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FULL TEST INSTRUCTIONS
Time : 3 hrs. Chemistry (120 marks)
:
Question No. 1 to 30 are of 4 marks each.
Physics (120 marks)
:
Question No. 31 to 60 are of 4 marks each.
Mathematics (120 marks) :
Question No. 61 to 90 are of 4 marks each.
Negative Marking
One fourth (¼) marks will be deducted for indicating incorrect response of each question. . . . Best of Luck
:
6. 1.
2.
An azeotropic mixture of two liquids boil at a lower temperature than either of them when (a) It is saturated (b) It does not deviate from Raoult’s law (c) It shows negative deviation from Raoult’s law (d) It show positive deviation from Raoult’s law Which of the following statement is wrong ? (a) Geometrical isomers are diastereomers (b) Enantiomers have same chemical and physical properties (c) Conformers are non inter convertable to each other (d) 3-methyl haxane shows optical isomerism
7.
4.
5.
(a)
Kw Ka
(b)
Kw Ka ´ Kb
(c)
Kh C
(d)
Ka Kb
Correct IUPAC name of C
NO2
The conjugated base of (CH 3 ) 2 N H 2 is (a) CH3NH2 (b) (CH3)2N+ (c) (CH3)2N (d) (CH3)2NH The enthalpy of combustion of H2(g), to give H2O(g) is –249 kJ mol–1 and bond enthalpies of H – H and O = O are 433 kJ mol–1 and 492 kJ mol–1 respectively. The bond enthalpy of O – H is (a) 464 kJ mol-1 (b) –464 kJ mol-1 -1 (c) 232 kJ mol (d) –232 kJ mol-1 The specific heat of a metal is 0.11 and its equivalent weight is 18.61. Its exact atomic weight is
(a) 58.2 (b) 29.1 (c) 55.83 (c) 27.91 The correct relation for hydrolysis constant of NH4CN is
NH2
+
3.
Max. Marks : 360
8.
9.
10.
CH3
C
is
COOH
(a) E-3-amino - 3 - nitro - 2 - methyl propenoic acid (b) Z -3- amino - 3 - nitro - 2 - methyl propenoic acid (c) 3 - Amino - 3 - nitro - 2 - methyl propenoic acid (d) Trans - 3 - amino - 3 - nitro - 2 - methyl propenoic acid Which of the following undergoes hydrolysis by S 1 N
mechanism : (a) CH3CH2CH2CH2Cl (b) CH3CH2CH2Cl (c) CH3 – O – CH2Cl (d) CH3Cl In the esterification reaction of alcohol (a) OH– is replaced by C6H5OH (b) H is replaced by CH3OH- gp (c) OH is replaced by CH3COO- gp (d) OH is replaced by Cl The process of the extraction of Au and Ag is based on their solubility in
2
11.
12.
13.
14.
(a) NH3 or NH4OH (b) KCN or NaCN (c) HCl or HNO3 (d) H2SO4 Which of the following compounds having highest and lowest melting point respectively ? (1) CsF (2) LiF (3) HCl (4) HF Correct answer is (a) 2, 3 (b) 1, 4 (c) 4, 3 (d) 2, 1 Silver bromide when dissolve in hypo solution gives complex ..... in which oxidation state of silver is .... (a) Na3[Ag(S2O3)2], (I) (b) Na3[Ag(S2O3)3], (III) (c) Na3[Ag(S2O3)2], (II) (d) Na3[Ag(S2O3)4], (I) The freezing point of a solution, prepared from 1.25 gm of a non-electrolyte and 20 gm of water, is 271.9 K. If molar depression constant is 1.86 K mole–1, then molar mass of the solute will be (a) 105.7 (b) 106.7 (c) 115.3 (d) 93.9 Which of the following statements is incorrect? Oxidation state of oxygen is(a) – 1 in peroxide (b) + 2 in oxygen difluoride 1 in superoxides (d) – 2 in CO2 2 An organic compound (A) reacts with sodium metal and forms (B). On heating with conc. H2SO4, (A) gives diethyl ether, (A) and (B) are (a) C2H5OH and C2H5ONa (b) C3H7OH and CH3ONa (c) CH3OH and CH3ONa (d) C4H9OH and C4H9ONa Which one of the following esters cannot undergo Claisen self-condensation?
(c) CH3CH2OH and H2SO4 (d) CH2 – CH2 and NaHCO3 Cl
20.
21. 22.
23.
24.
16.
17.
18.
19.
