14949 + Interview Questions in Maths in Class 11

1.	Find the value of 'a' so that Find the values of a and b so that the function defined byf (x) = {{:(ax^(2) + 9x - 5 " if " x lt 1 ), (b "if " x = 1 ),((x + 3) (2x -9) " if " x gt 1 ):} is continuous on R .
Answer» ANSWER :`-1//2`

Discussion

2.	Match the following from List-I to List-II
Answer» C,E,B,a c,e,a,b a,c,d,e a,e,d,c Answer :B

Discussion

3.	A Kabaddi coach has has 14 players ready to play . How many different teams of 7 players could the coach put on the court ?
Answer» ANSWER :` = 13 xx 11 xx 2 xx 3 xx 4 = 3432 ` .

Discussion

4.	If baraxxbarr=barb+lamdabara,bara.barr=3, where bara=2~i+barj-bark,barb=-bari-2barj+bark then lamda=
Answer» `(-5)/6` `1/6` `(-1)/6` `5/6` ANSWER :D

Discussion

5.	Find the value of the following : (i^(592)+i^(590)+i^(588)+i^(586)+i^(584))/(i^(582)+i^(580)+i^(578)+i^(574))
Answer» ANSWER :`-(1)/(2)`

Discussion

6.	Let f: N to Y be a function defined as f(x) = 4x+3 where Y={y in N: y=4x+3 for some x in N}. Then inverse of f is:
Answer» `G(y)=(3y+4)/(3)` `g(y)=4 + (y+3)/(4)` `g(y)= (y+3)/(4)` `g(y)=(y-3)/(4)` ANSWER :C

Discussion

7.	The distance between the circumcentre and the orthocentre of the triangle formed by (1,2,3),(3,-1,5),(4,0,-3) is
Answer» ANSWER :`=(1)/(2)SQRT(66)`

Discussion

8.	A vector vec(OP) makes 60^(@) and 45^(@) with the positive direction of x and y axes respectively. Then the angle between vec(OP) and z axis is
Answer» `45^(@)` `60^(@)` `-90^(@)` `30^(@)` ANSWER :B

Discussion

9.	Find the calculation whether the points (13, 8), (26, -4) lie in the same, adjacent, or opposite angles formed by the straight lines 5x+6y-112=0, and 10x+11y-217=0.
Answer» ANSWER :OPPOSITE

Discussion

10.	The probability that the home team will win an upcoming football game is 0.77, the probability that it will tie the game is 0.08, and the probability that it will lose the game is ......
Answer» ANSWER :A

Discussion

11.	If y=((ax+b))/((x^2+c)), and (2xy'+y)y''=k(xy''+y'')y'' , where a,b,c are constants and y'denote differentiation w.r.t.x then the value of k is
Answer» ANSWER :3

Discussion

12.	A particle is moving along a striaght line so that t its displacement s from a fixed point on the line is given s=a sin (bt+c) where a,b,c are cosntants. If v and f are the velocity and the acceleration of the particle respectively at time t, prove that (i)v^(2)-fsis a constant (ii) (df)/(ds) is a constant and (ii) s, (df)/(ds)=f.
Answer» ANSWER :`-B^(2)s `

Discussion

13.	A source of light is hung h mts. Directly above a straight horizontal path on which a boy a mts. In height is walking. If a boy walks at a rate of b mts/sec. from the light then the rate at which his shadow increasese.
Answer» `(AB)/(h-a)mt//sec` `(ab)/(h+a)mt//sec` `(ab)/(2(h-a))mt//sec` `(ab)/(2(h+a))mt//sec` ANSWER :A

Discussion

14.	Find equation of the circle passes from the points (1, 2) , (3,-4) and (5, -6).
Answer» Answer :`x^(2) + y^(2) - 2x + 2Y - 23 = 0`

Discussion

15.	If the angles of a triangles are30 ^(@), 45 ^(@)and the included side issqrt 3+ 1thenthe remainingsides are
Answer» ` 2, SQRT2` ` 2,2,sqrt2` ` sqrt2,4` ` 2,4sqrt3` ANSWER :A

