Information
AI Chat

Previous question (Maths)

Practices question for better improvements for mathematics

Course

Mathematics class 11 (041)

102 Documents

Students shared 102 documents in this course

University

University of Kerala

Academic year: 2016/2017

Uploaded by:

Anil Raju

University of Kerala

0followers

21Uploads

0upvotes

Recommended for you

Comments

Please sign in or register to post comments.

Preview text

1018 (a) The function f:N’N by f(x) = 2x is (1) one-one and onto (a) (i1) one-one but not onto (b) Find gof(x), if f(x) = & and g(x) = x, (b) (111) notone-one and notonto (c) (iv) onto, but not one-one (a) Ifxy <l, tan-'x + tan-'y =

(6) Prove that 2 tan- +tan-'=tan:

Let * be an operation such that a * b= LCM of a and b defined on the set A={1,2, 3,4, 5}. Is * a binaryoperation ? Justify your answer. @)

Write A=

Find the inverse 3 (a) The value of (i) 1 (iii) x+ X- 31 then BA= |is 17 2 (ii) (Score : (i) x

(Scores:

(iv) 0 as the sum of a symmetric and a

skew-symmetric matrix.

(Scores;

(Score: (Scores: (Score (Scores (Scores (Scor

6. 1018

(b) Using

properties of

determinants, showthat

(a) Find all points of discontinuity

of f, where f is defined by

f(x) =

(b) Ife-=,then prove that

=(

2x +3, xs

|2r-3, x>

dy

(1)

dx

(ii) 1

log x

(a) The slope of the tangent to the curve given by

[log ex]?

x=l-cos , y = 0- sin at =-is

(i) f(x) =+x

OR

(iii) f(x)=-3x +

(ii) -

(iv) Not defined

(b) Find the intervals in which the function f(x) =

x-4x+ 6 is strictly decreasing.

(c) Use differential to

approximate y36.

(c) Find the minimum and

maximum value, if any, of the function f(x) = (2x- 1

+3.

4 (Scores:

(ii) f(o) =

log x

(b) Find the equation of the tangent to

the

curvey=3x at (1, 1).

(Scores:

(a) Which of the

following functions has neither local

maxima nor local minima?

(iv) f() =

+|x|

(Scores:

(Score

(Scores

(Scor

(Score

(Scor (c

(a) The area bounded by the curve y =f), above the x-axis, between x=a and=b () (iü)
(a) y dy () fla) (b) Find the area of the circle +y'=4 using integration.

####### d²ydy2+y=

(ii)+dy y= 12. (a) y=acos x+ b sin xis the solution of the differential equation. y=0 when x =1. (i)

f

(ii) 13. Find the shortest distance between the lines (iv) 2r +3y + 4z = 1 (ii) 6x+ 4y+ 3z= 1

1?o

B(-2, -3, 5) and C(5, 3, -3). f(b) ydr (iv) (") -y= (b) Find the soluion of the differential equation x+ 2y = x (r 0) given that

d²y

8 dy dy Equation of the plane with intercepts 2. 3, 4 on the x, y and z axis respectively is (Score : 1 (ii) 2x+3y + 4z = 12 (Scores :$ (iv) 6x + 4y + 3z= 12 (Score : (Scores : (Scores:

####### aEind the Cartesian equation of the plane

passing through the points A(2, 5, - (Scor (Score

####### 15. Consider the following L.P.

Maximize Z=3x + 2y Subject to the constraints x+2ys 10 3x + y s 15 x, y 20 (a) Draw its feasible region. (b) Find the corner points of the feasible region. (b) (c) Find the maximum value of Z. independent events is 16. (a) If P(A) = 0, P(B) = 0, then the value of P(AUB) where A and B are i) 0. (ii) 0. (ii) 0. (iv) 0. OR (Scores : Apair of dice is thrown 4 times. If getting a doublet is considered as a success, (Scores : (1) find the probability of getting a doublet. (2) hence, find the probability of two successes. (Score: 1 A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be diamonds. Find the probability of the lost card being a diamond. (Score : 1 (Scores : (Score : (Scores :

Was this document helpful?