(a) CH 3 - CH 2 - CH 2 - CH 2 - COOC 2 H 5 (b) C6H5COOC2H5 (c) C6H5CH2COOC2H5 (d) C6H11CH2COOC2H5 In recovery of silver from photographic film, you have decided to dissolve the silver ion with dilute nitric acid. Addition of dilute HCl to precipitate AgCl seems to result in unacceptable losses. You might improve recovery by addition of_______ in the latter step. (a) NaNO3 (b) NaCl (c) Ag2SO4 (d) sodium acetate The reaction of phenol with concentrated HNO3 gives (a) Picric acid (b) Benzoic acid (c) Salicylic acid (d) Phthalic acid In the reaction, HOCl
25.
(a) 2.36V (b) –2.36V (c) 2.42V (d) –2.42V Among the following compounds (I-III) the correct order of reactivity with electrophile is
OCH3
26.
27.
No2
I II III (a) II > III > I (b) III < I < II (c) I > II > III (d) I = II > III One desires to prepare a positively charged sol of silver iodide. This can be achieved by (a) adding a little AgNO3 solution to KI solution in slight excess (b) adding a little KI solution to AgNO3 solution in slight excess (c) mixing equal volumes of equimolar solutions of AgNO3 and KI (d) none of these In the reaction of KMnO4 with an oxalate in acidic medium, MnO-4 is reduced to Mn 2 + and C 2 O 24 - is oxidised to
B
CO2. Hence, 50 ml of 0.02 M KMnO4 is equivalent to
CH 2 = CH2 ¾¾¾¾ ® A ¾¾® CH2 - OH |
(a) 100 ml of 0.05 M H 2C 2O 4
CH2OH
(b) 50 ml of 0.05 M H 2C 2O 4
The molecule ‘A’ and the reagent ‘B’ are (a) CH2 – CH2 and Hot water (b) CH3CH2Cl and NaOH O
Alkali metals dissolve in liquid NH3 then which of the following observations is not true? (a) H2 gas is liberated (b) Solution turns into blue due to solvated electrons (c) It becomes diamagnetic (d) Solution becomes conducting Which of the following species involves sp3 hybridisation? (b) PCl5 (c) N2Cl2 (d) SiF62– (a) SbF6– The temperature at which the density of O2 at 1 atm is the same as that of methane at S.T.P. is (a) 100oC (b) 150oC (c) 273oC (d) 546oC Schottky defect in crystals is observed when (a) An ion leaves its normal site and occupies an interstitial site (b) Unequal number of cations and anions are missing from the lattice (c) Density of the crystal is increased (d) Equal number of cations and anions are missing from the lattice The electrode potential of Mg2+/Mg electrode, in which conc. of Mg2+ is 0.01M, is ( E o Mg2+ / Mg = -2.36V)
(c) +
15.
OH
(c) 25 ml of 0.2 M H 2C 2O 4 28.
(d) 50 ml of 0.10 M H 2C 2O 4 Lassaigne’s test for nitrogen is positive for which compound?
3
29.
30.
31.
(a) NH2OH (b) NH2NH2 (c) H2NCONH2 (d) All the three Which of the following is true? (a) Tollens’ reagent gives a positive result with all aldehydes (b) Tollens’ reagent gives a negative result with all ketones (c) Both are true (d) None is true Which of the following complexes will give white precipitate with BaCl2 (aq.)? (a) [Co(NH3)4SO4]NO2 (b) [Cr(NH3)4SO4]Cl (c) [Cr(NH3)5Cl]SO4 (d) Both (b) & (c)
A block is placed on a frictionless horizontal table. The mass of the block is m and springs are attached on either side with force constants K1 and K2. If the block is displaced a little and left to oscillate, then the angular frequency of oscillation will be (a)
(c)
é K 1K 2 ù ê ú ë ( K1 - K 2 ) m û
(b)
(d)
é K2 + K2 ù 1 2 ú ê ê ( K1 + K 2 ) m ú ûú ëê
1/ 2
32.
33.
34.
35.
A particle of mass m moves with a constant velocity. Which of the following statements is not correct about its angular momentum ? Y D
E C A
1m
B O
37.
X
1m (a) it is zero when it is at A and moving along OA. (b) the same at all points along the line DE. (c) of the same magnitude but oppositely directed at B and D. (d) increases as it moves along the line BC Three progressive waves A, B and C are shown in the figure below. With respect to the wave A, the wave C B
A
C
1/ 2
é K1K 2 ù ê ú ë m (K 1 + K 2 ) û
1/ 2
æ K1 + K 2 ö ÷ ç m ø è
36.
