MATHEMATICS SAMPLE PAPER FOR CBSE + 2 [ FOR FIRST SEMESTER EXAM]

MATHS TEST FOR CBSE + 2 There are three sections in this paper. Section A contains 10 questions carrying 3 marks each Section B contains 8 questions carrying 5 marks each Section C contains 5 question carrying 6 marks each ================================== Time : 2 h Maximum Marks : 100 TOPICS: RELATIONS FUNCTIONS BINARY OPERATIONS , INVERSE TRIGONOMETRY CONTINUITY DIFFERENTIATION APPLICATIONS OF DIFFERENTIATION [SECTION A ] [Each question in this section carries 3 marks ] [Question 1] Let L be the set of all lines in a plane and R be the relation in L defined as given below: R = { ( L1 , L2): L1 is perpendicular to L2 }. Explain briefly why the above relation is not transitive. [Question 2] Find the derivative of with respect to x , where a is a constant. [Question 3] The radius of a sphere (r) is increasing at the rate of 0.1 cm / s . How fast is its surface area (A) increasing when its radius is 5 cm ? [Question 4] Evaluate : [Question 5] Show that the modulus function , is continuous at x = 0 [Question 6] Given that y = - 7 + 9x2 – 2x3, find the range of values of x for which y is an increasing function. [Question 7] Differentiate with respect to x: ( log x ) cos x [Question 8 ] Given y = sin x + cos x , Find the maximum possible value of y in the given range. [Question 9] If f : R ( R be given by , Find f o f (x) [Question 10] Differentiate with respect to x : cos-1 ( e x) SECTION B [Each question in this section carries 5 marks ] [Question 11] Show that f : [ -1 , 1 ] ( R given by is a one-one function. Find the inverse of f [Question 12] Given and Find [Question 13] Find the equation of the normal to the curve , y = 2 sin 2 3x at [Question 14 ] Using differentials find the approximate value of [Question 15] Let A = N X N and * be the binary operation on A defined by ( a , b) * (c , d) = (a + c , b + d ) Prove that * is commutative and associative [Question 16 ] Discus the continuity of the function f where [Question 17 ] Differentiate with respect to x: [Question 18 ] Solve : tan-1 2x + tan-1 3x = [SECTION C] [Each question in this section carries 6 marks ] [Question 19] Given x y = e(x – y) , find dy/dx [Question 20 ] Sand is pouring from a pipe at the rate of 12 cm3/sec. The falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand-cone increasing when height is 4 cm ? [Question 21 ] Verify Rolle’s theorem for the function, f(x) = x (x - 3 )2 defined in the interval [ 0 , 3 ] [Question 22 ] If log y = tan-1 x , prove that : (1 + x2) y1 = y ( 1 + x2 ) y2 + ( 2x – 1 ) y1 = 0 [Question 23 ] Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius a is ======================================= ONLINE MATHS TUTOR ???????????? I OFFER EXCELLENT PRIVATE TUITION AT AFFORDABLE RATE http://www.youlikemathstutor@bloggerspot.com http://www.wiziq.com/ign Just 6 US dollars per hour payable through PAY PAL INSTANT HELP AT ANY TIME OF THE DAY !!!!!!!!! CONTACT ME AT : georgeignatius9 [Skype] gntsgeorge@yahoo.co.in [Y / Messenger] georgeignatiusxx@gmail.com [ G-mail]