14949 + Interview Questions in Maths in Class 11 Page 51 InterviewSolution

2501.	If z_(1) and z_(2) are two fixed points in the Argand plane, then find the locus of a point z in each of the following \|z-z_(1)\|= k\|z-z_(2)\|, k in R^(+), k ne 1
Answer» <P> ANSWER :P LIES on a CIRCLE

Discussion

2502.	If z_(1) and z_(2) are two fixed points in the Argand plane, then find the locus of a point z in each of the following \|z-z_(1)\|-\|z-z_(2)\|= constant (ne \|z_(1)-z_(2)\|)
Answer» <P> Answer :P lies on a HYPERBOLA having its foci at A and B RESPECTIVELY

Discussion

2503.	If z_(1) and z_(2) are two fixed points in the Argand plane, then find the locus of a point z in each of the following \|z-z_(1)\| + \|z-z_(2)\|= constant ne (\|z_(1)-z_(2)\|)
Answer» <P> ANSWER :P lies on an ELLIPSE having its foci A and B

Discussion

2504.	If z_(1) and z_(2) are two fixed points in the Argand plane, then find the locus of a point z in each of the following \|z-z_(1)\| - \|z-z_(2)\|= \|z_(1)-z_(2)\|
Answer» <P> ANSWER :P LIES on the line joining A and B but does not lie between A and B

Discussion

2505.	Check whether the statement is true or not:" 8 is aprime number."
Answer» ANSWER :F

Discussion

2506.	Prove that (1)/(cos 290^(@))+(1)/(sqrt3 sin 250^(@) )=(4)/(sqrt3)
Answer» `2SQRT3` `4sqrt3` `2/sqrt3` `4/sqrt3` ANSWER :D

Discussion

2507.	If the line joining A (1,3, 4 )and B is divided by the point (-2, 3,5 )in the ratio 1:3, then B is
Answer» (-11, 3, 8) (-11, 3, -8) (-8, 12, 20) (13, 6, -13) ANSWER :a

Discussion

2508.	Let the function defined in column 1 have domain (0,pi//2) the
Answer» ANSWER :A-r,B-p,C-q,D-s

Discussion

2509.	For the cubic function f(x)=2x^(3)+9x^(2)+12x+1 , which one of the following statement/statements hold good ?
Answer» f(X) is non - monotonic f(x) INCREASES in `(-oo,-2)uu(-1,oo)` and decreases in `(-2,-1)` `f:RtoR` is bijective . inflection point OCCURS at `x=-3//2` ANSWER :A::B::D

Discussion

2510.	For three vectors barμ, barv, bar(omega) , which of the following is not equal to any of the remaining three
Answer» `barmu.(barvxxbaromega)` `(barvxxbaromega).barmu` `BARV.(barmuxxbaromega)` `(barmuxxbarv).baromega` ANSWER :C

Discussion

2511.	One end point of the focal chord of the parabola is (at_(1)^(2),2at_(1)) then find its other end point. Also prove that its lenghts is (t_(1) + (l)/(t_(1))^(2))
Answer» ANSWER :`((a)/(t_(1)^(2)), (-2A)/(t_(1)))`

Discussion

2512.	Odds9 to 5 againsta personwho is 40 yearsoldlivingtill heis 70and 4 to 3againstanotherpersonnow50till he will beliving80. Probabilitythat oneof them will be alive next30 years .
Answer» `(59)/(91)` `(44)/(91)` `(51)/(91)` `(32)/(91)` ANSWER :B

Discussion

2513.	If the parabola y^(2)=4ax passes through the point (2,-3) then find the co-ordinates of the focus and the length of latus rectum.
Answer» Answer :FOCUS `((9)/(8),0)`, LATUS RECTUM `=(9)/(2)`

Discussion

2514.	Find the equation of th parabola with latus rectum joining points (4,6) and (4,-2).
Answer» ANSWER :`(y-2)^(2)-8X`

Discussion

2515.	If a family of straight line (x+y)+lambda(2x-y+1)=0. Find the equation of the staright line belonging to this family that is farthest from (1,-3).
Answer» 3x-3y+2=0 6x+15y-7=0 5x+2y+1=0 6x-15y+7=0 Answer :C

