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2019 29 questions

1. Q282019 · 11 Jan 2019 · Shift 2

   Let $S_n=1+q+q^2+\dots +q^n$ and $T_n=1+\left(\frac{q+1}{2}\right)+{\left(\frac{q+1}{2}\right)}^2+\dots +{\left(\frac{q+1}{2}\right)}^n$ where q is a real number and $q\ne 1$. If ${}^{101}{\mathrm{C}}_1+{}^{101}{\mathrm{C}}_2\cdot S_1+\dots +{}^{101}{\mathrm{C}}_{101}\cdot S_{100}=\alpha T_{100}$ then $\alpha$ is equal to

   1. A.202
   2. B.200
   3. C.$2^{100}$
   4. D.$2^{99}$
   Show answer

   Answer: C

2. Q12019 · 9 Jan 2019 · Shift 1

   Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is :

   1. A.500
   2. B.350
   3. C.200
   4. D.300
   Show answer

   Answer: D

3. Q82019 · 9 Jan 2019 · Shift 1

   If the fractional part of the number $\left\{\frac{2^{403}}{15}\right\}$ is $\frac{k}{15}$, then k is equal to :

   1. A.8
   2. B.14
   3. C.6
   4. D.1
   Show answer

   Answer: A

4. Q112019 · 9 Jan 2019 · Shift 1

   Let $A=\left\{\theta \in \left(-\frac{\pi }{2},\pi \right):\frac{3+2i\sin \theta }{1-2i\sin \theta }\text{ is purely imaginary}\right\}$. Then the sum of the elements in A is :

   1. A.$\frac{5\pi }{6}$
   2. B.$\pi$
   3. C.$\frac{3\pi }{4}$
   4. D.$\frac{2\pi }{3}$
   Show answer

   Answer: D