1/ 2
At ground level, there is a downard vertical electric field of about 100 V/m. From this data calculate order of surface charge density on earth by assuming that earth is a conductor. (a) 10–9 C/m2 (b) –10–9 C/m2 +6 2 (c) 10 C/m (d) –10+6 C/m2 When a particle moves with variable velocity which of the following statements are not correct. (A) Average speed = Average velocity (B) Instantaneous speed = Instantaneous velocity (C) Distance covered = Magnitude of displacement (a) A, B, C (b) A,B (c) B, C (d) A, C The velocity of projection of a body is increased by 2%, other factors remaining unchanged, what will be the percentage change in the maximum height attained (a) 1 % (b) 2 % (c) 4 % (d) 8 % A river is flowing at the rate of 6 km/hr. A swimmer swims across with a velocity of 9 km/hr. The resultant velocity of the man will be (a)
117 km / hr
(b)
340 km / hr
(c)
17 km / hr
(d)
3 40 km / hr
38.
(a) leads in phase by p and B lags behind by p (b) lags behind in phase by p /2 and B leads by p /2 (c) lags behind in phase by p and B leads by p (d) leads in phase by p /2 & B lags behind by p /2. The amplitude of velocityof a particle acted on by a force F 1
cos w t along the x direction, is given by x =
[aw 2 - bw + c]
where a, b, c, are constants and b2 < 4 ac. For what value of w does the resonance occur ? (a)
39.
40.
w=
b 2a
(b)
w=
b a
(c) w = c (d) w = 0 The insulation property of air breaks down at E = 3 × 106 volts/ metre. The maximum charge that can be given to a sphere of diameter 5 m is approximately (a) 2 × 10–2 coulomb (b) 2 × 10–3 coulomb –4 (c) 2 × 10 coulomb (d) 2 × 10–5 coulomb In the following diagram the reading of the ammeter is (when the internal resistance of the battery is zero) A
4W
5W
10V
4 40 A 29
(a) 41.
(b)
10 A 9
(c)
45.
5 A 3
(d) 2 A
If in figure below R = 200W and on connecting a 3 volt battery in the circuit, the barrier potential developed in diode is 0.5 volt, then the value of current in the circuit is
R = 200 W
0.5V
(a) T1 = 116ºC, T2 = 74ºC (b) 46.
3V
42.
43.
(a) 5.2 mA (b) 8.25 mA (c) 12.5 mA (d) 15.5 mA If a bar magnet of magnetic moment 80 units be cut into two halves of equal lengths, the magnetic moment of each half will be (a) 80 units
(b)
40 units
(c) 160 units
(d)
20 units
The angular velocity of a rotating disc decreases linearly with angular displacement from 60 revolutions per minute to zero during 10 revolutions as shown. The angular velocity of the disc 3 seconds after it begins to slow down is
Three bars each of area of cross - section A and length L are connected in series. The thermal conductivities of their materials are K, 2K, 1.5K. If the temperatures of the external ends of the first and last bar are 200 & 18ºC, then the temperatures of both the junctions are
47.
48.
w Rev/min
T1 = 120ºC, T2 = 84ºC
(c) T1 = 132ºC, T2 = 98ºC (d) T1 = 164ºC, T2 = 62ºC A compound microscope has an objective and eye-piece as thin lenses of focal lengths 1 cm and 5 cm respectively. The distance between the objective and the eye-piece is 20 cm. The distance at which the object must be placed in front of the objective if the final image is located at 25 cm from the eye - piece, is numerically (a)
95 cm 6
(b)
95 cm 89
(c)
5 cm 6
(d)
25 cm 6
When light of 3000 Å is incident on sodium chloride, the stopping potential is 1.85 volt and when light of 4000 Å is incident, then the stopping potential becomes 0.82 volt. The threshold wavelength for sodium is: (h = 6.6 × 10–34 J-sec.) (a) 5451 Å (b) 5154 Å (c) 5320 Å (d) 5211 Å A steel wire is suspended vertically from a rigid support. When loaded with a weight in air, it extends by la and when the weight is immersed completely in water, the extension is reduced to lw. Then the relatively density of material of the weight is
60
O
(a)
20p 10
(c)
10p 17
10 rev
(b)
17p 10
(d)
10p 13
q (Radians)
49.
50.
44.
