{
 "version": 1,
 "note": "CBSE Jeopardy boards, generated by scripts/build-cbse-jeopardy.js from the verified CBSE chapter banks (question_banks/cbse): one-part, diagram-free, no-calculator questions; each answer is the bank's keyed option, re-solved independently in question_banks/verification/cbse/verify_cbse_teacher_tools.py. Each cell's src is its question id. Do not edit by hand.",
 "tiers": [
  100,
  200,
  300,
  400,
  500
 ],
 "courses": {
  "cbse10": {
   "label": "CBSE Class 10 Mathematics",
   "categories": [
    {
     "title": "Numbers & poly­nomials",
     "cells": [
      {
       "q": "The LCM of \\(84\\) and \\(120\\) is",
       "a": "\\(840\\)",
       "src": "cbse10-ch01-q003"
      },
      {
       "q": "If \\(2\\) is a zero of \\(3x^2 - 8x + k\\), then the value of \\(k\\) is",
       "a": "\\(4\\)",
       "src": "cbse10-ch02-q003"
      },
      {
       "q": "The HCF of any two consecutive even natural numbers is",
       "a": "\\(2\\)",
       "src": "cbse10-ch01-q008"
      },
      {
       "q": "If the zeroes of \\(2x^2 + kx - 6\\) are equal in magnitude but opposite in sign, then \\(k\\) equals",
       "a": "\\(0\\)",
       "src": "cbse10-ch02-q009"
      },
      {
       "q": "If \\(\\alpha, \\beta\\) are the zeroes of \\(x^2 - 6x + k\\) and \\(\\alpha^2 + \\beta^2 = 20\\), then \\(k\\) is",
       "a": "\\(8\\)",
       "src": "cbse10-ch02-q010"
      }
     ]
    },
    {
     "title": "Equations & APs",
     "cells": [
      {
       "q": "The roots of \\(x^2 = 3x\\) are",
       "a": "\\(0\\) and \\(3\\)",
       "src": "cbse10-ch04-q012"
      },
      {
       "q": "The sum of the first \\(20\\) odd natural numbers is",
       "a": "\\(400\\)",
       "src": "cbse10-ch05-q006"
      },
      {
       "q": "If the \\(n\\)th term of an AP is \\(a_n = 5 - 3n\\), then its common difference is",
       "a": "\\(-3\\)",
       "src": "cbse10-ch05-q007"
      },
      {
       "q": "The \\(10\\)th term from the end of the AP \\(4, 9, 14, \\ldots, 254\\) is",
       "a": "\\(209\\)",
       "src": "cbse10-ch05-q008"
      },
      {
       "q": "A bus covers \\(480\\) km at a uniform speed of \\(x\\) km/h. Had the speed been \\(20\\) km/h more, it would have taken \\(2\\) hours less. The equation satisfied by \\(x\\) is",
       "a": "\\(x^2 + 20x - 4800 = 0\\)",
       "src": "cbse10-ch04-q011"
      }
     ]
    },
    {
     "title": "Triangles, circles & coordi­nates",
     "cells": [
      {
       "q": "All ________ triangles are similar.",
       "a": "equilateral",
       "src": "cbse10-ch06-q001"
      },
      {
       "q": "The number of tangents to a circle that are parallel to a given secant is",
       "a": "2",
       "src": "cbse10-ch10-q001"
      },
      {
       "q": "In \\(\\triangle ABC\\) and \\(\\triangle PQR\\), \\(\\dfrac{AB}{PQ} = \\dfrac{AC}{PR}\\) and \\(\\angle A = \\angle P\\). The triangles are similar by",
       "a": "SAS",
