MATHS FOR CLASS 12TH. Your shortcut to success. SCHOLAR'S ACADEMY
BOOK CO. ☎9868220237. 1. Sample Paper-1. Class XII. Maths. Time : 3 Hours.
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MATHS FOR CLASS 12TH
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Sample Paper -1 Class XII Maths www.yogenius.com
by Tarun Gaur
Sample Paper-1 Class XII Maths Time : 3 Hours Maximum marks 100 General Instruction: 1. All Question are compulsory 2. There are three - sections of 29 questions i.e, section A, section B, section C. 3. Section A contain 10 question of 1 mark each, Section B of 12 question of 4 marks each and section C contains 7 question of 6 marks each. 4. There is no overall choice. However internal choice has been provided in 04 question of 4 marks and 02 question of 6 marks. You have to attempt only are of the alternatives in all such question.
(√
-1
1 - cos x 1 + cos x
)
Section - A ; 0 ≤ x ≤ π.
Q1
Simplify, tan
Q2
Give an example of an equivalence relation.
Q3
Give an example of a matrix which is symmetric as well as skew symmetric.
Q4
If ∆ =
Q5
Give an example of a function which is continous every where but not differentiable at exactly two points.
Q6
Evaluate I = ∫ ex (log sin x + cot x). dx
Q7
Find the direction ratio of parallel vector and passing point of a line 3 - 5x = -2 + 7x = -1 - 9x 3 14 15
Q8
Q9
x+2 x+5
3 4
= 3, find values of ‘x’.
∧ ∧ ∧ ∧ ∧ ∧ → a = i - j + k and b = 2 i - j + 3 k If → → projection of vector→ a on b find → projection of vector b on→ a → ∧ ∧ ∧ If a = i + j + k , find its direction ration and direction cosines.
Q 10 Evaluate I =
∫
dx -x 2e + 1 Section - B
Q 11 (i) (ii) (iii)
Give examples of Binary operation which is Commutative but not associative. Associative but not commutative. Commutative as well as associative.
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(iv)
MATHS FOR CLASS 12TH
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Neither commutative nor associative.
Q 12 If tan-1
( xx --12 ) + tan (xx ++ 21) = 4π , then find the value of ‘x’. -1
OR Find the value of ‘x’ if sin-1 (1 - x) + 2 sin-1x = π . 2 Q 13 Prove that 2ab -2b 2 2 1- a +b 2a -2a 1- a2-b2
1+ a2-b2 2ba 2b
= (1+a2+b2)3
Q 14 Discuss the continuity of the function ‘f’ defined by : f (x) =
{ xx -+22 ifif xx ≤> 11}
Q 15 If y = Aemx + Benx, then prove that
d2y dy - (m + n) + mny = 0 2 dx dx
OR -1 d2y dy 2 acos x -ay=0 If y = e ; + ≤ x ≤ 1, show that (1 - x2) 2 - x dx dx y2 x2 Q 16 Find the equation of tangent and normal to the ellipse2 + 2 = 1 at point (x1 , y1). b a Q 17 Integrate I=
I=
∫√
∫
2x + 5 . dx 9x - 4x2
OR x2 + 1 . dx x2 - 5x + 6
Q 18 Solve the Differential equation. (xdy - ydx) y sin( y ) = (ydx + xdy) x cos ( y ) x x Q 19 Form the different equation of family of cirles in the second quadrant which touching the coordinate axes. ∧ ∧ ∧ ∧ ∧ Q 20 The scaler product of vector i + ∧j + k with a unit vector along the sum of vector 2 i + 4 j - 5 k ∧ ∧ ∧ and λ i + 2 j + 3 k in equal to one. Find the value of ‘λ’. Q 21 Find the vector equation of line passing through (1,2,3) and parallel to planes 2x + 3y – 5z = 7 and 3x -2y + 4z = 11. OR Find the equation of plane passing through the points P(1,-1,2) and Q(2,-2,2) and perpendicular to the plane 6x – 2y + 2z = 9. Q 22 A problem in mathematics in given to three students, whose chaces of solving it are 1 , 1 and 1 . 3 4 5 SCHOLAR’S ACADEMY BOOK CO.
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MATHS FOR CLASS 12TH
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What is the prob. that the problem is solved.
1 Q 23 Find the inverse of matrix -3 2 p If a a
b q b
Section C 3 -2 0 5 , if exists using elementary row transformation. 5 0
OR c p r q c = 0, find the value of p - a + q - b + r - c ; (p = a, q = b, r = c) r
Q 24 Show that the height of a cylinder of maximum volume that can be inscribed in a sphere of radius R is 2R . √3 Q 25 Evaluate dx sin3x + cos3x
∫
OR Integrate by limit as a sum 4 I= (2x2 + 5x + 9). dx
∫
2
Q 26 Using integration, find the area of traingle ABC, if A is (2,3), B is (4,7) and C is (6,2). Q 27 A line makes anglesα , β, γ and δ with the four diagonals of a cube. Prove that cos2α + cos2β + cos2γ + cos2δ = 34 Q 28 Suppose that 5% of men and 0.25% of women have grey hair. A grey haired person in selected at random. What in the prob. that person being male, if there are equal number of males and females. Q 29 A company produces two types of belts, A and B. Profit on these types are, Rs. 2 and Rs. 1.5 on each belt resp. A belt of type ‘A’ requires the twice as much time as B. The company can produces atmost 1000 belts of type ‘B’ per day. Material for 800 belts in available per day. At the most 400 buckles of type A and 700 for those of type B are available per day. How many belts of each type should the company produces so as to maximise the profit?
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