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Browse complete papersIf the number obtained after subtracting x from 2035 leaves the same remainder 5 when it is divided by 9,10 and 15, then the smallest possible x is
50
55
150
220
Correct answer
50
\(1 . \overline{27}+0 . \overline{94}=\)
\(2 . \overline{21}\)
\(2 . \overline{2}\)
\(1. \overline{2794}\)
\(\frac{219}{53}\)
Correct answer
\(2 . \overline{21}\)
Let A = {(a, b, c)/c2 = a2 + b2}. If (3, 5, x), (y, 3, 7), (1, z, 5) are three elements of the set 'A' and the LCM of x2, y2, z2 is \(\rm p_1^{\alpha_1} p_2^{\alpha_2} p_3^{\alpha_3} p_4^{\alpha_4}\) where p1, p2, p3, p4 are primes, then \(\rm \frac{p_1+p_2+p_3+p_4}{\alpha_1+\alpha_2+\alpha_3+\alpha_4}=\)
\(\frac{9}{2}\)
\(\frac{7}{9}\)
\(\frac{26}{8}\)
\(\frac{9}{5}\)
Correct answer
\(\frac{9}{2}\)
If the number of numbers between 100 and 1000 that are divisible by 11 is x, then the number of total divisors of x is
81
5
3
4
Correct answer
81
Match the items of the following lists.
| List - A | List - B | ||
|---|---|---|---|
| (a) | a, b are prime numbers | (i) | LCM of a, b ≤ ab |
| (b) | a, b are composite numbers | (ii) | Conjugate surds |
| (c) | \(1.34 \overline{54}\) | (iii) | Irrational number |
| (d) | \((\sqrt[3]{2}+3 \sqrt{5})(\sqrt[3]{2}-3 \sqrt{5})\) | (iv) | Rational number |
| (v) | Co-prime numbers |
Correct answer is
a - i, b - v, c - iii, d - ii
a - i, b - ii, c - iv, d - iii
a - v, b - i, c - iv, d - iii
a - v, b - i, c - iii, d - ii
Correct answer
a - i, b - v, c - iii, d - ii
Let P1, P2, P3 be prime numbers and α, β, γ be positive integers. If \(\rm P_1^\alpha P_2^\beta P_3^\gamma\) is a divisor of 34864764 lying between 100 and 200, then (P1 + P2 + P3) (α + β + γ) =
64
35
72
88
Correct answer
64
\(x=\frac{1}{2+\frac{1}{2+\frac{1}{2+\cdot \ddots_{\infty}}}}\) then x =
\(\frac{\sqrt{2}-1}{2}\)
\(\frac{\sqrt{2}+1}{2}\)
√2 - 1
-1 - √2
Correct answer
\(\frac{\sqrt{2}-1}{2}\)
If x, y, z are three positive numbers such that (A - x) ∶ (A - y) ∶ (A - z) 1 ∶ 7 ∶ 4 and 2A = x + y + z, then x ∶ y ∶ z =
8 ∶ 5 ∶ 11
9 ∶ 4 ∶ 12
11 ∶ 5 ∶ 8
12 ∶ 4 ∶ 9
Correct answer
8 ∶ 5 ∶ 11
If x ≠ y ≠ z ≠ 0, ax = by = cz and \(\frac{a}{b}=\frac{b}{c} \), then \(\frac{y-x}{z-y}=\)
\(\frac{x}{z}\)
\(\frac{x}{y}\)
\(\frac{y}{z}\)
\(\frac{x+y}{y+z}\)
Correct answer
\(\frac{x}{z}\)
Two different discounts x% and y% are allowed on two items having same cost price and marked price. If P1% and P2% are respectively the profits on them, x - y = 20 and P2 - P1 = 32, then the ratio of their cost price to their marked price is
52 ∶ 12
10 ∶ 18
5 ∶ 8
16 ∶ 5
Correct answer
52 ∶ 12