Discussion

2516.	If f(x)=3x-5, then f^(-1)(x)
Answer» is GIVEN by `(1)/((3x-5))` is given by `((x+5))/(3)` does not exist because f is not one-one does not exist because f is not onto Answer :B

Discussion

2517.	Assetion (A) : If x= sin(alpha- beta) sin (gamma- delta), y= sin(beta- gamma) sin (alpha- delta) z=sin (gamma- alpha). Sin (beta- delta) then x+y+z=0 Reason (R) : 2 sin A sin B=cos (A-B)+cos (A+B)
Answer» A is TRUE, R is true and R is correct explanation of A A is true, R is true and R is not correct explanation of A A is true, R is FALSE A is false, R is true Answer :C

Discussion

2518.	Find the probability of the occurrence of the digit 3 when an unbiased die is thrown .
Answer» ANSWER :`=(1)/(6)`.

Discussion

2519.	The points on the hyperbola x^(2)-y^(2)=2 closest the point (0,1) are
Answer» `(+-(3)/(2),(1)/(2))` `((1)/(2),+-(3)/(2))` `((1)/(2),(1)/(2))` `(+-(3)/(4),+-(3)/(2))` ANSWER :A

Discussion

2520.	An integer is chosen at random from the first twohundred positive integers . What is the probability that the integer chosen is divisible by 6 or 8 ?
Answer» ANSWER :`=(1)/(4)`.

Discussion

2521.	Find the distance between the mid point of the line segment bar(AB) and the point (3,-1,2) where A = (6,3,-4), B = (-2,-1,2).
Answer» ANSWER :`SQRT(14)`

Discussion

2522.	Iff R to Ris defined by f (x) = {{:(( 2 sin x - sin 2x)/(2x cos x ) " if " x ne 0) , ( alpha"for " x =0 ):} then the value ofalpha so that f is continuous at 0 is
Answer» 2 1 -1 0 Answer :D

Discussion

2523.	Find the product [{:(0,c,-b),(-c,0,a),(n,-a,0):}][{:(a^2,ab,ac),(ab,b^2,bc),(ac,bc,c^2):}]
Answer» ANSWER :(3,-2)

Discussion

2524.	tan 9^(@) - tan 27^(@) - tan 63^(@) + tan 81^(@) =
Answer» 2 3 4 none of these ANSWER :C

Discussion

2525.	A man buys a motorcycle in Rs 60,000. If its price decreases every year 10%, then what will be its price at the end of fourth year?
Answer» ANSWER :RS 39,366

Discussion

2526.	If A and B are two matrices such that A+B and AB are both defined, then:
Answer» A and B are two MATRICES not NECESSARILY of order same A and B are SQUARE matrices of same order Number of column of A is EQUAL to the number of rows of B A=B Answer :B

Discussion

2527.	Out of 100 students, 15 passed in English, 12 passed in Mathematics, 7 in Mathematics and Science, 4 in English and Science, 4 in all the three. Find how many passed. In Mathematics and Science but not in English.
Answer» ANSWER :`= 3`

Discussion

2528.	Out of 100 students, 15 passed in English, 12 passed in Mathematics, 7 in Mathematics and Science, 4 in English and Science, 4 in all the three. Find how many passed. In more than one subject only.
Answer» ANSWER :`= 9`

Discussion

2529.	Out of 100 students, 15 passed in English, 12 passed in Mathematics, 7 in Mathematics and Science, 4 in English and Science, 4 in all the three. Find how many passed. In Mathematics only.
Answer» ANSWER :`= 3`

