Grade 12 Maths Practice Exam

VELAMMAL VIDHYASHRAM SURAPET
CLASS: XII Revision Exam-1 MARKS: 80

DATE: MATHEMATICS TIME: 3.00 Hrs
GENERAL INSTRUCTIONS:
1. This Question paper contains - five sections A, B, C, D and E. Each section is
compulsory. However, there are internal choices in some questions.
2. Section A has 18 MCQs and 02 Assertion-Reason based questions of 1 mark each.
3. Section B has 5 Very Short Answer(VSA)-type questions of 2 marks each.
4. Section C has 6 Short Answer(SA)-type questions of 3 marks each.
5. Section D has 4 Long Answer(LA)-type questions of 5 marks each.
6. Section E has 3 source based/case based/passage based/integrated units of assessment
(4 marks each)with sub parts.
SECTION – A
(Multiple Choice Questions)
Each question carries 1 mark
1. If a matrix A is both symmetric and skew-symmetric matrix,then
a) A is a diagonal matric b) A is null matric
c) A is a square matric d) A is a unit matric
[ cosα
2. If A= sinα
−sinα
cosα ]
,then A+AT=I,if the value of α is
π π 3π
a) 6 b) 3 c) 2 d) π
3. The value(s) of k,if area of triangle is 4 sq unit and vertices are (k,0),(4,0),(0,2)
a) 0 b) 8 c) 0,8 d) 0 ,-8
4. Find the value(s) of x,if 5 1 = 6 |2 4| |2 x 4x|

a) √ 3 b) √ 2 c) −√ 2 d)± √ 3
5. Let A={ 1,2 , 3 } .Then the number of equivalence relations containing (1,2) is
a) 1 b) 2 c) 3 d) 4
6. The total revenue in rupees received from the sale of x units of a product is given by
R(x)=3x2+3x+5.The marginal revenue,when x=15 is
a) 116 b) 96 c) 90 d) 126
7. Solution of differential equation xdy – ydx = 0 represents
a) a rectangular hyperbola b) parabola whose vertex is at origin
c) straight line passing through origin d) a circle whose centre is at origin
dy y +1
8. The number of solutions of dx = x−1 , when y(1) = 2 is
a) none b) one c) two d) infinite

9. The order and degree of the differential equation
( ) ( ) ( )
2
d3 y d2 y dy 4
−3 +2 = y 4 are
dx 3
dx 2
dx
a) 1, 4 b) 3, 4 c) 2, 4 d) 3, 2
dy
10.Integrating factor of the differential equation cos x dx + y sinx = 1 is
a)cosx b) tanx c) secx d) sin x

^
11.The vector in the direction of the vector i−2 ^j+2 k^ that has magnitude 9 is
^
i−2 ^j+2 k^
^
a) i−2 ^j+2 k^ b) ^
c) 3(i−2 ^j+ 2 k^ ) ^
d) 9( i−2 ^j+2 k^ ¿
3
12.If a⃗ , b⃗ and c⃗ are three vectors such that a⃗ + ⃗b+ c⃗ =0 and |⃗a| = 2, |b⃗| =3, |c⃗| =5, then the
value of a⃗ . ⃗b+ ⃗b . c⃗ + c⃗ . ⃗a is
a) 0 b) 1 c) -19 d) 38
13. If a⃗ , b⃗ and are unit vectors enclosing an angle θ and |⃗a +⃗b|<1 , then
π π 2π 2π 2π
a) θ= 2 b) θ< 3 c) π ≥θ> 2 d) 2 <θ< 2
14. A line makes angle α , β∧γ with the co-ordinate axes. If α + β=90 ° , then γ is equal to
a) 0 b) 90° c) 180 ° d) None of these
15. The vector equation of the symmetrical form of equation of straight line
x−5 y+ 4 z−6
3
=
7
=
2
is
a) r⃗ =( 3î+ 7^j+ 2^k ) + μ(5î+ 4^j−6^k) b) r⃗ =( 5î+ 4^j−6^k ) + μ (3î+ 7^j+ 2^k)
c) r⃗ =( 5î−4^j−6^k ) + μ(3î−7^j−2^k ) d) r⃗ =( 5î−4^j+ 6^k ) + μ ( 3î+ 7^j+ 2^k)
16. Which of the following statement is false?
a) The feasible region is always a concave region.
b) The maximum (or minimum) solution of the objective function occurs at the vertex
of the feasible region.
c) If two corner points produce the same maximum (or minimum) value of the objective
function, then every point on the line segment joining these points will also give the
same maximum (or minimum) value.
d) None of these.
17. Corner points of the feasible region determined by the system of linear constraints are (0,
3), (1, 1) and (3, 0). Let Z = px +qy, where p, q > 0. Condition on p and q, so that the
minimum of Z occurs at (3, 0) and (1, 1) is
q
a) p = 2q b)p = 2 c) p = 3q d) p = q
18.Which of the following sets is convex?

a) {(x, y) : x2 + y2 ≥1} b) {(x, y) : y2 ≥ x }
c) {(x,y) : 3x2 + 4y2 ≥ 5 } d) {(x, y) : y ≥ 2 , y ≤ 4 }
ASSERTION – REASON BASED QUESTIONS
In the following questions, a statement of assertion (A) is followed by a statement of
Reason (R). Choose the correct answer out of the following choices.
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but Rt is not the correct explanation of A
(c) A is true but R is false.
(d) A is false but R is true.
19. Assertion (A) : In ∆ ABC , ⃗
AB+ ⃗
BC+ ⃗
CA =0
Reason (R) : If ⃗ BC =⃗b, then ⃗

