MBSE HSSLC Sample Question Paper Maths

Total number of printed pages – 4 HSS/020

MATHEMATICS
SAMPLE QUESTION PAPER
Full Marks – 80
Time – 3 hours
General Instructions :
(i) All questions are compulsory.
(ii) Marks for each question are indicated against it.
(iii)Use of calculator is not permitted; however, you may ask for logarithmic tables if required.
(iv) Please write down the serial number of the questions before attempting it.

1. Choose the correct answer from the following: 16×1=16

(a) Let S be the set of all real numbers and let R be a relation in S, defined by
R= {(a,b): a≤b}. Then R is

(i) Reflexive and symmetric but not transitive

(ii) Reflexive and transitive but not symmetric

(iii) Symmetric and transitive but not reflexive

(iv) Equivalence relation

(b) Let : → : = is

(i) one-one and onto (ii) one-one and into

(iii) many-one and onto (iv) many-one and into

(c) If = , then =

− −
− −
(i) (ii)

− − −
−
(iii) (iv)

(d) If A is singular, then A(Adj A) is

(i) a unit matrix (ii) a null matrix

(iii) a symmetric matrix (iv) none of these

(e) If = √ , then is

√ √ √ √

√ !√
(i) (ii) (iii) (iv)
√ √
"

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(f) When is positive, the minimum value of is
$
(i) (ii) # (iii) # (iv)

(g) The solution of the differential equation + = 0 is

(i) + = ' (ii) =' (iii) ()* + = ' (iv) none of these
0
(h) +$0 ,-. / + /
=?
0
(i) 22 (ii) 0 (iii) (iv) 572
!

6 6
(i) + 5 − 7 =?
6
(i) 5log + 7 + C (ii) − +C

6
(iii) . +C (iv) none of these

<=> √
(j) + =?
√

(i) 2 ),√ + ' (ii) −2 ),√ + '

(iii) 2,-.√ + ' (iv) −2,-.√ + '

(k) If ? @ + A@? = ? @ − A@?,

(i) | @| = ? A@? (ii) @ ∥ A@

(iii) @ ⊥ A@ (iv) none of these

(l) If |AAA@| = 2, | A@| = 7, @ × A@ = 3F̂ + 2Ĥ + 6JK, then the angle between @ and A@ is
0 0 !0 M0
(i) (ii) (iii) (iv)
L M M

(m) The direction cosines of the normal to the plane 5y + 4 = 0 are
(i) 0, -4/5, 0 (ii) 0, 1, 0 (iii) 0, -1, 0 (iv) none of these

(n) The intercepts made by the plane N@. O2F̂ − 3Ĥ + 4JK Q = 12 are
(i) 2, -3, 4 (ii) -2, 3, 4 (iii) 6, -4, 3 (iv) -6, 4, -3

(o) If and S are independent events, then T ̅/SW =?

(i) 1-P(A) (ii) 1-T S (iii) 1- T /SW (iv) 1-T /S

(p) Three cards are drawn successfully without replacement from a pack of 52 well - shuffled
cards. The probability that the first two cards are queens and the third card drawn is a
king is
(i) 2/5525 (ii) 1/5525 (iii) 125/140608 (iv) 125/156

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$√M 0
2. Evaluate ), 5cos$6 Z ! [ + L 7. 2

√6^ $√6$
3. If = sin$6 5 !
7, find . 2

!^M
4. Evaluate + . 2
M$!

5. A and B appear for an interview for two posts. The probability of A’s selection is 1/3 and that of
B’s selection is 2/5. Find the probability that only one of them will be selected. 2

6. Find the range and domain of the real function defined by = . Show that is many-
6^
one. 4

2 −3
4 6
7. If A = , verify that (adjA)-1 = (adjA-1). 4

8. The sum of three numbers is 6. Twice the third number when added to the first number gives 7.
On adding the sum of the second and the third numbers to thrice the first number, we get 12.
Find the numbers using matrix method. 4

9. (a) If _ >
= + _^>
, prove that = . 4

OR

(b) If = 2 ),` − ),2` and = 2,-.` − ,-.2` , find Z [ c. 4
ab

10. Evaluate: (a) + sin$6 !
. OR (b) + "^ ^6
4

11. Find the particular solution of the differential equation √1 − ! = sin$6 − , it
being given that when = 0, then = 0. 4
$6 d$!
12. (a) Find the image of the point (1, 6, 3) in the line = = . 4
6 ! M
OR
(b) Find the length and equations of the shortest distance between the lines
^6 ^6 d^6 $M $ d$/
= = and = = . 4
/ $L 6 6 $! 6

13. A man is known to speak the truth 3 out of 4 times. He throws a die and reports that it is a six.
Find the probability that it is not a six. 4

14. (a) Show that the semi-vertical angle of a right circular cone of given surface area
and maximum volume is sin-1(1/3). 6
OR
2
(b) Show that the curves = and = k cut at right angles if 8k2 =1. 6
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15. Find the area of the region e , : !
≤ ≤ | |h. 6

OR

Find the area of the region e , :0 ≤ !
+ 1 ,0 ≤ ≤ + 1 ,0 ≤ ≤ 2h. 6
$i^ $i d$i$ $l^m $l d$l$m
16. Show that the lines = = , and = = are coplanar and find
j$k j j^k n$o n n^o
the equation of the plane containing them. Also find the length of perpendicular drawn from
the origin to this plane. 6

17. A company makes two types of belts, A and B; profits on these belts being Rs. 4 and Rs. 3
respectively. Each belt of type A requires twice as much time as a belt of type B, and if all
belts were of type B, the company could make 1000 belts per day. The supply of leather is
sufficient for only 800 belts per day (A and B combined). At the most 400 buckles for belts of
type A and 700 for those of type B are available per day. How many belts of each type should
the company make per day so as to maximize the profit? 6

__________________

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