Discussion

2530.	Solve the following equations : 27x^(2)-10x+1=0
Answer» ANSWER :`(5)/(27)+-(SQRT(2))/(27)i`

Discussion

2531.	If A =(1,3,-5), B=(3,5,-3) then the vector equation of the plane passing through the midpoint of AB and perpendicular to AB is
Answer» `BARR.(bari+barj+bark)=1` `barr.(bari+barj+bark)=2` `barr.(bari+barj+bark)=3` `barr.(bari+barj+bark)=4` Answer :B

Discussion

2532.	If for positive integers r gt 1, n gt 2, the coefficients of the (3r)th and (r+2)th powers of x in the expansion of (1+x)^(2n) are equal, then prove that n=2r+1.
Answer» Answer :`r=(N)/(2)`, provided `n` is an EVEN integer `( gt2)`, OTHERWISE `r` has no value.

Discussion

2533.	If e^(g(y)) - e^(-g(y)) = 2 f(x) then (dy)/(dx) =
Answer» `(f^1(X))/(G^1(y)) sqrt(1 + f(x)^2))` `(f^1(x))/(g^1(y)) 1/(sqrt(1 + (f(x))^2))` `(f^1(x))/(g(y)) 1/(sqrt(1 + (f(x))^2))` `2(f^1(x))/(g^1(y)) sqrt(1 + (f(x))^2)` Answer :B

Discussion

2534.	If the vector bar(a)=2bar(i)+3bar(j)+6bar(k) and bar(b) are collinear and abs(bar(b))=21" then "bar(b)=
Answer» `pm(2BAR(i)+3BAR(j)+6bar(k))` `PM3(2bar(i)+3bar(j)+6bar(k))` `BAR(i)+bar(j)+bar(k)` `pm21(2bar(i)+3bar(j)+6bar(k))` Answer :B

Discussion

2535.	Find the angle of rotation to eliminate xy term in the equation x^(2)+2sqrt3xy-y^(2)=18.
Answer» ANSWER :`PI/6`

Discussion

2536.	If cosec theta = (x^(2) -y^(2))/(x^(2) + y^(2)) where x, y are two unequal non-zero real numbers then prove that theta has no real value.
Answer» ANSWER :HENCE, there is no REAL VALUE of `THETA`.

Discussion

2537.	Solve sqrt(3) cos theta + sin theta = sqrt(2)
Answer» Answer :`2npi PM(pi)/(4) + (pi)/(6) ; N in Z`

Discussion

2538.	If the side of anequilateraltriangle is2sqrt3 then each of exradiiis
Answer» ` 1` ` 2` ` 3` ` 4` Answer :C

Discussion

2539.	Given thatf(x)gtg(x) for all real x, and f(0)=g(0). Thenf(x)ltg(x) for all x belong to
Answer» `(0,OO)` `(-oo,0)` `(-oo,oo)` `(-oo,1)` ANSWER :B

Discussion

2540.	Find the mean and standard deviation using shout-cut method.
Answer» SOLUTION : LET assumed mean `A=64` `:.` Mean `=A+(sumf_(i)d_(i))/(sumf_(i))=64+0/100` `=64` STANDARD deviation `=SQRT((sumf_(i)d_(i)^(2))/N-((sumf_(i)d_(i))/N)^(2))` `=sqrt(286/100-0)=sqrt(286/100)` `=sqrt(2.86)=1.69`

Discussion

2541.	Each sides of a square is of lemgth 4 units. The centre of the square is (3,7) and one of its diagonals is parallel to y=x. Find the co-ordinates of its vertices.
Answer» ANSWER :`(1,5),(1,9),(5,9),(5,5)`

Discussion

2542.	A candidate is required to answer 7. questions out of 12 questions which are divided into two groups each containing 6 questions. He is not permitted to attempt more than 5 questions fromeach group. The number of ways in which he can choose the 7 questions is
Answer» (a)780 (B)640 (c)820 (d)none of these Answer :A

Discussion

2543.	sin^(-1)(3/5)+sin^(-1)(5/13)=
Answer» `SIN(-1)(63/65)` `sin^(-1)(56/65)` `sin^(-1)(56/63)` `sin^(-1)(16/63)` ANSWER :B