       "src": "cbse10-ch06-q009"
      },
      {
       "q": "\\(ABCD\\) is a trapezium with \\(AB \\parallel DC\\) and \\(AB = 2\\,DC\\). Its diagonals meet at \\(O\\). If \\(OC = 4\\) cm, then \\(OA\\) is",
       "a": "\\(8\\) cm",
       "src": "cbse10-ch06-q010"
      },
      {
       "q": "In \\(\\triangle ABC\\), \\(DE \\parallel BC\\) with \\(D\\) on \\(AB\\) and \\(E\\) on \\(AC\\). If \\(AD = x + 1\\), \\(DB = x - 1\\), \\(AE = x + 5\\) and \\(EC = x\\) (all in cm), then \\(x\\) equals",
       "a": "\\(\\dfrac53\\)",
       "src": "cbse10-ch06-q011"
      }
     ]
    },
    {
     "title": "Trigono­metry",
     "cells": [
      {
       "q": "If \\(\\cos A = \\frac{5}{13}\\), where \\(A\\) is acute, then \\(\\tan A\\) equals",
       "a": "\\(\\frac{12}{5}\\)",
       "src": "cbse10-ch08-q002"
      },
      {
       "q": "From the top of a 25 m high cliff, the angle of depression of a boat is \\(45^\\circ\\). The distance of the boat from the foot of the cliff is",
       "a": "\\(25\\) m",
       "src": "cbse10-ch09-q004"
      },
      {
       "q": "If \\(2\\sin 2\\theta = \\sqrt{3}\\) and \\(2\\theta\\) is acute, then \\(\\theta\\) is",
       "a": "\\(30^\\circ\\)",
       "src": "cbse10-ch08-q005"
      },
      {
       "q": "An observer walks towards the foot of a tall building along level ground. The angle of elevation of the top of the building",
       "a": "increases",
       "src": "cbse10-ch09-q006"
      },
      {
       "q": "Points \\(A\\) and \\(B\\) on level ground are on the same side of a tower of height \\(h\\) and in line with its foot. The angles of elevation of the top of the tower from \\(A\\) and \\(B\\) are \\(45^\\circ\\) and \\(60^\\circ\\) respectively. Then \\(AB\\) equals",
       "a": "\\(\\dfrac{h(\\sqrt3-1)}{\\sqrt3}\\)",
       "src": "cbse10-ch09-q008"
      }
     ]
    },
    {
     "title": "Mensur­ation, statis­tics & proba­bility",
     "cells": [
      {
       "q": "The probability of a sure event is",
       "a": "1",
       "src": "cbse10-ch14-q009"
      },
      {
       "q": "Two coins are tossed together. The probability of getting at least one head is",
       "a": "\\(\\frac34\\)",
       "src": "cbse10-ch14-q003"
      },
      {
       "q": "A card is drawn from a well-shuffled pack of 52 cards. The probability that it is a black card bearing a number from 2 to 10 is",
       "a": "\\(\\frac{9}{26}\\)",
       "src": "cbse10-ch14-q004"
      },
      {
       "q": "In the step-deviation method, \\(a = 45\\), \\(h = 10\\), \\(\\sum f_iu_i = 8\\) and \\(\\sum f_i = 40\\). The mean is",
       "a": "47",
       "src": "cbse10-ch13-q005"
      },
      {
       "q": "The digits 1, 2 and 3 are arranged at random to form a three-digit number, each digit used exactly once. The probability that the number is even is",
       "a": "\\(\\frac13\\)",
       "src": "cbse10-ch14-q006"
      }
     ]
    }
   ]
  },
  "cbse12": {
   "label": "CBSE Class 12 Mathematics",