Discussion

16.	Find the point on y-axis which is at a distance of 3 units from the point (2,3,-1).
Answer» ANSWER :(0,5,0)or(0,1,0)

Discussion

17.	Lt_(x to 0)(log_(sinx)sin2x)=
Answer» ANSWER :1

Discussion

18.	Use the graph to find the limits (if it exists).If the limit does not exist ,explain why? lim_(xrarr0)secx
Answer» ANSWER :1

Discussion

19.	If 2x+y-4=0 is bisector of the angle between the lines a(x-1)+b(y-2)=0,c(x-1)+d(y-2)=0, then the other bisector is
Answer» x-2y+1=0 x-2y-3=0 x-2y+3=0 x-2y-5=0 Answer :B

Discussion

20.	If A and B are two sets such that A ⊂ B, then what is A ∪ B ?
Answer» ANSWER :B

Discussion

21.	(d ^(2) x)/(dy ^(2))equals :
Answer» `1/(((DY)/(DX))^2)` `(((d^2y)/(dx)))/(((dy)/(dx))^2)` `((d^2y)/(dx^2))` `(-((d^2y)/(dx)))/(((dy)/(dx))^2)` ANSWER :D

Discussion

22.	"cosec" 15^(@) + sec 15^(@) =
Answer» `2sqrt(2)` `SQRT(6)` `2sqrt(6)` `sqrt(6) + sqrt(2)` ANSWER :C

Discussion

23.	A bag contains 9 discs of which 4 are red, 3 are blue and 2 are yellow. The disce are similar in shape and size. A disc is drawn at rendom from the bag. Calculate the probability that it will be (i) red, (ii) yellow, (iii) blue, (iv) not blue, (v) either red or blue.
Answer» ANSWER :` = 0.11`

Discussion

24.	Assertion (A) : Absolute minimum of f(x)= overset(x) underset(0) int (t^(2)+2t+2) in [2,4] 32//3 Reason (R) : f(x) is incrasing in [a,b] and continuous rArr absolute minimum of f(x) in [a,b] is f(a)
Answer» Both A and R are TRUE and R is the CORRECT explanation of A Both A and R are true and R is not the correct explanation of A A is TRU, R is false A is false, R is true Answer :A

Discussion

25.	Vector equation of the plane through theorigin and perpendicular to the vector 2bari-3barj-5bark is
Answer» `BARR.(2bari-3barj-5bark)=0` `barr.(bari-2barj+2bark)=0` `barr.(3bari-2barj+5bark)=0` `barr.(2bari-3barj-2bark)= 5sqrt2` ANSWER :A

Discussion

26.	If f : RtoRis defined by f (x) = {:{((x+2)/(x^(2)+3x+2), if x in R - { 1,-2}), ( -1, if x = -2) , ( 0 , ifx = -1 ) :}then f is continuouson the set
Answer» R ` R - (-2)` `R - (-1)` R -{ -1, -2} ANSWER :D

Discussion

27.	Simplify and express each of the following in the form (a + ib) : {:((i),(2 + sqrt(-3))^(2),(ii),(5-2i)^(2),(iii),(-3+5i)^(3)),((iv),(-2-(1)/(3)i)^(3),(v),(4-3i)^(-1),(vi),(-2+sqrt(-3))^(-1)),((vii),(2+i)^(-2),(viii),(1+2i)^(-3),(ix),(1+i)^(3)-(1-i)^(3)):}
Answer» Solution :`(iii) (-3+5i)^(3) = (5i-3)^(3) = (5i)^(3)-3^(3) - (3xx5ixx3)(5i-3)=(-125i-27+225+135i)=(198+10i)`. `(iv) (-2-(1)/(3)i)^(3)=(-1)^(3)(2+(1)/(3)i)^(3) = -{8+(1)/(27)i^(3)+2i(2+(!)/(3)i)}`. `(v) (4-3i)^(-1)=(1)/((4-3i))XX((4+3i))/((4+3i))=((4+3i))/(25)`. `(VI) (-2+sqrt(3)i)^(-1) = (1)/((-2+sqrt(3)i))xx((-2-sqrt(3)i))/((-2+sqrt(3)i))`. `(vii)(2+i)^(-2)=(1)/((2+i)^(2))=(1)/((4+i^(2)+4i))=(1)/((3+4i))xx((3-4i))/((3-4i))`. `(VIII) (1 + 2i)^(-3)=(1)/((1+2i)^(3))=(1)/({1+8i^(3)+6i(1+2i)})=(1)/((-11+2i))xx((-11+2i))/((-11+2i))`.