Discussion

2544.	cosec x cot x
Answer» ANSWER :`-COSEC^(3)X-cosecxcot^(2)x`

Discussion

2545.	If x = a sec^2 theta, y = aTan^3 theta then (d^3y)/(dx^3) =
Answer» `(-3)/(8a^2)COT^3theta` `(3)/(8a^2)cot^3theta` `3 sec^2 theta tan theta` `3/(4A)cot theta` ANSWER :A

Discussion

2546.	Find the mean and standard deviation using short-cut method.
Answer» ANSWER :64, 1.69

Discussion

2547.	Find f[(-3)^-] and f[(-3)^+] if{f(x) = \|x+3\|/(x+3),xne0f(0)=0,x-0
Answer» ANSWER :`-1 and 1`

Discussion

2548.	Assume that the cost of the petrol burnt (per hour) in driving a motor boat varies as the cube of its velocity. Show that the most economical speed of the boat when going against a current of 6km per hour is 9km. Per hour.
Answer» ANSWER :SPEED of the BOAT = 9 km/h

Discussion

2549.	Let f(x)=x^(3)-x^(2)+12x-3 then at x=2 , f(x) has
Answer» MAXIMUM a minimum both a maximum ANDA minimum neither a maximum nor a minimum Answer :D

Discussion

2550.	Two circlesx^(2) + y^(2) = 25and 2x^(2) + 2y^(2) - 2x + y = 0
Answer» TOUCH externally touch INTERNALLY are ORTHOGONAL are CONCENTRIC SOLUTION :N/A

Discussion

Explore topic-wise InterviewSolutions in .

If z_(1) and z_(2) are two fixed points in the Argand plane, then find the locus of a point z in each of the following |z-z_(1)|= k|z-z_(2)|, k in R^(+), k ne 1

If z_(1) and z_(2) are two fixed points in the Argand plane, then find the locus of a point z in each of the following |z-z_(1)|-|z-z_(2)|= constant (ne |z_(1)-z_(2)|)

If z_(1) and z_(2) are two fixed points in the Argand plane, then find the locus of a point z in each of the following |z-z_(1)| + |z-z_(2)|= constant ne (|z_(1)-z_(2)|)

If z_(1) and z_(2) are two fixed points in the Argand plane, then find the locus of a point z in each of the following |z-z_(1)| - |z-z_(2)|= |z_(1)-z_(2)|

Check whether the statement is true or not:" 8 is aprime number."

Prove that (1)/(cos 290^(@))+(1)/(sqrt3 sin 250^(@) )=(4)/(sqrt3)

If the line joining A (1,3, 4 )and B is divided by the point (-2, 3,5 )in the ratio 1:3, then B is

Let the function defined in column 1 have domain (0,pi//2) the

For the cubic function f(x)=2x^(3)+9x^(2)+12x+1 , which one of the following statement/statements hold good ?

For three vectors barμ, barv, bar(omega) , which of the following is not equal to any of the remaining three

One end point of the focal chord of the parabola is (at_(1)^(2),2at_(1)) then find its other end point. Also prove that its lenghts is (t_(1) + (l)/(t_(1))^(2))

Odds9 to 5 againsta personwho is 40 yearsoldlivingtill heis 70and 4 to 3againstanotherpersonnow50till he will beliving80. Probabilitythat oneof them will be alive next30 years .

If the parabola y^(2)=4ax passes through the point (2,-3) then find the co-ordinates of the focus and the length of latus rectum.

Find the equation of th parabola with latus rectum joining points (4,6) and (4,-2).

If a family of straight line (x+y)+lambda(2x-y+1)=0. Find the equation of the staright line belonging to this family that is farthest from (1,-3).

If f(x)=3x-5, then f^(-1)(x)

Assetion (A) : If x= sin(alpha- beta) sin (gamma- delta), y= sin(beta- gamma) sin (alpha- delta) z=sin (gamma- alpha). Sin (beta- delta) then x+y+z=0 Reason (R) : 2 sin A sin B=cos (A-B)+cos (A+B)

Find the probability of the occurrence of the digit 3 when an unbiased die is thrown .