   "categories": [
    {
     "title": "Relations & inverse trig",
     "cells": [
      {
       "q": "The range of the principal value branch of \\(\\sec^{-1}x\\) is",
       "a": "\\([0, \\pi] - \\left\\{\\dfrac{\\pi}{2}\\right\\}\\)",
       "src": "cbse12-ch02-q005"
      },
      {
       "q": "The value of \\(\\sin^{-1}\\left(\\sin\\dfrac{4\\pi}{5}\\right)\\) is",
       "a": "\\(\\dfrac{\\pi}{5}\\)",
       "src": "cbse12-ch02-q006"
      },
      {
       "q": "The value of \\(\\cot^{-1}(-1) + \\sin^{-1}\\left(-\\dfrac{\\sqrt3}{2}\\right)\\) is",
       "a": "\\(\\dfrac{5\\pi}{12}\\)",
       "src": "cbse12-ch02-q002"
      },
      {
       "q": "The relation \\(R = \\{(1, 1), (2, 2), (1, 2), (2, 1), (2, 3)\\}\\) on the set \\(\\{1, 2, 3\\}\\) is",
       "a": "neither reflexive, nor symmetric, nor transitive",
       "src": "cbse12-ch01-q001"
      },
      {
       "q": "The value of \\(\\sin^{-1}(\\sin 3) + \\cos^{-1}(\\cos 5)\\), where the angles are in radians, is",
       "a": "\\(3\\pi - 8\\)",
       "src": "cbse12-ch02-q012"
      }
     ]
    },
    {
     "title": "Matrices & deter­minants",
     "cells": [
      {
       "q": "The \\(3 \\times 3\\) matrix \\(A = [a_{ij}]\\) with \\(a_{ij} = i^2 - j^2\\) is",
       "a": "a skew-symmetric matrix",
       "src": "cbse12-ch03-q002"
      },
      {
       "q": "If \\(A\\) is an invertible square matrix such that \\(A^2 = A\\), then \\(A\\) equals",
       "a": "\\(I\\)",
       "src": "cbse12-ch03-q011"
      },
      {
       "q": "The product of the values of \\(x\\) satisfying \\(\\begin{vmatrix}x & 3 & 0\\\\ 2 & x & 1\\\\ 0 & 4 & 1\\end{vmatrix} = 0\\) is",
       "a": "\\(-6\\)",
       "src": "cbse12-ch04-q012"
      },
      {
       "q": "If \\(A = \\begin{bmatrix}0 & 1\\\\ -1 & 0\\end{bmatrix}\\), then \\(A^{2026}\\) equals",
       "a": "\\(-I\\)",
       "src": "cbse12-ch03-q005"
      },
      {
       "q": "\\(A\\) is a square matrix of order \\(3\\) such that \\(A(\\mathrm{adj}\\,A) = 5I\\). Then \\(|\\mathrm{adj}(2A)|\\) equals",
       "a": "\\(1600\\)",
       "src": "cbse12-ch04-q010"
      }
     ]
    },
    {
     "title": "Calculus",
     "cells": [
      {
       "q": "\\(\\dfrac{d}{dx}\\left[\\sin^2 (3x)\\right]\\) equals",
       "a": "\\(3\\sin 6x\\)",
       "src": "cbse12-ch05-q003"
      },
      {
       "q": "If the area of the region bounded by the line \\(y = kx\\) \\((k > 0)\\), the \\(x\\)-axis and the line \\(x = 3\\) is \\(18\\) sq units, then \\(k\\) equals",
       "a": "\\(4\\)",
       "src": "cbse12-ch08-q007"
      },
      {
       "q": "If \\(f(x) = x^3 + ax^2 + bx\\) has local extrema at \\(x = 1\\) and \\(x = 3\\), then",
       "a": "\\(a = -6,\\ b = 9\\)",
       "src": "cbse12-ch06-q011"
      },
      {
       "q": "If \\(y = e^{mx}\\) is a solution of \\(\\dfrac{d^2y}{dx^2} - 5\\dfrac{dy}{dx} + 6y = 0\\), then the set of possible values of \\(m\\) is",
