Fill in the blanks in each of the following, using the answers given against each of them : The lines 2x - 3y + 1 = 0 and 3x+ ky - 1 = 0 are perpendicular to each other if k = _____ .

Show that the four common tangents can be drawn for the circles given by x^(2) + y^(2) -14 x + 6y + 33 = 0"(1)" and x^(2) + y^(2) + 30x-2y +1 =0"_(2)" and find the internal and external centres of similitude.