Q If tan-1 x−3x−4 + tan -1 x+3

x+4 = π4 ,then find the value of x.(4)

2017

Q Consider f:R−[−43 ]→R-[ 4

3 ] given by f(x)= 4+33x+4.

Show that f is bijective. Find the inverse of f and hence find f-1(0) and x such that f-1 (x)=2. ORLet A = Q x Q and let * be a binary operation on A defined by (a,b) * (c,d) = (ac,b+ad) for(a,b), (c,d) є A. Determine, whether * is commutative and associative. Then, with respect to * on A.

(i) Find the identity element in A.(ii) Find the invertible elements of A.

(6)

2017

Q Solve for x: tan−1(x-1) + tan−1x + tan−1(x+1) = tan−13x.

OR Prove that tan-1 { 6 x−8 x3

1−12x2 } – tan-1 { 4 x1−12x2 }

= tan-1 2x; |2 x| < 1√3 . (4)

2016

Q Let A = R × R and * be the binary operation on A defined by (a, b) * (c, d) = (a + c, b + d)Show that * is commutative and associative. Find the identity element for

2016

* ON A. Also find inverse of every element (a,b). (6)

Q Evaluate: tan{2tan-1(1/5)+π/4}. (4)

2015

Q Determine whether the relation R defined on the set R of all real numbers as R = {(a,b) : a, b R and a – b + S, where S is the set of all irrational numbers}, is reflexive, symmetric and transitive.

ORLet A = R x R and * be the binary operation on A defined by (a, b) * (c, d) = (a + c, b + d). Prove that * is commutative and associative. Find the identity element for * on A. Also write inverse element of the element (3, -5) in A.(6)

2015

Q If R={(x,y): x+2y=8} is a relation on N, write the range of R.(1)

2014

Q If the function f: R→R be given by f(x)=x2+2 and g:R →R be given by g(x)=x

x−1, x ≠ 1, find fog and gof and hence find fog(2) and gof(-3).(4)

2014

Q If tan-1x + tan-1y=π4 , xy < 1, then write the 2014

value of x+y+xy. (1)

Q Prove that

Tan-1¿-1/2COS-1X,, (4)

2014

Q 1.Write the value of tan−1[2sin (2 cos−1 √32 )].(1) 2013

Q 2.Write the principal value of tan−1 (√3 )−cot−1 (−√3 ). (1)

2013

Q 3.Show that : tan ( 12

sin−1 34 )=4−√7

3 .OR

Solve the following Equation:cos ( tan−1 x )=sin (cot−1 3

4 )(4)

2013

Q 4.Consider F : R+→ [4,∞) given by f(x)= x2 +4. Show that f is invertible with the inverse f-1 of f given by f-1(y)= √ y−4, where R+ is the set of all non-negetive real numbers. (4)

2013

Q If for any 2x2 square matrix A, A(adj A)= 2017

[8 00 8], then write the value of |A| (1)

Q If A is a skew-symmetric matrix of order 3, than prove that det A=0.(2)

2017

Q Using properties of determinants, prove that [a

2+2a 2a+1 12a+1 a+2 1

3 3 1]= (a-1)3

ORFind matrix A such that [ 2 −1

1 0−3 4 ]A=[−1 −8

1 −29 22 ] (4)

2017

Q If A = [2 −3 53 2 −41 1 −2], find A=-1. Hence using A-1

solve he system of equations 2x-3y+5z=11, 3x+2y-4z=-5, x+y-2z=-3.(6)

2017

Q If A= [ cosα sinα−sinα cosα ], find α satisfying 0 < α < π2

when A + AT = √2I2 ;where AT is transpose of A. (1)

2016

Q If A is a 3×3 matrix and |3 A| = k|A|, then write the value of k. (1)

2016

Q For what values of k , the system of linear equations X + y + z = 22x + y -z = 3

2016

3x + 2y + kz = 4has a unique solution ? (1)

Q A typist charges Rs.145 for typing 10 English and 3 Hindi pages, while charges for typing 3 English and 10 Hindi pages are Rs. 180. Using matrices , find the charges of typing one English and one Hindi page separately. However typist charges only Rs. 2 per page from a poor student Shyam for 5 Hindi pages. How much less was charged from this poor boy? Which values are reflected in this problem? (4)

2016

Q Using properties of determinants . Show that

|(x+ y)2 zx zyzx (z+ y)2 xyzy xy (z+x)2| =2xyz(x+y+z)3.