Discussion

28.	A five digit number is formed by the digits 1, 2, 3, 4, 5 without repetition. Find the probability that the number is divisible by 4.
Answer» ANSWER :`(1)/(5)`

Discussion

29.	Evaluate the following limits in lim_(zrarr1)(z^((1)/(3))-1)/(z^((1)/(6))-1)
Answer» ANSWER :2

Discussion

30.	A purchasing agent obtained samples of 60 watt bulbs from a standard company. He had the samples tested in his own laboratory for length of life with the following results: Calculate the standard deviation for these samples.
Answer» ANSWER :236.27 HOURS

Discussion

31.	Find the range of the function f(x)=(1)/(1-3cos x)
Answer» ANSWER :`(-OO, -(1)/(2)]UU[(1)/(2), oo)`.

Discussion

32.	If "tan"(x-y)/(2),tanz,"tan"(x+y)/(2) are in G.P., then show that cosx=cosy*cos2z.
Answer» ANSWER :1,7,13 or 25,7,-11

Discussion

33.	Two oppositive verticies of rectangle are (-3,1) and (1,1). Also equation of one side is along the line 4x+7y + 5=0. Find equation of other sides of rectangle.
Answer» Answer :`7x - 4y- 3 = 0, 7x - 4X + 25 = 0, 4x + 7Y - 11 = 0`

Discussion

34.	Evaluateint (x^(2) + 5x+ 3)/(x^(2) + 3x + 2) dx
Answer» ANSWER :`I = x + log \|x^(2) + 3x + 2\| - 2 log \|(x + 1)/(x + 2)\| + C `

Discussion

35.	Find the values of theta lying between 0^(@) and 360^(@) when sec theta=-2
Answer» ANSWER :`120^(@),240^(@)`

Discussion

36.	Find an A.P whose sum of n terms is equal to three times the square of n.
Answer» ANSWER :3, 9 ,15

Discussion

37.	If the line joining the points (2, 3, 4), (0,1,2) is perpendicular to the line joining the points (x, 0, 4), (7, -4,3) then x =
Answer» 1 2 3 4 Answer :B

Discussion

38.	Evaluate the following limits: Lim_( x to pi/2 )(1-sin x)/((pi/2-x)^(2))
Answer» ANSWER :`1/2`

Discussion

39.	If A = {3, 6, 9, 12, 15, 18, 21}, B = { 4, 8, 12, 16, 20 }, C = { 2, 4, 6, 8, 10, 12, 14, 16 }, D = {5, 10, 15, 20 }, find B – A
Answer» ANSWER :`={4, 8, 16, 20}`

Discussion

40.	(1+ x)^(n) -nx -1 is divisible by (where n in N )
Answer» `2X` `X^(2)` `2x^3` all of these Answer :B

Discussion

41.	Find m so that the roots of the equation (x^(2)-bx)/(ax-c)=(m-1)/(m+1) may be equal in magnitude and opposite in sign.
Answer» ANSWER :`(a-b)/(a+b)`

Discussion

42.	Out of 18 points in a plane, no three are in the same line except five points which are collinear. Find the number of lines that can be formed joining the point.
Answer» ANSWER :`= 153 - 10 + 1 = 144`

Discussion

43.	Find the vertex, focus, and directrix of the following parabolas: x^(2)+8x+12y+4=0
Answer» Answer :Latus RECTUM `12`,vertex `(-4,-2)`, AXIS `x+4=0`, DIRECTRIX `y-4`.

