If the roots of the quadratic equation x² − 5x + k = 0 are real and equal, what is the value of k?
Mathematics
Question · Easy
What is the value of lim(x→0) (sin 3x)/(tan 5x)?
A particle moves in a straight line with velocity v = 3t² − 6t m/s. What is its acceleration at t = 2 s?
Physics
Which of the following compounds exhibits geometrical (cis-trans) isomerism?
Chemistry
Choose the option that best fills the blank: 'The committee ____ divided in its opinion on the new policy.'
English
If A = {1, 2, 3} and B = {3, 4, 5}, what is A ∩ B?
What is the derivative of f(x) = x³ ln(x)?
Question · Medium
The value of ∫(0 to 1) x² dx equals:
If sin θ = 3/5 and θ is in the first quadrant, what is cos 2θ?
A car accelerates uniformly from rest and covers 100 m in 10 s. What is its acceleration?
Two charges +4 μC and −4 μC are placed 10 cm apart. What is the electric dipole moment magnitude?
A ball is thrown vertically upward with initial velocity 20 m/s. Take g = 10 m/s². What is the maximum height reached?
The de Broglie wavelength of a particle is inversely proportional to its:
Which of the following has the highest first ionization energy?
The hybridization of carbon atoms in ethene (C₂H₄) is:
What is the pH of a 0.01 M HCl solution?
A train travels from City P to City Q at 60 km/h and returns at 40 km/h. What is the average speed for the round trip?
Quantitative Aptitude
Choose the word most opposite in meaning to 'BENEVOLENT':
If log₁₀ 2 = 0.301 and log₁₀ 3 = 0.477, what is log₁₀ 6?
The number of ways to arrange the letters of the word 'AEEE' is:
The vectors a = 2î + 3ĵ − k̂ and b = î − ĵ + 2k̂ are:
What is the equation of the line passing through (2, 3) with slope 4?
The eccentricity of the ellipse x²/25 + y²/16 = 1 is:
A force of 10 N acts on a body of mass 2 kg. What is the acceleration?
What is the moment of inertia of a uniform thin rod of mass M and length L about an axis through its center and perpendicular to its length?
A wave on a string has frequency 200 Hz and wavelength 0.5 m. What is its speed?
The empirical formula of a compound with 40% carbon, 6.67% hydrogen, and 53.33% oxygen by mass is:
Which of the following is the strongest reducing agent?
Question · Hard
Identify the part of the sentence that contains an error: 'Neither of the boys (A)/ have completed (B)/ their assignments (C)/ on time. (D)'
If 2x + 3y = 12 and 3x + 2y = 13, what is the value of x + y?
What is the determinant of the matrix [[2, 3], [4, 5]]?
The probability of drawing a king from a standard 52-card deck is:
The sum of the first n natural numbers is given by:
What is the value of i⁴⁹, where i = √(−1)?
If f(x) = 2x + 3 and g(x) = x², what is f(g(2))?
The angle between vectors a = î + ĵ and b = î − ĵ is:
The sum of the geometric series 1 + 1/2 + 1/4 + ... to infinity is:
What is the area enclosed by the parabola y = x² and the line y = 4?
If sin x = cos x, what is the smallest positive value of x in degrees?
The distance between the points (3, 4) and (−1, 1) in a Cartesian plane is:
The general solution of the differential equation dy/dx = y is:
If the mean of 5 numbers is 12 and one of them is 16, what is the mean of the remaining 4 numbers?
The work done in stretching a spring of force constant k by distance x is:
A 60-W bulb operates at 120 V. What current does it draw?
The unit of magnetic flux is:
The refractive index of a medium with respect to vacuum is 1.5. What is the speed of light in this medium?
Which law states 'the rate of change of momentum of a body is proportional to the applied force'?
The angle of incidence for total internal reflection at a water-air interface (n_water = 4/3) is approximately:
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