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equations which are reducible to quadratics, properties of solutions of simultaneous equations, pharmaceutical applications of determinants and the concepts of matrices, Cramer’s rule, definitions of the concepts of special kinds of matrices
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Roll No.
TotalNo.of Questions : 101
lTbtal No. of Pages: 03
lPlease fill this Paper ID in ONIR Sheet)
Time : 03 Hours
Maximum Marks : 80
Instruction fo Candidates:
Section- A is compulsory.
v
Section
QI)
(ts x2 = 30)
a) Distinguishbetweenmatricesand
deterrninants.
b) Showthat
(3, l), (7,3) and (-3, -2) lie on the samestraightline.
c) Reducingthe equation5x + 2y + ct= 0 to slope-intercept
form, er.'aluate
its interceptand slope.
d ) P r o v e c o s C - c o sD = 2 r i n
[ c * D ).
s i n
f P l )
v
e) Solvelogro
(2x
f) What are syffurretric,scalarand singularmatrices?
g) A strip of l0 capsuleshas mean weight of 260 mg. If the mean of 6
capsulesof theseis 250 mg. thenfind themeanof theremainingcapsules.
h) Expressall t-ratiosof A intermsof sin A.
i) Integratex2 log x with respect to
',r'.
j) Diff'erentiate.v2from the first principles(ab initio).
k ) I f. r ' =l o g ( s i n. r ) ,f i n d 4 - 4
u n C.
rl.t cl.t'' r1_r''
PT.O.
r) Solvefbr.r and1,:
x * ] t = 5
x 2 + ' l ' 2
= 1 3
in) Differentiatebetween:
n )
o)
(i) Naperiomand cornmonlogarithms.
(ii) Real and complex numbers.
Finclthe slopeof a line whoseinclinatiolls are
ft/,
md
Differentiatebetweer] lnean,nlode and rnedian.
Section
Q2) Giventlreco-ordinatcs
ot'3 vertices.derii,eth.:forrnulir for
triangle.Hclw can it def"ectcoiiinearity?L.lsrng the fbr-nrula,
triangleforrnedby (2, -3), (4,6) and (3, 2).
Q3) A cylindricalreservoircontainingan expectorant
syrupmeasrlres2.25 ntin
height and3.64m in external diarneter.If it is rnadeof 7 cm thick metal.tind
(i) how many cubic metelsof syrup wor-rldtre removeclto lorverthe levels
from 1.9m to 1.2m (ii) costincr.trrecl t;n
painting theinnr'lsur{ace@ Rs"25-
per m:.
1 1
anclcos fi
=i,
find the values of sin
{a* fr), cos {a-F)
and
( 4 x 5 = 2 ( t )
finding arcaof a
find the aleaof a
0 4 l f s i n. l = l l
t 7
tan
\a
Q5)
Diti'els'ntiate
( i ) , r n - ' f- l l l - i t i i l
1 * - \ i i f
' r. \ ' '
r r i. r r ( r .? +
\ I + cos.r.l
.L il
Q6) Find rnean,mediatrand
urodcfiom the follorving frequencytable.
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