ORIF A=[1 0 2

0 2 12 0 3] and A3-6A2+7A+KI3=0 Find

K. (6)

2016

Q If A= [ cosθ sinθ−sin θ cosθ] , then for any natural

number n, find the value of Det (An ¿.(1)2015

Q There are two families A and B. There are 4 men, 6 women and 2 children in family

2015

A, and 2 men, 2 women and 4 children in family B. the recommended daily amount of calories is 2400 for men, 1900 for women and 1800 for children and 45 grams of protein for men, 55 grams for women and 33 grams for children. Represent the above information using matrices. Using matrix multiplication, calculate the total requirement of calories and protein for each of the 2 families. What awareness can you create among people about the balanced diet from this question? (4)

Q Using properties of determinants, prove that |a

32ab32bc32c| = 2(a – b) (b - c) (c – a) (a + b

+ c) (4)

2015

Q Using elementary row operations (transformations), find the inverse of the following matrix:

(01 21 2 33 1 0)OR

If A =[ 0 6 7−6 0 87−8 0] , B = [0 11

10 212 0], C = [ 2

−23 ] , then

calculate AC, BC and (A+B) C. Also verify that (A+B) C= AC + BC. (4)

2015

Q If A is a square matrix such that A2=A, then write the value of 7A-(I+A)3, where I is the identity matrix.(1)

2014

Q If [ x− y z2x− y w ]= [−1 4

0 5] , find the value of x+y.(1) 2014Q If |3 x 7

−2 4|=|8 76 4| , find the value of x.(1) 2014

Q Using the properties of determinants, prove that:

| x+ y x x5 x+4 y 4 x 2 x

10 x+8 y 8x 3 x|=x3 (4)

2014

Q Two schools A and B want to award their selected students on the values of sincerity, truthfulness and helpfulness. The school A wants to award Rs. x each, Rs. y each and Rs. z each for the three respective values to 3,2 and 1 students respectively with a total award money of Rs. 1,600. School B wants to spend Rs. 2,300 to award its 4, 1 and 3 students on the respective values(by giving the same award money to the three values as before). If the total amount of award for one prize on each value is Rs. 900, using matrices, find the award money for each value. Apart from these three values, suggest one more value which should be considered for award.(6)

2014

Q5.If Aij is the co-factor of the element aij of the determinant |2 −3 5

6 0 41 5 −7|, then write the

value of a32.A32.(1)

2013

Q6.For what value of x , is the matrix A=

[ 0 1 −2−1 0 3x −3 0 ] a skew-symmetric matrix? (1)

2013

Q7.If a matrix A=( 2 −2−2 2 ) and A2=pA , then write

the value of p. (1)2013

Q8.Using properties of determinants , prove the following:| x x+ y x+2 y

x+2 y x x+ yx+ y x+2 y x |=9 y2 ( x+ y ). (4)

2013

Q. Find: ∫ sin2 X−cos2X

sin X cosXdx (1)

2017

Q. Determine the value of ‘k’ for which the following function s continuous at x=3: f(x)¿ (x+3)2−36

x−3 ,x≠3 k ,x=3 (1)

2017

Q. Find: ∫ dx

5−8 x−x2 (2)2017

Q. Find the value of c in Rolle’s theorem for the function f(x)=x3-3x in [-√3 , 0]. (2)

2017

Q. Show that the function f(x)=x3-3x 2+6x-100 2017

is increasing on R.(2)Q. The length x, of a rectangle is decreasing at

the rate of 5 cm/minute and the width y, is increasing at the rate of 4 cm/ minute. When x=8 cm and y=6 cm, find he rate of change of the area of the rectangle.(2)

2017

Q. Evaluate: ∫

0

π x tan xsex x+ tan xdx

OR ∫

1

4

{[ x−1]+[ x−2 ]+[ x−4 ]}dx(4)

2017

Q. If x y+ yx=ab, then find dydx . OR If e y (x+1 )=1,then show that d

2 ydx2 = ( dydx )2.(4)

2017

Q. Find: ∫ sinѲdѲ

( 4+cos2Ѳ ) (2−sin2Ѳ ) (4)2017

Q Find the general solution of the differential equation y dx-(x+2y2)dy=0.(4)

2017

Q Find the particular solution of the differential equation (x-y) dydx=(x+2y), given that y=0 when x=1.(6)

