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The values of x satisfying sin-1 x + sin-1 (1- x) = cos-1 x are
0
b)\(\frac{1}{2}\)
c)1
d)2
The area bounded by the curve y = f(x), the x-axis and the ordinates x = 1 and x = b is (b - 1) cos (3b + 4) sq unit. Then f(x) is given by
(x - 1) sin (3x + 4)
b)3 (x - 1) sin (3x + 4) + cos (3x + 4)
c)cos (3x + 4) - 3(x - 1) sin (3x + 4)
d)none of the above
If the function f(x)=2x3-9ax2+12a2x+1 has a local maximum at x=x1 and a local minimum at x=x2 such that x2=x12 then a is equal to
0
b)\(\frac{1}{4}\)
c)2
d)either (a) or (c)
If P(x) is a polynomial such that P(x2 + 1) = {P(x)}2 + 1 and P(0) = 0, then P' (0) is equal to
-1
b)0
c)1
d)none of these
If \(y={ 2 }^{ \frac { 1 }{ \log _{ x }{ 4 } } }\) , then x is equal to
\(\sqrt { y } \)
b)y
c)y2
d)y3
If the roots of the equation ax2+bx+c=0 are of the form ∝/(∝-1) and (∝+1)/∝ then the value of (a+b+c)2 is
2b2-ac
b)b2-2ac
c)b2-4ac
d)4b2-2 ac
Let p : 7 is not greater than 4.
q : Paris is in France.
be two statements. Then ~ (p v q) is the statement
7 is greater than 4 or Paris is not in France
b)7 is greater than 4 and Paris is not in France
c)7 is greater than 4 and Paris is in France
d)7 is not greater than 4 or Paris is not in France
In \(\Delta ABC,\) if 2a2b2 + 2b2c2=a4 +b4+c4, then \(\angle B\) is equal to
45o
b)35o
c)120o
d)30o
The value of \(tan(cos^{-1}\frac{4}{5}+tan^{-1}\frac{2}{3})=\)
\(6\over17\)
b)\(7\over16\)
c)\(16\over7\)
d)None of these
sin x + cos x = 1+ sin x cos x, if
\(sin\left(x+{\pi\over 4}\right)={1\over \sqrt2}\)
b)\(sin\left(x-{\pi\over 4}\right)={1\over \sqrt2}\)
c)\(cos\left(x+{\pi\over 4}\right)={1\over \sqrt2}\)
d)\(cos\left(x-{\pi\over 4}\right)={1\over \sqrt2}\)
If the foci of the ellipse \({x^2\over 9}+{y^2\over 16}=1\) are (0, √7) and (0, -√7) then the foci of the ellipse \({x^2\over 9+t^2}+{y^2\over 16+t^2}=1, t\in R \), are
(0, √7) (0, -√7)
b)(0, √7) (0, -7)
c)(0, 2√7) (0, -2√7)
d)(√7, 0) (-√7,0)
The tangents drawn from the origin to the circle x2 + y2 - 2px - 2qy + q2 = 0 are perpendicular, if
p=q
b)p2=q2
c)q=-p
d)p2+q2=1
The angle between the lines \(\sqrt{3}\)X + Y = 1 and X + \(\sqrt{3}\)Y = 1 is equal to
30°
b)60°
c)90°
d)45°
The area enclosed by the curve y=\(\sqrt { x } \) and x = -\(\sqrt { y } \) , the circle x2 + y2 = 2 above the x-axis, is
\(\frac { \pi }{ 4 } sq.units\)
b)\(\frac { 3\pi }{ 2 } sq.units\)
c)\(\pi\) sq. units
d)\(\frac { \pi }{ 2 } sq.units\)
The sum to infinity of the series, \(1+2\left( 1-\frac { 1 }{ n } \right) +3{ \left( 1-\frac { 1 }{ n } \right) }^{ 2 }+....\) is
n2
b)n ( n+1)
c)\(n{ \left( 1+\frac { 1 }{ n } \right) }^{ 2 }\)
d)none of these
The value of \(^{ 50 }{ C }_{ 4 }+\overset { 6 }{ \underset { r=1 }{ \Sigma } } ^{ 56-r }{ C }_{ 3 }\) is
56C4
b)56C3
c)55C3
d)55C4
If A ={1,2,3} and B ={3,6,8}, then \(\left( A\cap B \right) \times A\) is equal to
{(1, 3), (2, 3), (3, 3)}
b){(3,1), (3, 2), (3,3)}
c){(1,3), (3,1), (3,2)}
d)None of the above
Let a, b, c be three cube roots of unity, the value of
\(\left| \begin{matrix} { e }^{ a } & { e }^{ 2a } & { e }^{ 3a }-1 \\ { e }^{ b } & { e }^{ 2b } & { e }^{ 3b }-1 \\ { e }^{ c } & { e }^{ 2c } & { e }^{ 3c }-1 \end{matrix} \right| \) is
(1 + a)3
b)(1+b)3
c)(a+b+c)3n,(n\(\epsilon\)N)
d)(a+2b+3c)2n,(n\(\epsilon\)1)
Lanthanoids and actinoids differ from each other because
of the presence of partially filled outermost shells
b)actinoids are radioactive in nature
c)they show common oxidation state of +3
d)both are known as inner transition elements
Which of the following represents correct order of first ionisation energy?
K > Na > Li
b)Be > Mg > Ca
c)B > C > N
d)Ce > Si > C
The density (in g mL-1) of a 3.60 M sulphuric acid solution that is 29% H2SO4 (98 g mol-1) by mass will be
1.64
b)1.88
c)1.22
d)1.45
Which of the following reactions is not correct according to the law of conservation of mass?
2Mg(s) + O2(s) \(\rightarrow\) 2MgO(s)
b)C3H8(g) + O2 (g) \(\rightarrow\) CO2(g) + H2O(l)
c)P4(s) + 5O2(g) \(\rightarrow\) P4O10(s)
d)CH4(g) + 2O2(g) \(\rightarrow\) CO2(g) + 2H2O(g)
Which of the folllowing is not an organic water pollutants?
animal waste
b)sewage
c)chemical fertilizers
d)decaying animals
Which one of the following fertilisers contains the maximum percentage of nitrogen?
ammonium sulpate
b)CAN
c)NH4Cl
d)Urea
Glycogen is a branched chain polymer of \(\alpha -D\)-glucose units in which chain is formed by C1-C4 glycosidic linkage whereas branching occurs by the formation of C1-C6 glycosidic linkage. Structure of glycogen is similar to
amylose
b)amylopectin
c)cellulose
d)glucose
Commercial name of PMMA is
lucite
b)plexiglass
c)acrylite
d)all of these
The process of concentrating Ag and Au ores is based on their solubility in
NH3
b)HCL
c)HNO3
d)KCN
azobenzene
b)hydrazobenzene
c)aniline
d)N-phenyl hydroxylamine
Which one of the following is known as Hinsberg reagent?
ZnCl/HCl
b)Na/C2H5OH
c)LiAlH4
d)C6H5SO2Cl
dimerisation
b)attached alkyl radical
c)resonance
d)cyclic structure