A ball is projected upwards from the top of the tower with a velocity 50 m/sec. making angle 30° with the horizontal.The height of the tower is 70 m. After how many seconds from the instant of throwing will the ball reach the ground. (a) 2 sec (b) 5 sec (c) 7 sec
(d)
9 sec
51.
52.
(a)
la lw
(b)
la la - l w
(c)
lw la - l w
(d)
lw la
In four complete revolution of the cap, the distance travelled on the pitch scale is 2 mm. If there are 50 divisions on the circular scale, then the least count of the screw gauge is (a) 0.001 mm (b) 0.01 mm (c) 0.10 mm (d) 1.0 mm The length of a second's pendulum is about (a) 99.4 m (b) 9.94 m (c) 99.4 cm (d) 9.94 cm In laboratory, a potentiometer is generally used (a) to determine the resistivity of a given wire (b) to compare the emfs of two primary cells (c) to determine the internal resistance of a cell (d) both (b) & (c) The reverse breakdown voltage of a Zener diode for which the following graph exists is
5 that the mass will land 1 meter below the track end. A photogatetimer system will allow the speed of the blocks to be measured just as they leave the track end. Some data from students is given in the table.
Output voltage (V)
Y
6 5 4 3 2 1 O
Block 1
1 2 3 4 5 6 7 8 9 Input voltage (V)
(a) 5 V
(b)
Block 2
X
Mass (grams)
Height (h) meters)
200
0.4
200
0.77
200
1.2
300
0.4
300
0.77
300
1.2
6V
æ6ö æ5ö (d) ç ÷ V ç ÷V è5ø è6ø In diagrams (1 to 4), variation of volume with changing pressure is shown. A gas is taken along the path ABCD. The change in internal energy of the gas will be (c)
53.
h V
D
V
D
C
C
45° 30° 0°
A
A
B (1)
D
P
1m
B (2) P
C
54.
D C
V
V A
B
(3)
(a) (b) (c) (d)
P
A
B (4)
P
Positive in all the cases (1) to (4) Positive in cases (1), (2), (3) but zero in case(4) Negative in cases (1), (2), (3) but zero in case (4) Zero in all the cases
PASSAGE TYPE QUESTIONS DIRECTIONS (Qs. 54 - 56) : Read the following passage and answer the questions that follows : The apparatus shown is designed for students to make measurements in mechanics. It consists of an essentially frictionless adjustable track down which different small metal blocks slide after being released from various heights, h. The blocks can collide with objects placed on the track end when the end is in the 0° (horizontal) position. The student can also allow the blocks to fly off the adjustable end section of the track at angles of 0°, 30°, and 45°. For all three angles of launch assume
55.
Block 1 is released from a height h = 0.77 m and collides with (inelastically) and sticks to a 500 gram mass on the horizontal (0°) track end. The photogate-timer system measures their combined speed to be 1.11 m/sec. What is the speed of Block 1 just before impact ? (a) 3.88 m/sec (b) 1.55 m/sec (c) 2.08 m/sec (d) 3.34 m/sec Both Block 1 and Block 2 are released from h = 1.2 m. Each is allowed to fly off the track end at elevation angles of 30° and 45° so that they fly through parabolic arcs. Ignoring air friction, their speeds at the top of their parabolic arcs : (a) are greater for the 30° arc than for the 45° arc.
6
56.
57.
(b) are smaller for the 30° arc than for the 45° arc. (c) are the same for the 30° arc and 45° arc. (d) depend on their masses. Block 1 and Block 2 are again released from h = 1.2 m. Block 1 flies off the track end at 30° and Block 2 at 45°. Their speeds when they hit the floor 1 meter below the track end: (a) are smaller for Block 1 than Block 2. (b) are larger for Block 1 than Block 2. (c) are the same for Block 1 and Block 2. (d) depend on mass and angle, so the question cannot be answered. The most common isotope used in diagnostic work is Technicium. It is furnished from a generator or "cow" in which the negative beta decay of Molybdenum-99 produces the desirable metastable isotope of Technicium according to the following decay scheme : ® z Tc A + -1e0 . What are the atomic number, Z, and mass number, A, of the Tc isotope ? (a) 41,99 (b) 42,99 (c) 43,98 (d) 43,99 The Thallium-201 half-life is 74 hours. If the sample has an activity of 80 millicuries initially, what will be the activity after 9.25 days ? 42 Mo
58.