2017

Q Using the method of integration, find the area of the triangle ABC, coordinates of whose vertices are A(4,1), B(6,6) and C(8,4). ORFind the area enclosed between the parabola 4y=3x2 and the straight line 3x-2y+12=0.(6)

2017

Q AB is the diameter of a circle and C is an point on the circle. Show that the area of

2017

triangle ABC is maximum, when it is an isosceles triangle.(6)

Q. Find the value of a and b,if the following

function f(x) = {sin ( a+1 ) x+2 sin x

x,if x<0

2, if x=0√1+bx−1

x , if x>0

is

continuous at x=0. (4)

2016

Q If x cos(a+y)= cosy then prove that dydx = cos2(a+ y)

sin a

hence show that sinad2 yd x2 + sin2(a+y)dydx =

0. OR Find dydx if y = sin-1 [6 x−4√1−4 x2

5 ] (4)

2016

Q. Find the equation of tangents to the curve y=x3 + 2x – 4, which are perpendicular to line x + 14y + 3 = 0. (4)

2016

Q Find : ∫ (2x−5)e2 x

(2 x−3)3 dx

OR

Find : ∫ x2+x+1(x2+1 )(x+2)

dx (4)

2016

Q Evaluate : ∫−2

2 x2

1+5x dx (4) 2016

Q Find : ∫(x+3)√3−4 x−x2 dx (4) 2016Q Find the particular solution of differential equation : dy

dx = - x+ y cosx

1+sinx

given that y = 1 when x = 0. (4)

2016

Q Find the particular solution of the differential equation

2y ex / y dx +(y-2x ex / y)dy = 02016

given that x=0 when y=1. (4)Q

Prove that   is an increasing

function of θ in . (6) orShow that the semi-vertical angle of the cone of the maximum volume and of given slant height is cos-1 ( 1

√3) (6)

2016

Q Using the method of integration , find the area of the triangular region whose vertices are (2,-2) , (4,3) , and (1,2). (6)

2016

Q Find the sum of the order and the degree of the following differential equation.

y= x(y’)3+y’’.(1)

2015

Q Find the solution of the following differential equation.

x √(1+ y2 )dx+ y √(1+x2 )dy=0 (1)

2015

Q Discuss the continuity and differentiability of the function f(x) = | x | + | x-1 | in the interval (-1, 2). (4)

2015

Q If x = a (cos 2t + 2t sin 2t) and y = a (sin 2t – 2t cos 2t), then find y”.(4)

2015

Q If (ax + b) e YX =x, then show that

X3(d2 y

d x2)=(xdydx

− y)2(4)2015

Q Evaluate: 2015

∫ sinx−xcosxx(x+sinx) dx (4) OR

Evaluate:∫ x3

( x−1 )(x2+1)dx(4)

Q Evaluate:

∫0

π4

cos2 x dx1+3sin2 x

(4)2015

Q Evaluate:∫0

π4

( sinx+cosx3+sin 2 x

)dx(4) 2015

Q Tangent to the circle x2+ y2=4 at any point on it the first quadrant makes intercepts OA and OB on x and y axes respectively, O being the centre of the circle. Find the minimum value of (OA + OB).(6)

2015

Q If the area bounded by the parabola y2 = 16ax and the lines y = 4mx is a2 / 12 sq. units, then using integration, find the value of m.(6)

2015

Q Show that the differential equation (x – y) dydx = x + 2y is homogeneous and solve it also.

ORFind the differential equation of the family of curves (x - h)2 + (y – k)2 = r2, where h and k are arbitrary constants. (6)

2015

Q If f(x)= ∫0

x

t sin t dt, then write the value of f’(x).(1)

2014

Q Evaluate : 2014

∫2

4 xx2+1

dx(1)

Q Find the value of dydx

at θ=π4

, if x=aeθ(sinθ - cosθ) and y=aeθ(sinθ+cosθ)(4)

2014

Q If y=peax+qebx , show that

d2 yd x2

_ (a+b)dydx

+ aby=0 (4)

2014

Q Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is 4 r

3 . Also show that the maximum volume of the cone is 8

27 of the volume of the sphere.(6)

2014

Q using integration, find the area of the region bounded by the triangle whose vertices are (-1,2), (1,5) and (3,4).(6)

2014

Q For what value of x, the function f(x) =(x(x-2) )2 ,is increasing function.(4)

2014

Q Find the equation of tangent and normal to the curve x

2

a2 −y2

b2 =1atthe point (√2a,b). (4)2014

Q Find the particular solution of the differential equation:dydx=1+x+ y+xy , givent hat y=0w henx=1.(4)