The points on the hyperbola x^(2)-y^(2)=2 closest the point (0,1) are

An integer is chosen at random from the first twohundred positive integers . What is the probability that the integer chosen is divisible by 6 or 8 ?

Find the distance between the mid point of the line segment bar(AB) and the point (3,-1,2) where A = (6,3,-4), B = (-2,-1,2).

Iff R to Ris defined by f (x) = {{:(( 2 sin x - sin 2x)/(2x cos x ) " if " x ne 0) , ( alpha"for " x =0 ):} then the value ofalpha so that f is continuous at 0 is

Find the product [{:(0,c,-b),(-c,0,a),(n,-a,0):}][{:(a^2,ab,ac),(ab,b^2,bc),(ac,bc,c^2):}]

tan 9^(@) - tan 27^(@) - tan 63^(@) + tan 81^(@) =

A man buys a motorcycle in Rs 60,000. If its price decreases every year 10%, then what will be its price at the end of fourth year?

If A and B are two matrices such that A+B and AB are both defined, then:

Out of 100 students, 15 passed in English, 12 passed in Mathematics, 7 in Mathematics and Science, 4 in English and Science, 4 in all the three. Find how many passed. In Mathematics and Science but not in English.

Out of 100 students, 15 passed in English, 12 passed in Mathematics, 7 in Mathematics and Science, 4 in English and Science, 4 in all the three. Find how many passed. In more than one subject only.

Out of 100 students, 15 passed in English, 12 passed in Mathematics, 7 in Mathematics and Science, 4 in English and Science, 4 in all the three. Find how many passed. In Mathematics only.

Solve the following equations : 27x^(2)-10x+1=0

If A =(1,3,-5), B=(3,5,-3) then the vector equation of the plane passing through the midpoint of AB and perpendicular to AB is

If for positive integers r gt 1, n gt 2, the coefficients of the (3r)th and (r+2)th powers of x in the expansion of (1+x)^(2n) are equal, then prove that n=2r+1.

If e^(g(y)) - e^(-g(y)) = 2 f(x) then (dy)/(dx) =

If the vector bar(a)=2bar(i)+3bar(j)+6bar(k) and bar(b) are collinear and abs(bar(b))=21" then "bar(b)=

Find the angle of rotation to eliminate xy term in the equation x^(2)+2sqrt3xy-y^(2)=18.

If cosec theta = (x^(2) -y^(2))/(x^(2) + y^(2)) where x, y are two unequal non-zero real numbers then prove that theta has no real value.

Solve sqrt(3) cos theta + sin theta = sqrt(2)

If the side of anequilateraltriangle is2sqrt3 then each of exradiiis

Given thatf(x)gtg(x) for all real x, and f(0)=g(0). Thenf(x)ltg(x) for all x belong to

Find the mean and standard deviation using shout-cut method.

Each sides of a square is of lemgth 4 units. The centre of the square is (3,7) and one of its diagonals is parallel to y=x. Find the co-ordinates of its vertices.

A candidate is required to answer 7. questions out of 12 questions which are divided into two groups each containing 6 questions. He is not permitted to attempt more than 5 questions fromeach group. The number of ways in which he can choose the 7 questions is

sin^(-1)(3/5)+sin^(-1)(5/13)=

cosec x cot x

If x = a sec^2 theta, y = aTan^3 theta then (d^3y)/(dx^3) =

Find the mean and standard deviation using short-cut method.

Find f[(-3)^-] and f[(-3)^+] if{f(x) = |x+3|/(x+3),xne0f(0)=0,x-0

Assume that the cost of the petrol burnt (per hour) in driving a motor boat varies as the cube of its velocity. Show that the most economical speed of the boat when going against a current of 6km per hour is 9km. Per hour.

Let f(x)=x^(3)-x^(2)+12x-3 then at x=2 , f(x) has

Two circlesx^(2) + y^(2) = 25and 2x^(2) + 2y^(2) - 2x + y = 0