99
(a) 2.5 mCi
(b)
5 mCi
(c) 10 mCi
(d)
20 mCi
ASSERTION & REASON DIRECTIONS (Qs. 59 – 60) : Each of these questions contains two statements: Statement-1(Assertion) and Statement-2 (Reason). Choose the correct answer (ONLY ONE option is correct) from the following (a) Statement-1 is false, Statement-2 is true. (b) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. (c) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1. (d) Statement-1 is true, Statement-2 is false.
59.
Statement -1 : Two simple harmonic motions are given by
pö æ y1 = 10sin ç 3pt + ÷ and y 2 = 5 sin 3pt + 3 cos 3pt . è 4ø
(
)
These have amplitudes in the ratio 1 : 1 . Statement -2 : y2 represents two waves each of amplitude 5 and so total amplitude is 10, same as that of y1. 60.
Statement-1 : NAND or NOR gates are called digital building blocks. Statement-2 : The repeated use of NAND (or NOR) gates can produce all the basic or complicated gates.
7
68.
ASSERTION & REASON DIRECTIONS (Qs. 61 - 65) : Each of these questions contains two statements: Statement-1(Assertion) and Statement-2 (Reason). Choose the correct answer (ONLY ONE option is correct) from the following (a) Statement-1 is false, Statement-2 is true. (b) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. (c) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1. (d) Statement-1 is true, Statement-2 is false. 61.
Statement-1 : A random variable X follows binomial distribution with mean and variance then
62.
63.
64.
65.
70.
71.
-
67.
p 2
p , then 2
1
([12 x ] + [ 2 2 x ] + [32 x ] + ........+ [ n 2 x ]) =
x 3
(a)
x 2
(b)
(c)
x 6
(d) 0
The co-efficient of x in the expansion of æç x 2 + c ö÷ is è xø (a) 20 c (b) 10 c (c) 10 c3 (d) 20 c3 Let Sp and Sq be the coefficient of xp and xq respectively in (1 + x)p + q, then (a) Sp ¹ Sq
q (b) Sp = p Sq
p (c) Sp = q Sq
(d) Sp = Sq.
Number of ways to distribute 10 distinct balls to 3 persons. One getting 2, 2nd getting 3 and 3rd getting 5 balls is 10! 2!.3!.5!
(b)
10! 2!.(3!) 2 .5!
10! (d) 10! 2!.5! The medians of a triangle meet at (0, –3) and two vertices are at (–1, 4) and (5, 2). Then the third vertex is at (a) (4, 15) (b) (–4, –15) (c) (–4, 15) (d) ( 4, –15)
(c)
72.
73.
74.
2 then B is equal to 3 (a) 30° (b) 60° (c) 90° (d) 120° If w is a cube root of unity, then a root of the following
In D ABC, a =2, b =3 and sin A =
w x +1 equation w x + w2
Statement-1 : h is a periodic function. Statement-2 : g (x + 2) – g (x) = g (2). The number of real roots of the equation 1 + a1 x + a2 x2 + …. + an xn = 0
If e
2 log cos q 3
If [x] denotes the greatest integer £ x, then
(a)
0
1 where |x| < and |an| < 2, is 3 (a) n if n is even (b) 0 for any natural number n (c) 1 if n is odd (d) none of these.
(d) cos log q =
5
69.
x
66.
(c) cos log q = log cos q
lim
integer. Statement-2 : In a binomial distribution Mean > Variance. Statement 1 : If f is even function, g is odd function then
Let g (x) = ò f (t) dt and h (x) = g (x + 2) – g (x).
(b) cos log q < log cos q
x ®3 n 3
a2 is a positive a -b
f , ( g ¹ 0 ) is an odd function. g Statement 2 : If f(–x) = –f(x) for every x of its domain, then f(x) is called an odd function and if f(–x) = f(x) for every x of its domain, then f(x) is called an even function. Statement-1 : If the general equation x2 + y2 + 2xy + 2gx + 2fy + 4 = 0 represents a pair of real lines then | g |³ 2 . Statement-2 : The equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 represents pair of real lines if abc + 2fgh – af2 – bg2 – ch2 = 0. Let in a triangle ABC, the line joining orthocentre and circumcentre be parallel to the side BC. Statement-1 : tan A, tan B, tan C are in A.P. Statement-2 : If tan A, tan B, tan C are in A.P. then tan A tan C = 3. Let f be a periodic function of period 2.
(a) cos log q > log cos q
w2
75.
76.
