28 Questions
Which shape is described by the equation x^2 + y^2 = 3?
Circle
If a particle moving in a circle of radius $R$ with uniform speed takes time $T$ to complete one revolution, what is the angle of projection ($\theta$) when the particle is projected at the maximum height equal to 4R?
$60^\circ$
What is the center of the circle with the equation x^2 + y^2 = 3?
(0, 0)
A galvanometer with a resistance of 50 ohms can be converted into a voltmeter to measure up to 100V by connecting a resistor in series. What should be the resistance of this additional series resistor?
19950 ohms
If a line passes through the point of intersection of a circle and a parabola in the first quadrant, which quadrant(s) can this point lie in?
First Quadrant
If the de Broglie wavelengths of a proton and an alpha particle are $\lambda$ and $2\lambda$ respectively, what is the ratio of their velocities?
1:2
In a Vernier caliper where 10 main scale divisions coincide with 11 Vernier scale divisions, and each main scale division is 5 units, what is the least count of the instrument?
$\frac{10}{11}$ units
In which quadrant can the centers Q1 and Q2 of circles C1 and C2 lie if the line they lie on intersects the y-axis?
First Quadrant
In a series LCR circuit where the capacitance changes from C to 4C while keeping the resonance frequency unchanged, how should the inductance change?
Reduced by L/3
What is the shortest distance between two lines L1 and L2 at points P and Q respectively called?
Perpendicular Distance
If (α, β, γ) is the midpoint of a line segment PQ, what is 2(α + β + γ)?
(0, 6, 0)
What is the position of the particle when the time is t = 4s?
28 m
At what time does the velocity of the particle reach its maximum value?
3 s
What is the magnitude of the force acting on the particle when its acceleration is zero?
$45, \text{N}$
What is the total charge that flows through the conductor from t = 0s to t = 2s?
120 C
What is the ideal lift force acting on the plane during level flight?
$7,200, \text{N}$
If the air density is doubled, what will be the new lift force acting on the plane?
$6,480, \text{N}$
What is the correct reagent for the conversion CH3(CH2)5–C–OC2H5 to CH3(CH2)5CHO?
CH3MgBr, H2O
Which of the following reagents is NOT correctly matched with its respective conversion?
CH3COCH2COOC2H5 → CH3C(OH)CH2COOC2H5: DIBAL-H, H2O
In Kjeldahl’s method for estimation of nitrogen, what role does CuSO4 play?
Oxidising agent
Which statement about Potassium hydrogen phthalate (KHP) as a primary standard is true?
KHP is a primary standard often employed in standardizing sodium hydroxide solutions
What is the correct order of Vant' Hoff factor (i) for the NaCl solutions with concentrations 0.1 M, 0.01 M, and 0.001 M?
$i_A < i_C < i_B$
According to the given reactions and reagents list, which sequence correctly matches the conversions with the corresponding reagents?
A-(III), B-(IV), C-(II), D-(I)
Which of the following statements is correct regarding aminobenzene and aniline?
Statement I is correct but Statement II is incorrect
Which of the following complexes is homoleptic?
[Fe(NH3)4Cl2]+
In the given reaction sequence, which compound will most easily be attacked by an electrophile?
(A) = CHO
Ionic reactions with organic compounds primarily proceed through:
Heterolytic bond cleavage
Arrange the bonds in order of increasing ionic character in the molecules LiF, K2O, N2, SO2, and ClF3.
N2 < SO2 < ClF3 < K2O < LiF
Test your knowledge of geometry and analytical mathematics with questions involving circles, lines, and areas of triangles. Solve problems related to intersections, points, and distances in the first quadrant.
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