AB=⃗a , ⃗ AC =⃗a + ⃗b ( Triangle law of addition).
2 1 1
20. Assertion (A) : If A, B, C are three events such that P (A) = 3 , P (B) = 4 and P (C) = 6
,
then A, B, C are mutually exclusive events.
Reason (R) : If P (A∪ B ∪ C ¿= P (A) + P (B) + P (C), then A, B, C are mutually
exclusive events.
SECTION – B
( This section comprises of very short answer type- questions (VSA) of 2 marks each)
21. Check whether the relation R defined on the set A = {1, 2, 3, 4, 5, 6} as R = {(a, b): b = a + 1} is
reflexive, symmetric or transitive. (OR)
Find the integral of sin(ax+b)cos(ax+b)
22. Find the principal value of

tan-1√3 – sec-1 (- 2).
23. Find a unit vector perpendicular to each of the vectors a⃗ and b⃗ where
a⃗ = 5î+ 6^j−2^k ∧⃗b=7î+ 6^j+ 2^k
24. Find the second order derivatives of the function sin(log x)

25. The volume of a cube is increasing at the rate of 8 cm3/s. How fast is the surface area
increasing when the length of an edge is 12 cm?
SECTION – C
( This section comprises of short answer type questions (SA) of 3 marks each)
26. Write the anti-derivative of (3√x + 1/√x).

27. Find ∫ sinxsin 2 xsin3 x dx
5
28. ∫ ¿ x +2∨¿ ¿
−5
29.Solve the following differential equation (cot-1y+x) dy = (1+y2)dx

30. Using vectors, find the area of the triangle ABC with vertices A (1, 2, 3), B (2, -1, 4) and
C (4, 5, -1)
31. Solve the following LPP graphically:
Minimise Z = 5x + 10y subject to the constraints
x + 2y ≤ 120
x + y ≥ 60,
x – 2y > 0 and x, y ≥ 0
SECTION – D
( This section comprises of long answer – type questions (LA) of 5 marks each)
32. Using integration, find the area bounded by the curve x2 = 4y and the line x = 4y -2.(OR)
Find the area of the region bounded by the parabola y=x2 and y = ¿ x∨¿
33. If A = {1, 2, 3, .. ,9} and R is the relation in A × A defined by (a , b) R(c, d), if a + d = b + c for (a,b), (c,
d) in A × A. Prove that R is an equivalence relation. Also, obtain the equivalence class [(2, 5)].
34. Find the coordinates of the foot of perpendicular drawn from the point A (- 1, 8, 4) to the line joining the
points B(0, – 1, 3) and C(2, – 3, – 1). Hence, find the image of the point A in the line BC. (OR)
Find the vector p⃗ which is perpendicular to both α⃗ = 4î + 5ĵ – k̂ and β⃗ = î – 4ĵ + 5k̂ and p⃗ . q⃗ =
21, where q⃗ = 3i + j – k.

35. The cost of 4 kg onion, 3 kg wheat and 2 kg rice is Rs 60. The cost of 2 kg onion,4 kg
wheat and 6 kg rice is Rs 90. The cost of 6 kg onion 2 kg wheat and 3 kg rice is Rs 70. Find
cost of each item per kg by matrix method.
SECTION – E
( This section comprises of 3 case – study/ passage – based questions of 4 marks each with
two sub-parts. First two case study questions have three sub-parts (i), (ii), (iii) of marks 1,
1, 2 respectively. The third case study question has two sub-parts of 2 marks each)
36. Case – Study 1 :
Two motorcycles A and B are running at the speed more than allowed speed on the road
^ ^j−k^ )∧⃗r =3î+ 3^j+ μ ( 2î + ^j+ k^ ) ,respectively .
along the lines r⃗ =λ ( i+2
Based on the above information, answer the following questions.

i) Write the Cartesian equation of the line along which motorcycle a is running.
ii) In which the point motorcycles will meet an accident.
iii ) Find the shortest distance between the gives lines.
37. In an office three employees Vinay, Sonia and lqbal process incoming copies of a
certain form. Vinay process 50 % of the forms, Sonia processes 20 % abd lqbal the
remaining 30 % of the forms. Vinay has an error rate of 0.06, Sonia has an error rate of 0.04
and lqbal has an error rate of 0.03.
i) What is the conditional probability that an error is committed in processing given that
Sonia processed the form.
ii)What is the probability that Sonia processed the form and committed an error.
iii) Let A be the event of committing an error in processing the form and let E1, E2 and E3
be the events that Vinay, Sonia and lqbal processed the form. Find the value of
3
∑ P ( Ei| A ¿ . ¿
i=1
dy f (x , y ) dy
( y)
38. If the equation is of the form dx = g ( x , y ) ∨ dx =F x , where f(x, y), g(x, y) are
dy dv
homogeneous functions of the same degree in x and y, and dx =v +x dx , so that the
dependent variable y is changed to another variable v and then apply variable separable
method.
2 dy 2 2
i) Find the general solution of x dx =x + xy+ y .
dy 2 2
ii) What is the solution of the differential equation 2xy dx =x +3 y ?

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VELAMMAL VIDHYASHRAM SURAPET

CLASS: XII Revision Exam-1 MARKS: 80

4. Find the value(s) of x,if 5 1 = 6 |2 4| |2 x 4x|

a) none b) one c) two d) infinite

a)cosx b) tanx c) secx d) sin x

18.Which of the following sets is convex?

Reason (R) : If ⃗ BC =⃗b, then ⃗

22. Find the principal value of

24. Find the second order derivatives of the function sin(log x)

26. Write the anti-derivative of (3√x + 1/√x).

29.Solve the following differential equation (cot-1y+x) dy = (1+y2)dx

21, where q⃗ = 3i + j – k.

Based on the above information, answer the following questions.

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