1
w2 1 =0 is x+w
(a) x = 1 (b) x = w (c) x = w2 (d) x = 0 . The lines lx + my + n = 0, mx + ny + l = 0 and nx + ly + m = 0 are concurrent if (a) l – m – n = 0 (b) l + m – n = 0 (c) l – m + n = 0 (d) l2 + m2 + n2 = lm + mn + nl If (x, y) are the co-ordinates of a point in the plane , then
8 3 4 2
84.
5 8 2 = 0 represent x y 2
77.
78.
79.
80.
81.
(a) a. st. line || to y-axis (b) a st. line || to x-axis (c) a st. line (d) a circle The equation of the circle whose radius is 5 and which touches the circle x2 + y2– 2x – 4y–20 = 0 at the point ( 5,5) is (a) x2 + y2 + 18 x + 16 y + 120 = 0 (b) x2 + y2 – 18 x – 16 y + 120 = 0 (c) x2 + y2 – 18 x + 16 y + 120 = 0 (d) x2 + y2 + 18 x – 16 y + 120 = 0 If two circle (x – 1)2 + (y – 3)2 = r2 and x2 + y2 – 8x + 2y + 8 = 0 intersect in two distinct point , then (a) 2 < r < 8 (b) r = 2 (c) r < 2 (d) r > 2 If p : I study and q : I fail Then negation of 'I study or I fail' is (a) I do not study and I do not fail (b) I do not study or I do not fail (c) Either I study and I do not rail or I study and I do not fail (d) I study and I do not fail
h(x) = –
p 4
(b) x = n p + (–1)n + (c) x =2n p +
p ,n ÎI 4
85.
86.
83.
(a) a = 1, b = –1 (c) a = –1, b = ± 1
(b) a = 1, b = ± 1 (d) a = ± 1, b = 1
, then
(b) –1
(a)
ab (r + 1) (s + 2) (s + r) 2
(b)
ab (r – 1) (s – 1) (s – r) 2
-
(c)
ab (r – 1) (s + 1) (s – r) 2 (d) (r + 1) (s + 1) (s – r).
87.
If P and Q be two given points on the curve y = x +
1 x
uuur uuur such that OP.iˆ = 1 and OQ.iˆ = -1 where ˆi is a unit vector
along the x–axis , then the length of vector 2OP + 3OQ is (a)
88.
(b) 3 5 (c) 2 5 (d) 5 5 5 2 The area bounded by parabola y = x, st. line y = 4 and y-axis is (a)
(a) 1 (b) 6 (c) 0 (d) 3 r r r ˆ B = 4iˆ + 3jˆ + 4kˆ and C = ˆi + aˆj + bkˆ If A = ˆi + ˆj + k, r are linearly dependent vector and C = 3 , then
x 2 + x - 12
(c)
16 3
(b)
64 3
(c)
(d) x = n
82.
2(2 x + 1)
2 (d) 0 7 p : Every quadratic equation has one real root and q : Every quadratic equation has two real roots, then truth value of p and q are (a) p is true and q is false (b) p is false and q is true (c) p and q both true (d) p and q both false If (a, b), (c, d), (e, f) are the vertices of a triangle such that a, c, e are in G.P. with common ratio r and b, d, f are in G.P. with common ratio s then the area of the triangle is
(a) –2
p ,n ÎI 2
p , n ÎI 2 r r r r r r r r The value of [A - B, B - C, C - A] where | A |= 1, | B |= 2 r and | C |= 3 is
x -3 2 and , g (x) = x -3 x+4
lim [f(x) +g(x) +h(x)] is equal to x ®3
é 4 æ 3p ù ö - a ÷ + sin 4 (3p + a ) ú The expression 3 êsin ç è ø 2 ë û é ù æp ö -2 êsin 6 ç + a ÷ + sin 6 (5p - a ) ú is equal to è2 ø ë û (a) 0 (b) 1 (c) 3 (d) sin 4a + cos6a The general solution of the trigonometric equation sin x – cos x = 1 is given by (a) x = 2n p, n Î I
If f(x) =
89.
(d) None 7 2 If for a real number y, [y] is the greatest integer less than or 3p / 2
equal to y, then the values of the integral òp / 2 [2 sin x ]dx
90.
is (a) –p (b) p (c) p /2 (d) -p/2 2 If f(x) = ax + b, b ¹ 0 x £ 1; = bx2 + ax + c, x > 1, then f(x) is continuous and differentiable at x = 1 if (a) c = 0, a = 2b (b) a = b, c arbitrary (c) a = b, c = 0 (d) a = b, c ¹ 0
9