Discussion

44.	The periodof sin^4 x + cos^(4) xis
Answer» `(pi)/(2)` `pi` `(3PI)/(2)` `2PI` ANSWER :1

Discussion

45.	g(x+y)= g (x) + g(x) +3xy (x+y)AA, y in R and g'(0) = -4 The value of g'(1) is
Answer» 1 0 -1 none of these Answer :C

Discussion

46.	In a triangle ABC, (s-a)/11=(s-b)/12=(s-c)/13, then tan^2 (A//2)=
Answer» ` (143)/( 432)` ` ( 13)/(33)` ` ( 11)/( 39 ) ` ` ( 12)/(37 )` ANSWER :B

Discussion

47.	The sum of two numbers is 6. The minimum of theof their reciprocals is
Answer» `(3)/(4)` `(6)/(5)` `(2)/(3)` `(2)/(5)` ANSWER :C

Discussion

48.	The distance from the orgin to the image of (1,1) with respect to the line x+y+5=0 is
Answer» `7sqrt(2)` `3sqrt(2)` `6sqrt(2)` `4sqrt(2)` ANSWER :C

Discussion

49.	A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual instalments of Rs 500 plus 12% interest on the unpaid amount. How much will the tractor cost him?
Answer» ANSWER :RS. 16680

Discussion

50.	Match each of the set on the left in the roster form with the same set on the right described in set-builder form: (i) {1, 2, 3, 6} (a) {x : x is a prime number and a divisor of 6} (ii) {2, 3} (b) {x : x is an odd natural number less than 10} (iii) {M,A,T,H,E,I,C,S} (c) {x : x is natural number and divisor of 6} (iv) {1, 3, 5, 7, 9} (d) {x : x is a letter of the word MATHEMATICS}.
Answer» ANSWER :C, a, d, B

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Find the value of 'a' so that Find the values of a and b so that the function defined byf (x) = {{:(ax^(2) + 9x - 5 " if " x lt 1 ), (b "if " x = 1 ),((x + 3) (2x -9) " if " x gt 1 ):} is continuous on R .

Match the following from List-I to List-II

A Kabaddi coach has has 14 players ready to play . How many different teams of 7 players could the coach put on the court ?

If baraxxbarr=barb+lamdabara,bara.barr=3, where bara=2~i+barj-bark,barb=-bari-2barj+bark then lamda=

Find the value of the following : (i^(592)+i^(590)+i^(588)+i^(586)+i^(584))/(i^(582)+i^(580)+i^(578)+i^(574))

Let f: N to Y be a function defined as f(x) = 4x+3 where Y={y in N: y=4x+3 for some x in N}. Then inverse of f is:

The distance between the circumcentre and the orthocentre of the triangle formed by (1,2,3),(3,-1,5),(4,0,-3) is

A vector vec(OP) makes 60^(@) and 45^(@) with the positive direction of x and y axes respectively. Then the angle between vec(OP) and z axis is

Find the calculation whether the points (13, 8), (26, -4) lie in the same, adjacent, or opposite angles formed by the straight lines 5x+6y-112=0, and 10x+11y-217=0.

The probability that the home team will win an upcoming football game is 0.77, the probability that it will tie the game is 0.08, and the probability that it will lose the game is ......

If y=((ax+b))/((x^2+c)), and (2xy'+y)y''=k(xy''+y'')y'' , where a,b,c are constants and y'denote differentiation w.r.t.x then the value of k is

A source of light is hung h mts. Directly above a straight horizontal path on which a boy a mts. In height is walking. If a boy walks at a rate of b mts/sec. from the light then the rate at which his shadow increasese.

Find equation of the circle passes from the points (1, 2) , (3,-4) and (5, -6).

If the angles of a triangles are30 ^(@), 45 ^(@)and the included side issqrt 3+ 1thenthe remainingsides are

Find the point on y-axis which is at a distance of 3 units from the point (2,3,-1).

Lt_(x to 0)(log_(sinx)sin2x)=

Use the graph to find the limits (if it exists).If the limit does not exist ,explain why? lim_(xrarr0)secx

If 2x+y-4=0 is bisector of the angle between the lines a(x-1)+b(y-2)=0,c(x-1)+d(y-2)=0, then the other bisector is

If A and B are two sets such that A ⊂ B, then what is A ∪ B ?

