Maths imp questions for 2018

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MOST IMPORTANT QUESTIONS (FOR 2018)
Relations & Functions (7 Marks)
1 Mark Questions:
1. What is the range of the function...

9) A binary operation * on Q-{-1} such that a*b= a+b+ab. Find the identity element on Q. Also find the inverse of an
eleme...

3. If sin sin−1 1
5
+ cos−1
x = 1, find x.
4. Find the value of cos (sec-1
x + cosec -1
x).
5. Find the value of cot (tan ...

2 MARKS QUESTIONS.
1. In the matrix eqn.
1 2
3 4
4 3
2 1
=
8 5
20 13
apply𝑅2 → 𝑅2 − 𝑅1 and then apply𝐶2 → 𝐶2 − 𝐶1.
2. If A...

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v)
𝑎2
𝑏𝑐 𝑎𝑐 + 𝑐2
𝑎2
+ 𝑎𝑏 𝑏2
𝑎𝑐
𝑎𝑏 𝑏2
+ 𝑏𝑐 𝑐2
= 4a2
b2
c2
vi)
𝑎2
+ 1 𝑎𝑏 𝑎𝑐
𝑎𝑏 𝑏2
+ 1 𝑏𝑐
𝑎𝑐 𝑏𝑐 𝑐2
+ 1
= (1 + a2
+ b2
+ c2
)
...

14. Find A-1
, where A =
1 −2 0
2 1 3
0 −2 1
. Hence solve the equations x – 2y = 10, 2x + y + 3z = 8, -2y + z = 7.
15. If...

14. Differentiate log ( xsin x
+ cot2
x) with respect to x.
15. If y = log [ x + 𝑥2 + 𝑎2 ], show that ( x2
+ a2
)
𝑑2 𝑦
𝑑𝑥2...

7. The volume of a spherical balloon is increasing at the rate of change of its surface area at the instant when radius is...

17. Show that the function f defined f(x) = tan-1
(sin x + cos x) is strictly increasing in (0,
𝜋
4
) .
18. Find the inter...

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16. Evaluate :- ∫
𝑥2
𝑥2+ 3𝑥−3
𝑑𝑥
17. Evaluate :- ∫ 𝑒 𝑥 sin 4𝑥−4
1−cos 4𝑥
dx
18. Evaluate :- ∫
𝑥2
𝑥−1 3 (𝑥+1)
dx
19. Evalua...

(i)∫ 2𝑥2
− 5 𝑑𝑥
3
0
(ii) ∫ 𝑥2
+ 5𝑥 𝑑𝑥
3
1
(iii) ∫ 𝑥2
+ 𝑥 + 1 𝑑𝑥
2
0
(iv) ∫ 3𝑥2
+ 2𝑥 𝑑𝑥
3
1
APPLICATION OF INTEGRATION (6 M...

8. Find the differential equation representing the curve y = e-x
+ax+b.
9. Form the differential equation of family of cur...

VECTORS AND THREE DIMENSIONAL GEOMETRY(1+2+4+4+6=17 MARKS)
1 MARK QUESTIONS.
1. If 𝑝 is a unit vector and (𝑥 − 𝑝) 𝑥 + 𝑝 = ...

28. If 𝑎 , 𝑏 𝑎𝑛𝑑 𝑐 are three unit vectors such that 𝑎 = 5, 𝑏 = 12 and 𝑐 = 13 , and 𝑎 + 𝑏 + 𝑐 = 0 , find the value of
𝑎 . 𝑏...

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14. If 𝑎 , 𝑏 and 𝑐 are mutually perpendicular vectors of equal magnitudes, show that the vector 𝑎 + 𝑏 + 𝑐 is equally
incli...

12. Find the equation of plane which contains two parallel lines:
𝑥−3
3
=
𝑦+4
2
=
𝑧−1
1
and
𝑥+1
3
=
𝑦−2
2
=
𝑧
1
.
13. Find...

3. P(A)= 6/11, P(B) = 5/11 and P(𝐴 ∪ 𝐵) = 7/11 𝑓𝑖𝑛𝑑 𝑃(𝐵/𝐴)
4. An unbiased die is thrown twice.Let the event A be `odd numb...

7. In answering a question on a MCQ test with 4 choices per question, a student knows the answer, guesses or copies
the an...

20. There are three coins. One is two headed coin (having head on both faces), another is a biased coin that comes up tail...

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4. A shopkeeper sells only tables and chairs. He has only Rs. 6000 invest and has space for at most 20 items. A
table cost...

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