2014

Q

(4)

2014

Q

(4)

2014

Q Solve the diffential eq.:

(4)

2014

Q Write the D.Eq. representing the family of curves y=mx. Where m is the arbitrary constant (1)

2013

Q 9. The money to be spent for the welfare of the employees of a firm is proportional to the rate of change of its total revenue (marginal revenue).If the total revenue received from the sale of x units of a product is given by R(x)=3x2+36x+5, find the marginal revenue, when x=5, and write which value does the question indicate. (1)

2013

Q 10. Differentiate the following with respect to x : sin−1( 2x+ 1 .3x

1+(36 )x )(4)

2013

Q 11. Evaluate : ∫ cos2 x−cos2αcos x−cos α

dx OR Evaluate : ∫ x+2

√ x2+2 x+3dx. (4)

2013

Q 12. Find the value of k, for which

f ( x )={√1+kx−√1−kxx

,if−1≤x<0

2x+1x−1

,if 0≤ x<1 is continuous at x=0.

OR

2013

If x=a cos3θ and y=a sin3θ , then find the value of d

2 ydx2 at θ=π

6 .(4)

Q Evaluate: ∫ 1x (x3+8 )

dx(4) 2013Q 13. Evaluate:∫

0

π x sin x1+cos2 x

dx.(4) 2013

Q 14. Find area of the greatest rectangle that can be inscribed in an ellipse x

2

a2 + y2

b2 =1.OR

Find the equations of the tangents to the curve 3 x2− y2=8 which passes through the point (4/3, 0). (6)

2013

Q 15. Find the area of the region {( x , y ): y2≤6 ax∧x2+ y2≤16 a2} using the method of integration. (6)

2013

Q 16. Show that the D.Eq. [ xsin2( yx )− y ]dx+ xdy=0 is homogeneous. Find the particular solution of this D.Eq, given that y=π/4 when x=1. (6)

2013

Q Find the distance between the planes 2x-y+2z=5 and 5x-2.5y+5z=20. (1)

2017

Q The x-coordinate of the point on the line joining the points P(2, 2, 1) and Q(5, 1, -2) is 4. Find its z-coordinate.(2)

2017

Q Show that the points A, B, C with position 2017

vectors 2i− j+ k , i−3 j−5 k and 3i−4 j−4 k respectively, are the vertices of a right-angled triangle. Hence find the area of the triangle.(4)

Q Fin the value of x such that the points A(3,2,1), B(4,x,5), C(4,2,-2) and D(6,5,-1) are coplanar. (4)

2017

Q Find the coordinates of the point where the lie through the points (3,-4,-5) and (2,-3,1), crosses the plane determined by the points (1,2,3), (4,2,-3) and (0,4,3). ORA variable planes which remains at a constant distance 3p from the origin cuts the coordinate axes at A,B,C. Show that the locus of the centroid of triangle ABC is 1x2 + 1

y2 + 1z2 =

1p2. (6)

2017

Q Write the sum of intercepts cut off by the plane r. (2i + j - k ) – 5 = 0 on the three axes. (1)

2016

Q Find λ and µ if (i + 3 j + 9k ) × ( 3 I−λ J+ µK ) = 0 . (1)

2016

Q If vectors a =4 i - j+k,b =2 i -2 j+k and c =3i + j

,then find a unit vector parallel to vector a +b . (1)

2016

Q Find the coordinates of the foots of perpendicular drawn from the 2016

point A(-1,8,4) to the line joining the points B(0,-1,3) and C(2,-3,-1) . Hence find the image of then points A in the line BC. (4)

Q Show that the four points A(4,5,1) , B(0,-1,-1) , C(3,9,4) , D(-4,4,4) are coplanar. (4)

2016

Q Find the equation of the plane passing through the line of intersection of the planesr(i - 2 J + 3k) -4 = 0 and r(−2 i + J + k) + 5 = 0. and and whose intercepts on x-axis is equal to y- axis. (6)

2016

Q In a triangle OAC, if B is the mid-point of side AC and OA = a , OB = b , then what is OC ? (1)

2015

Q Find a vector of magnitude √171 which is perpendicular to both of the vectors a=i+2 j−3 k and b=3 i− j+2 k . (1)

2015

Q Find the angle between the lines 2x = 3y = - z and 6x = -y = -4z.(1)

