with actual JEE/NEET standard questions as type=DPS (PrepPilot AI)
and a separate Mock CBT test as type=CBT (Mock Tests section)
"""
importuuid
fromsqlmodelimportSession,select
fromdatetimeimportdatetime
fromdatabaseimportengine
importmodels
PHYSICS_QUESTIONS=[
{
"text":"A body of mass 5 kg is acted upon by two perpendicular forces 8 N and 6 N. The magnitude and direction of the resultant with respect to the 6 N force is:",
"options":{"A":"10 N at 53°","B":"10 N at 37°","C":"8 N at 45°","D":"14 N at 0°"},
"answer":"A",
"solution":"Resultant R = √(8² + 6²) = √(64+36) = √100 = 10 N. tan θ = 8/6 = 4/3 → θ = 53° from the 6N force."
},
{
"text":"A ball is thrown vertically upward with velocity 20 m/s. The maximum height reached is: (g = 10 m/s²)",
"solution":"Using v² = u² - 2gh. At max height v=0. h = u²/2g = (20)²/(2×10) = 400/20 = 20 m."
},
{
"text":"The ratio of radii of gyration of a circular disc to that of a circular ring, each of the same mass and radius, about their axes passing through their centres and perpendicular to their planes is:",
"text":"Two charges of +4μC and -4μC are placed at (3, 0) and (-3, 0) cm. The electric field at origin due to this dipole is:",
"options":{"A":"4 × 10⁸ N/C along +x","B":"4 × 10⁸ N/C along -x","C":"8 × 10⁸ N/C along +x","D":"Zero"},
"answer":"A",
"solution":"Each charge contributes E = kq/r² = (9×10⁹ × 4×10⁻⁶)/(0.03)² = 4×10⁷ N/C. Both fields point in +x direction. Total = 8×10⁷ N/C along +x."
},
{
"text":"A wire of length L and resistance R is uniformly stretched to double its length. New resistance is:",
"options":{"A":"R/2","B":"R","C":"2R","D":"4R"},
"answer":"D",
"solution":"ρ is constant. Volume = AL = constant. New length L' = 2L → new area A' = A/2. R' = ρ(2L)/(A/2) = 4ρL/A = 4R."
},
{
"text":"In Young's double slit experiment, the slits are 0.5 mm apart and interference fringes are observed on a screen 1.0 m away. It is found that the 9th bright fringe is at a distance of 8.835 mm from the 2nd dark fringe. Find the wavelength of light:",
"text":"A solid sphere of radius R has a charge Q uniformly distributed over its volume. The magnitude of electric field at distance r from the center (r < R) is:",
"solution":"Gamma rays have the highest penetrating power due to their extremely short wavelength and high energy. They can penetrate through several cm of lead."
},
{
"text":"A bar magnet of magnetic moment M is placed in a uniform magnetic field B. The torque on the magnet when it makes angle 30° with the field is:",
"text":"The de Broglie wavelength associated with a proton moving with velocity v is λ. For an alpha particle moving with the same speed, the de Broglie wavelength will be:",
"solution":"Lattice energy ∝ (charge of ions)²/distance. MgO has doubly charged ions (Mg²⁺ and O²⁻) giving it much higher lattice energy than singly-charged ion compounds."
},
{
"text":"The pH of 0.001 M H₂SO₄ solution is:",
"options":{"A":"3","B":"2.7","C":"2","D":"1"},
"answer":"B",
"solution":"H₂SO₄ is a strong diprotic acid. [H⁺] = 2 × 0.001 = 0.002 M. pH = -log(0.002) = -log(2×10⁻³) = 3 - log2 = 3 - 0.301 ≈ 2.7."
},
{
"text":"Which of the following undergoes SN1 reaction most readily?",
"solution":"SN1 rate depends on carbocation stability. Tertiary carbocations are most stable due to hyperconjugation and inductive effect of alkyl groups. (CH₃)₃C⁺ is tertiary."
},
{
"text":"The oxidation state of Cr in K₂Cr₂O₇ is:",
"solution":"H₂O has highest BP due to hydrogen bonding. Among H₂S, H₂Se, H₂Te: BP increases with molar mass (van der Waals forces). So H₂O > H₂Te > H₂Se > H₂S."
},
{
"text":"Identify the product formed when acetaldehyde reacts with excess HCN followed by hydrolysis:",
"text":"Which of the following is NOT a property of transition metals?",
"options":{"A":"They show variable oxidation states","B":"They form colored compounds","C":"They have low melting points","D":"They act as catalysts"},
"answer":"C",
"solution":"Transition metals generally have high melting points due to strong metallic bonds involving d electrons. Options A, B, and D are characteristic properties of transition metals."
},
{
"text":"The reaction of glucose with excess acetic anhydride gives:",
"solution":"Increasing pressure favors the reaction with fewer moles of gas. N₂+3H₂→2NH₃: reactants have 4 mol gas, products have 2. Pressure increase shifts equilibrium right."
},
]
MATH_QUESTIONS=[
{
"text":"If f(x) = x² - 3x + 2, then f(f(x)) = 0 has how many solutions?",
"solution":"Mitochondria produce ATP through cellular respiration (oxidative phosphorylation), providing energy for cellular activities. Hence called the powerhouse."
},
{
"text":"The process by which organisms maintain internal equilibrium is called:",
"solution":"Homeostasis is the ability of an organism to maintain a stable internal environment (temperature, pH, glucose levels) despite external changes."
"solution":"Chloroplasts contain chlorophyll and are the sites of photosynthesis. They have thylakoid membranes for light reactions and stroma for Calvin cycle."
},
{
"text":"Which of the following is an example of a vestigial organ in humans?",
"solution":"The vermiform appendix is a vestigial organ in humans - it was functional in ancestors who digested cellulose but has reduced to a non-functional remnant."
"solution":"The Krebs (citric acid) cycle occurs in the matrix of mitochondria. It oxidizes acetyl-CoA and generates NADH, FADH₂, and ATP."
},
{
"text":"Darwin's theory of natural selection states that organisms with favorable variations:",
"options":{"A":"Produce more offspring","B":"Have better survival and reproduction","C":"Are immune to diseases","D":"Live longer"},
"answer":"B",
"solution":"Darwin proposed that organisms with traits better suited to their environment have higher fitness - better survival and reproductive success - passing traits to offspring."
},
{
"text":"The enzyme responsible for DNA replication is:",
<CardclassName="border-border bg-card shadow-[0_4px_24px_rgba(0,0,0,0.3)] flex-1 flex flex-col group hover:border-[#00F0FF]/30 transition-colors">
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