Math Test 1
The remainder when −46 is divided by 3 is :
  • −1
  • 1
  • 2
Explanation: Find a number that multiplies with 3 close to – 46 • 3 × (–16) = –48 Now: – 46 – (– 48) = –46 + 48 = 2 Ans: The remainder is 2
If Pn represents the product of the natural numbers from 1 to n, then P1+P2+P3+P4 is :
  • 23
  • 33
  • 37
  • 31
Explanation:

To find P1+P2+P3+P4, we first need to calculate the factorials for each value of nn:

  • P1=1!
  • P2=2!=2×1=2
  • P3=3!=3×2×1=6
  • P4=4!=4×3×2×1=24

Now, we sum them up:

P1+P2+P3+P4=1+2+6+24

Calculating the sum:

1+2=3
3+6=9
9+24=33

Thus, the value of P1+P2+P3+P4 is: (B) 33.

A cone has a base radius of 4 cm and height of 9 cm. The volume of the cone is :
  • 36π cm3
  • 48π cm3
  • 13π cm3
  • 24π cm3
Explanation: Volume of a Cone Formula: V=1/3πr2h Given: • Radius (r) = 4 cm • Height (h) = 9 cm Step-by-step: • Square the radius: r2=42=16 • Multiply: 16×9=144 • Multiply by 1/3 : 1/3×144=48 Add π: V=48π cm3 Ans: Volume = 48π cm³
If sinθ=cosθ then the value of 1+tanθ is :
  • 1
  • 2
  • 0
  • sqrt 2
Explanation: Given: Sinθ = Cosθ Divide both sides by Cosθ Sinθ / Cosθ = Cosθ/cosθ tanθ=1 Add 1 to tanθ 1+tanθ = 1+1 = 2 Ans: 2
The least natural number which when divided by 2 gives remainder 1, when divided by 3 gives remainder 2 and when divided by 4 gives remainder 3, is :
  • 23
  • 17
  • 31
  • 11
Explanation: We are given: • N = 1(mod 2) • N = 2(mod 3) • N = 3(mod 4) Notice a pattern We can rewrite each condition like this: • N+1 is divisible by 2 • N+1 is divisible by 3 • N+1 is divisible by 4 So: N+1 is a common multiple of 2,3,4 Find the least common multiple (LCM) LCM(2,3,4)=12 So: N+1=12 ⇒ N=11 But 11 doesn't work for all conditions. Try: N+1=24 ⇒ N=23 Check N=23 • 23mod  2=1 • 23mod  3=2 • 23mod  4=3 Ans: 23 is the smallest natural number that satisfies all 3 conditions.
72 toffees were distributed to some boys in a group. Each boy in the group got twice as many of the toffees as the number of boys. The number of boys in the group is :
  • 6
  • 7
  • 8
  • 9
Explanation: Given: • Each boy gets 2×(number of boys) toffees. • Total toffees = 72 Let number of boys = x • Each boy gets 2x toffees • Total toffees = x × 2x = 2x² So: 2x²=72 Solve: x² = 36 (Divide both sides by 2) x = 6 (Take square root) Ans: Number of boys = 6
The product of the roots of the quadratic equation 2x2−5x+6=0 is :
  • 2
  • 3
    • Explanation: Given equation: 2x^2−5x+6=0 Coefficients: • a=2 • b=−5 • c=6 Formula for product of roots: Product of roots = c/a Substitute values: 6/2 = 3 Final Answer: Product of the roots = 3