Name of the Organisation : Higher Secondary Education, Government Of Kerala
Class : XII
Document Type : Sample Question Paper
Name of the Subject : Mathematics (Science)
Website : dhsekerala.gov.in
Download Sample Question Paper : https://www.pdfquestion.in/uploads/7693-MODELQP.pdf
Model Question Paper Mathematics (Science) :
HSE II
Time : 2. 30 Hours
Cool-off time: 15 Minutes
Related / Similar Question Paper :
DHSE Kerala HSE Accounting With AFS Question Paper
General Instruction to Candidates :
There is a ‘cool-off time’ of 15 minutes in addition to the writing time of 2. 30 Hrs.
You are not allowed to write your answer nor to discuss anything with others during the ‘cool off’ time.
Use the ‘cool-off’ time to get familiar with questions and to plan answers.
Read questions carefully before answering.
When you select a question, all the sub- questions must be answered from the same question itself.
I) i) Show that the relation R in the set A = {1.2.3.4.5.} given by R={(a,b) : |a-b| is even } is a equivalence relation
(2)ii) Let *be a binary operation on z defined by a* b = a+b-15 for a,b € z
a)show that * is commutative and associative
(3) b) Find the identity element
II) Match the following
1.Tan-1 x + Cot-1 x a) – p/3
2.Sin-1 (sin p/3) b) p/2
3.Cot-1(-x) c) p/3
4.Tan-1v3 – Sec-1 (-2) d) p – Cot-1 x
e) p + Cot-1 x
III) L et A =[ ]
1)Find A2
2)Find K ,so that A2 = KA+ 2 I
3)Find A-1 using elementary row transformations
IV ) 1) Find value of |sin – cos |
2) Using the properties of determinants prove that
V) Find the value of a and b such that the function defined by 5 if x = 2
f (x) = { ax+ b if 2<x<10 is a continuous function } 21 if x = 10
VII) 1) Prove that the curve x = y2 and xy= k cut at right angle if
2) Consider the function f(x) = x(x-2) x € [1,3] Verify Mean Value Theorem
Find the minimum value of the function using differentiation
VIII) Evaluate the following dx/(7-6x-x2)
Using integration find the area of the triangle whose vertices are (2,0) , (4,5) , (6,3) (6)
XI) Consider x2 = 2xy + y2
10Write order and degree of the above deferential equation
2)Solve the above differential equation
3)Find the particular solution of the differential equation
XIII 1) If is unit vector and ( – ) . ( + = 8 then find |x| (2)
2) Find the angle between the vectors – 2 +3 and 3 – 2 + 1
2) Find the equation of the plane passing thorugh the point (2,3,4) and parallel to the plane 5x – 6y +7z = 3
3) Find the distance of apoint (2,5,-3) from the plane
1)Find the direction ratio’s of the above line
2)Write the vector form of the lines
3)Find the valueof ‘P ’ if the above lines are at right angles
XV) Slove graphically
maximize z = 4x+y
subject to constraints x+y = 50
3x+y = 90
x = 0 , y = 0
2) A man is known to speak truth 3 out of 4 times. He throws a die and report that it is a six. Find the probability that it is actually a six.
1. a) If A and B are two disjoint events then P (A n B ) = ——-
b ) There are two urns ,the first urn contains 8green and 12 blue balls
1) The first urn [ 1+5 ] 2) The second urn
2. A card is drawn from a pack of cards. Find the probability of getting
a) a king b) a card of heart [ 2 ]
3 a ) I f E ( X ) = 10 then E(3X+ 2 ) =———–
b) Three unbiasded coins are tossed . The random variable X is defined as
the number of tails in the three tosses of a coin .Find :
1 ) Probability distribution of X . [ 1 + 4 ] 2 ) E ( X )
4 .a) Write any two properties of frequency distribution.
b) The probability distribution is X -2 -1 0 1 2
P(x) 1/12 1/3 2/12 1/4 2/12 Find 1) F (x ) 2) P ( X < 1 ) [ 2 + 3 ] 3) P ( -1<X < 2)
5 . A four digit number is formed of the integers 0,2,3 and 6 . In how many
1) it is divisible by 5. [ 4 ] 2 ) it is divisible by 2.
6. Find n such that 3 .n c = ( n-1 ) c
7 . Represent the following by o histogram :
8 . a) For a negatively skewed distribution :
[ 1) Mode < Median , 2) Mean > Median , 3)Mean < Mode , 4 ) None of these]
b) If the first four central moments of a distribution are 0 , 5 , -10 , and 30.
Find the measure of skewness and measure of kurtosis – [ 1 + 3 ]
9 . Calculate median for the following frequency distribution :
10 .a) Histogram can be used to estimate ———–
[ 1) mean , 2) median , 3 ) mode , 4 ) variance ]
b ) The average mark of 100 students was found to be 76.27. It was later
discovered that marks 87 and 54were mistakenly entered as 78 and 68.