2015

Q Let a=i+4 j+2 k ,b=3 i−2 j+7 k and c=2 i− j+4 k . Find a vector d which is perpendicular to both a∧b∧c .d=27. (4)

2015

Q Find the shortest distance between the following lines:

r=( i+2 j+3 k )+(2 i+3 j+4 k )

r=(2 i+4 j+5 k )+μ ( 4 i+6 j+8 k )

OR

2015

Find the equation of the plane passing through the lines of intersection of the planes 2x + y – z = 3 and 5x -3y +4z +9 =0 and is parallel to the linesx−1

2= y−3

4=5−z

−5 (4)Q Find the equation of a plane passing

through the point P(6, 5, 9) and parallel to the plane determined by the points A(3, -1, 2), B(5, 2, 4) and C(-1, -1, 6). Also find the distance of this plane from the point A.(6)

2015

Q IF a=(2i+j+3k) andb =-i+2j+k andc =3i+j+2k ,Find a . (b X c ) .(1)

2014

Q If the Cartesian equation of a line are line3−x

5= y+4

7=2 z−6

4 , write vector equation for the line.(1)

2014

Q Find the value of p when the vectors 3 i +2 j +9k and i -2p j+3k are parallel.(1)

2014

Q Find the equation of the plane through the line of intersection of the planes x+y+z=1 and 2x+3y+4z=5 which is perpendicular to the plane x-y+z=0. Also find the distance of the plane obtained above, from the origin. ORFind the distance of the point (2,12,5) from the point of intersection of the line r

2014

= 2i - 4 j + 2k + λ(3i + 4 j + 2k) and the plane r. (i−2 j+k ¿=0(6)

Q Show that the four points A,B,C and D with position vectors =(4 i+5 j+ k ,− j−k ,3 i+ 9 j+4 k

and 4(-i+ j+k) respectively are coplanar.OR The scalar product of the vector a = i + j + k with a unit vector along the sum of vectors b = 2i +4 j-5 k and c = λ i +2 j +3 k is equal to one. Find the value of λ and hence find the unit vector along b+ c .

2014

Q A line passes through (2,-1,3) and is perpendicular to the lines r=(i+ j− k)+λ(2 i−2 j+k

) and r=(2i− j−3 k)+µ(i+2 j+2k). Obtain its equation in vector and Cartesian form. (4)

2014

Q17. Find the length of the perpendicular drawn from the origin to the plane 2x-3y+6z+21=0. (1)

2013

Q18. Find |x|, if for a unit vector a, ( x−a ) . ( x+a )=15. (1)

2013

Q19. A and B are two points with p.v’s 2 a−3 b

and 6 b−a respectively. Write the p.v of a point P which divides the line segment AB

2013

internally in the ratio 1:2. (1)Q20. Show that the lines r=3 i+2 j−4 k+λ(i+2 j+2 k ) and

r=5 i−2 j+µ(3 i+2 j+6 k ) are intersecting. Hence find their point of intersection.

ORFind the vector equation of the plane passing through the point (2 , 1 , -1)and (-1 , 3 , 4) and perpendicular to the plane x-2y+4z=10. (4)

2013

Q21. Find the equation of the plane passing through the line of intersection of the planes r . ( i+3 j )−6=0∧r . ( 3 i− j−4 k )=0 whose perpendicular distance from origin .s unity.(6)

2013

Q. Two tailors, A and B, earn RS.300 and RS.400 per day respectively. A can stitch 6 shirts and 4 pairs of trousers while B can stitch 10 shirts and 4 pairs of trousers per day. To find how many days should each of them work and if It is desire to produce atleast 60 shirts and 32 pairs of trousers at minimum labour cost, formulate this as an LPP.(2)

2017

Q. Solve the following linear programming problem graphically: Maximize Z=34x+45y under the following constraints

2017

x+y≤300 2x+3y≤70 x≥0,y≥0 (4)

Q. A retired person wants to invest an amount of Rs. 50000. His

broker recommends investing in two type of bonds ‘A’ and

‘B’ yielding 10% and 9% return respectively on the invested

amount. He decides to invest at least Rs.20000 in bond ‘A’

and at least Rs.10000 in bond ‘B’ . He also wants to invest at

least as much in bond ‘A’ as in bond ‘B’ . Solve this linear

programming problem graphically to maximise his returns.