       "a": "\\(\\{2, 3\\}\\)",
       "src": "cbse12-ch09-q010"
      },
      {
       "q": "For \\(t > 0\\), let \\(A(t)\\) denote the area of the region bounded by the parabola \\(y^2 = 4x\\) and the line \\(x = t\\). Then \\(\\dfrac{A(4t)}{A(t)}\\) equals",
       "a": "\\(8\\)",
       "src": "cbse12-ch08-q012"
      }
     ]
    },
    {
     "title": "Vectors & 3D geo­metry",
     "cells": [
      {
       "q": "\\((2\\hat{i} - \\hat{j}) \\times (\\hat{i} + 3\\hat{k})\\) equals",
       "a": "\\(-3\\hat{i} - 6\\hat{j} + \\hat{k}\\)",
       "src": "cbse12-ch10-q008"
      },
      {
       "q": "A unit vector perpendicular to both \\(\\hat{i} + \\hat{j}\\) and \\(\\hat{j} + \\hat{k}\\) is",
       "a": "\\(\\tfrac{1}{\\sqrt3}(\\hat{i} - \\hat{j} + \\hat{k})\\)",
       "src": "cbse12-ch10-q011"
      },
      {
       "q": "A vector \\(\\vec{r}\\) makes an angle \\(\\dfrac{\\pi}{4}\\) with the \\(z\\)-axis and equal acute angles with the \\(x\\)- and \\(y\\)-axes. Its direction cosines are",
       "a": "\\(\\tfrac12,\\ \\tfrac12,\\ \\tfrac{1}{\\sqrt2}\\)",
       "src": "cbse12-ch10-q002"
      },
      {
       "q": "The points on the line \\(\\dfrac{x - 1}{2} = \\dfrac{y + 3}{-2} = \\dfrac{z - 2}{1}\\) at a distance of \\(6\\) units from \\((1, -3, 2)\\) are",
       "a": "\\((5, -7, 4)\\ \\text{and}\\ (-3, 1, 0)\\)",
       "src": "cbse12-ch11-q007"
      },
      {
       "q": "If \\(|\\vec{a}| = 2\\), \\(|\\vec{b}| = 3\\) and the angle between \\(\\vec{a}\\) and \\(\\vec{b}\\) is \\(\\dfrac\\pi3\\), then \\(|(\\vec{a} + 2\\vec{b}) \\times (3\\vec{a} - \\vec{b})|\\) equals",
       "a": "\\(21\\sqrt3\\)",
       "src": "cbse12-ch10-q010"
      }
     ]
    },
    {
     "title": "Linear program­ming & proba­bility",
     "cells": [
      {
       "q": "The feasible region for the constraints \\(x + y \\ge 6,\\ x + y \\le 4,\\ x \\ge 0,\\ y \\ge 0\\) is",
       "a": "empty",
       "src": "cbse12-ch12-q005"
      },
      {
       "q": "The system of constraints \\(y \\ge 2x + 3,\\ 2x - y \\ge 1,\\ x \\ge 0,\\ y \\ge 0\\) has",
       "a": "no feasible solution",
       "src": "cbse12-ch12-q008"
      },
      {
       "q": "The minimum value of \\(Z = x + y\\) subject to \\(x + 2y \\ge 8,\\ 3x + 2y \\ge 12,\\ x \\ge 0,\\ y \\ge 0\\) is",
       "a": "\\(5\\)",
       "src": "cbse12-ch12-q006"
      },
      {
       "q": "Three penalty takers score independently with probabilities \\(0.9\\), \\(0.8\\) and \\(0.5\\). The probability that exactly two of them score is",
       "a": "\\(0.49\\)",
       "src": "cbse12-ch13-q009"
      },
      {
       "q": "The corner points of the bounded feasible region of an LPP are \\(O(0, 0)\\), \\(A(4, 0)\\), \\(B(3, 3)\\) and \\(C(0, 5)\\). The objective function \\(Z = x + ky\\) \\((k \\gt 0)\\) has its maximum at \\(B\\) only, if and only if",
       "a": "\\(\\tfrac13 \\lt k \\lt \\tfrac32\\)",
       "src": "cbse12-ch12-q009"
      }
     ]
    }
   ]
  }
 }
}