(d ^(2) x)/(dy ^(2))equals :

"cosec" 15^(@) + sec 15^(@) =

A bag contains 9 discs of which 4 are red, 3 are blue and 2 are yellow. The disce are similar in shape and size. A disc is drawn at rendom from the bag. Calculate the probability that it will be (i) red, (ii) yellow, (iii) blue, (iv) not blue, (v) either red or blue.

Assertion (A) : Absolute minimum of f(x)= overset(x) underset(0) int (t^(2)+2t+2) in [2,4] 32//3 Reason (R) : f(x) is incrasing in [a,b] and continuous rArr absolute minimum of f(x) in [a,b] is f(a)

Vector equation of the plane through theorigin and perpendicular to the vector 2bari-3barj-5bark is

If f : RtoRis defined by f (x) = {:{((x+2)/(x^(2)+3x+2), if x in R - { 1,-2}), ( -1, if x = -2) , ( 0 , ifx = -1 ) :}then f is continuouson the set

Simplify and express each of the following in the form (a + ib) : {:((i),(2 + sqrt(-3))^(2),(ii),(5-2i)^(2),(iii),(-3+5i)^(3)),((iv),(-2-(1)/(3)i)^(3),(v),(4-3i)^(-1),(vi),(-2+sqrt(-3))^(-1)),((vii),(2+i)^(-2),(viii),(1+2i)^(-3),(ix),(1+i)^(3)-(1-i)^(3)):}

A five digit number is formed by the digits 1, 2, 3, 4, 5 without repetition. Find the probability that the number is divisible by 4.

Evaluate the following limits in lim_(zrarr1)(z^((1)/(3))-1)/(z^((1)/(6))-1)

A purchasing agent obtained samples of 60 watt bulbs from a standard company. He had the samples tested in his own laboratory for length of life with the following results: Calculate the standard deviation for these samples.

Find the range of the function f(x)=(1)/(1-3cos x)

If "tan"(x-y)/(2),tanz,"tan"(x+y)/(2) are in G.P., then show that cosx=cosy*cos2z.

Two oppositive verticies of rectangle are (-3,1) and (1,1). Also equation of one side is along the line 4x+7y + 5=0. Find equation of other sides of rectangle.

Evaluateint (x^(2) + 5x+ 3)/(x^(2) + 3x + 2) dx

Find the values of theta lying between 0^(@) and 360^(@) when sec theta=-2

Find an A.P whose sum of n terms is equal to three times the square of n.

If the line joining the points (2, 3, 4), (0,1,2) is perpendicular to the line joining the points (x, 0, 4), (7, -4,3) then x =

Evaluate the following limits: Lim_( x to pi/2 )(1-sin x)/((pi/2-x)^(2))

If A = {3, 6, 9, 12, 15, 18, 21}, B = { 4, 8, 12, 16, 20 }, C = { 2, 4, 6, 8, 10, 12, 14, 16 }, D = {5, 10, 15, 20 }, find B – A

(1+ x)^(n) -nx -1 is divisible by (where n in N )

Find m so that the roots of the equation (x^(2)-bx)/(ax-c)=(m-1)/(m+1) may be equal in magnitude and opposite in sign.

Out of 18 points in a plane, no three are in the same line except five points which are collinear. Find the number of lines that can be formed joining the point.

Find the vertex, focus, and directrix of the following parabolas: x^(2)+8x+12y+4=0

The periodof sin^4 x + cos^(4) xis

g(x+y)= g (x) + g(x) +3xy (x+y)AA, y in R and g'(0) = -4 The value of g'(1) is

In a triangle ABC, (s-a)/11=(s-b)/12=(s-c)/13, then tan^2 (A//2)=

The sum of two numbers is 6. The minimum of theof their reciprocals is

The distance from the orgin to the image of (1,1) with respect to the line x+y+5=0 is

A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual instalments of Rs 500 plus 12% interest on the unpaid amount. How much will the tractor cost him?