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Plus Two Maths Previous Year Question Papers and Answers 2018
|Category||Plus Two Previous Year Question Papers|
Time : 2 1/2 Hours
Cool off time : 15 Minutes
Maximum : 80 Score
General Instructions to Candidates :
- There is a ‘Cool off time’ of 15 minutes in addition to the writing time.
- Use the ‘Cool off time’ to get familiar with questions and to plan your answers.
- Read questions carefully before you answering.
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- When you select a question, all the sub-questions must be answered from the same question itself.
- Calculations, figures and graphs should be shown in the answer sheet itself.
- Malayalam version of the questions is also provided.
- Give equations wherever necessary.
- Electronic devices except non programmable calculators are not allowed in the Examination Hall.
Questions 1 to 7 carry 3 scores each. Answer any Six questions. (6 × 3 = 18)
If f(x) = , x ≠ 1
a. Find fof (x)
b. Find the inverse of f.
Using elementary row operations, find the inverse of the matrix [ ]
a. f (x) is a strictly increasing function, if f’ (x) is _____
iv.None of these
b. Show that the function f given by f (x) = x3 – 3x2 + 4x, x ∈ R is strictly increasing.
Find the area of the region bounded by the Curve y2 = x, x-axis and the lines x=1 and x=4.
Find the general solution of the differential equation x + 2y = x2 log x
A manufacturer produces nuts and bolts. It takes 1 hour of work on Machine A and 3 hours on Machine B to produce a package of nuts. It take 3 hours on Machine A and 1 hour on Machine B to produce a package of bolts. He earns a profit of ₹ 17.50 per package on nuts and ₹ 7.00 per package on bolts. Formulate the above L.P.P., if the machines operates for at most 12 hours a day.
Questions 8 to 17 carry 4 scores each. Answer any eight.
Let A=N x N and ‘*’ be a binary operation on A defined by (a,b)*(c,d)=(a+c, b+d)
a. Find (1,2)*(2,3)
b. Prove that ‘*’ is commutative.
c. Prove that ‘*’ is associative.
a. Identify the function from the above graph.
i. tan-1 x
ii. sin-1 x
iii. cos-1 x
b. Find the domain and range of the fun-ction represented in above graph.
c. Prove that tan-1 +tan-1 =tan-1
a. Find the slope of the tangent to the curve y = (x-2)2 at x=1
b. Find a point at which the tangent to the curve y = (x-2)2 is parallel to the chord joining the points A(2,0) and B(4, 4).
c. Find the equation of the tangent to the above curve and parallel to the line AB.
Consider the following figure :
a. The degree of the differential equation
b. Find the general solution of the differential equation sec2 x tan y dx + sec2 y tan x dy = 0
a. Find the equation of a plane which makes x, y, z intercepts respectively as 1, 2, 3.
b. Find the equation of a plane passing through the point (1,2,3) which is parallel to above plane
Solve the L.P.P. given below graphically :
Questions from 18 to 24 carry 6 scores each. Answer any five. (5 × 6 = 30)
a. Prove that the function defined by f (x) = cos (x2) is a continuous function
Evaluate the following :
a. Find the angle between the lines
b. Find the shortest distance between the pair of lines
a. The probability distribution of a random variable is given by P(x). What is ∑ P(x)?
b. The following is a probability distribution function of a random variable.
i. Find k
ii. Find P(x>3)
iii. Find p(-3<x<4)
iv. Find p(x<-3)
b. f(x) = x3-3x2+4x
f(x) is strictly increasing for all values of x at which
= 3(x-1) 2 + 1 > 0 for all x ∈ R
∴ f(x) is strictly increasing on R.
i. Let x = no. of packets of nuts
y = no. of packets of bolts
ii. LPP is maximise, z = 17.5x + 7y
subject to x + 3y < 12, 3x + y < 12 x > 0, y > 0
(4, 0),(3,3), (0, 4), (0,0) are the comers among these profit is maximum at (3, 3). Maximum profit = 17.5 x 3+7 x 3 = 73.5
a. (a,b) * (c,d) = (a+c, b+d)
(1,2) * (2,3) = (1+2, 2+3) = (3,5)
b. (a,b) * (c,d) = (a+c, b+d)
(c,d) * (a,b) = (c+a, d+b) = (a+c, b+d)
(a,b) * (c,d) = (c,d) * (a,b)
* is commutative
c. Let (a,b), (c,d), (e,f) ∈ A
(a,b) * [ (c,d) * (e,f)]
= (a,b)*[(c+ d), (d + f)]
= (a+c+e, b+d+f)
[(a,b)*(c,d)*(e,f) = (a+c, b+d)*(e,f) = (a+c+e. b+d+f)
i.e (a,b) * [(c,d)*(e,f)] = [(a,b) * (c,d)]*(e,f)
.’. * is associative
The given eqn are
x2 + y2 = 50 _______
y = x _______
(1) ⇒ x2+x2 = 50
2x2 = 50
x2 = 25, x=5
x lies on first quadrient so x= 5, y = 5 The point p (5,5).
a. + + = 1
+ + = 1
6x + 3y + 2z = 6
b. The normal vector for the plane is
(6.3.2) . The general equation of a plane is
n. (x-x0, y-y0, z-z0) = 0
(6.3.2) . (x-1, y-2, z-3)=0
6 ( x – 1 ) + 3 (y – 2) + 2 (z – 3) = 0
a. f(x) = cos(x2). The domain of F is R Let g(x) = cos x and h(x) = x2. Then g(x) and h(x) are continuous functions
(goh) (x) = g(h(x))
= g(x2) =cos(x2) = f(x)
Since g and h are continuous, goh is also continuous. Hence f is continous.
a. We know that derivative of mx is m. Thus, we make the substitution mx=t so that mdx=dt
a The probability distribution of a random variable is given by p(x).
then P(x) = 1 then ∑ P(x) = 1
ie, sum of all the probabilities in a prob¬ability distribution must be one.
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