(6)

2016

Q. Solve the following linear programming problem graphically.Minimise z = 3x + 5ySubject to the constraints x + 2y 10

x + y 63x + y 8 x, y 0(6)

2015

Q. A manufacturing company makes two types of teaching aids A and B of Mathematics for class 12th . each type of A requires 9 labour hours of fabricating and 1labour hour for finishing. Each type of B requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating

2014

and finishing, the maximum labour hours for available per week are 180 and 30 respectively. The company makes a profit of Rs. 80 on each piece of type A and Rs. 120 on each piece of type B. how many pieces of type A and type B should be manufactured per week to get a maximum profit? Make it as an LLP and solve graphically. What is the maximum profit per week?(6)

Q. 22. A manufacturer considers that men and women workers are equally efficient and so pays them at the same rate. He has 30 and 17 units of workers (male and female) and capital respectively , which he uses to produce two types of goods of A and B. to produce one unit of A, 2workers and 3units of capital are required ,while 3 workers and 1 unit of capital are is required to produce one unit of B. If A and B are priced at Rs. 100 and Rs. 120 per unit respectively, how should he use his resources to maximize the total revenue. Form the above as an LPP and solve it graphically. Do you agree with this view of the manufacturer that men and women workers are equally efficient and so should be paid at the same rate. (6)

2013

Q. A die, whose faces are marked 1, 2, 3 in red and 4, 5, 6 in green, is tossed. Let A be the event “number obtained is

2017

even” and B be the event “number obtained is red”. Find if A and B are independent events.(2)

Q. There are 4 cards numbered 1,3,5 and 7, one number on one card. Two cards are drawn at random without replacement. Let X denote the sum of the numbers on the two drawn cards. Find the man and variance of X.(4)

2017

Q.. Of the students in a school, it is known that 30% have 100% attendance and 70% are irregular. Previous year results report 70% of all students who have 100% attendance attain A grade and 10% irregular students attain A grade in their annual examination. At the end of the year, one student is chosen at random from the school and he was found to have an A grade. What is the probability that the student has 100% attendance? Is regularity required only in school? Justify your answer.(4)

2017

Q A bag X contains 4 white balls and 2 black balls , while another bag Y contains 3 white balls and 3 black balls. Two balls are drawn ( without replacement ) at random from one of the bags and were found to be one white and one black . Find the probability that the balls were drawn

2016

from bag Y. OR

A and B throw a pair of dice alternately , till one of them gets a total of 10 and wins the game . Find their respectively probabilities of winnings, if A starts first. (4)

Q. Three numbers are selected at random ( without replacement) from first six positive integers. Let X denote the largest of the three numbers obtained . Find the probability distribution of X . Also, find the mean and variance of the distribution. (6)

2016

Q A man takes a step forward with probability 0.4 and backward with probability 0.6. Find the probability that at the end of 5 steps, he is one step away from the starting point.

ORSuppose a girl throws a die. If she gets a 1 or 2, she tosses a coin three times and notes the number of ‘tails’. If she gets 3, 4, 5 or 6, she tosses a coin once and notes whether a ‘head’ or ‘tail’ is obtained. If she obtained exactly one ‘tail’, what is the probability that she

2015

threw 3, 4, 5 or 6 with the die?(4)Q. An urn contains 5 red and 2 black balls.

Two balls are randomly drawn, without replacement. Let X represent the number of black balls drawn. What are the possible values of X? Is X a random variable? If yes, find the mean and variance of X.(6)

2015

Q An experiment succeeds thrice as often as it fails. Find the probability that in the next five trials, there will be at least 3 succeeds(4)

2014

Q There are three coins. One is two-headed coin(having head on the both faces), another is a biased coin that comes up heads 75% of the times and third is also a biased coin that comes up tails 40% of the times. One of the three coins is chosen at random and tossed, and it shows head. What is the probability that it was the two-headed coin? ORTwo numbers are selected at random(without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find the probability distribution of the random variable X, and hence find the mean of the distribution.(6)

2014

Q23. The probabilities of two students A

and B coming to school in time are 3/7 and 5/7 respectively. Assuming that the events , ‘A come in time ‘ and ‘B come in time ‘ are independent , find the probability of only one of them coming to the school in time. Write at least one advantage of coming to the school in time.(4)

2013

Q 24. In a hockey match , both teams A and B scored same number of goals up to the end of the game, so to decide the winner , the referee asked both the captains to throw a die alternately and decided that the team, whose captain gets a six first, will be declared the winner. If the captain of team A was asked to start, find their respective probabilities of winning the match and state whether the decision of the referee was fair or not. (6)

2013