Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2016
Exam
NDA
Year
2016
Subject
Mathematics
Chapter
Sequences and Series

NDA 2016 · Mathematics · Sequences and Series

Paragraph: Let a, x, y, z, b be in AP , where x+y+z=15 . Let a, p,...

Paragraph: Let a,x,y,z,b\mathrm{a}, \mathrm{x}, \mathrm{y}, \mathrm{z}, \mathrm{b} be in AP , where x+y+z=15\mathrm{x}+\mathrm{y}+\mathrm{z}=15. Let a,p,q,r,b\mathrm{a}, \mathrm{p}, \mathrm{q}, \mathrm{r}, \mathrm{b} be in HP , where \mathrmp−1+\mathrmq−1+\mathrmr−1=53\mathrmp^{-1}+\mathrmq^{-1}+\mathrmr^{-1}=\frac{5}{3}
Question: What is the value of xyzx y z ?

Options

  1. A120120
  2. B105105
  3. C9090
  4. DCannot be determined

Correct answer

B. 105105

Step-by-step solution

On solving eq (1) \& (2), we get (i) a=1  and b=9⇒a+4d=9⇒d=2a=1 \ \text{ and } b=9 \Rightarrow a+4 d=9 \Rightarrow d=2 (ii) a=9  and b=1⇒a+4d=1⇒d=−2\mathrm{a}=9 \ \text{ and } \mathrm{ b}=1 \Rightarrow \mathrm{a}+4 \mathrm{ d}=1 \Rightarrow \mathrm{ d}=-2. For a=1  and d=2\mathrm{a}=1 \ \text{ and } \mathrm{ d}=2, x=3,y=5  and z=7x=3, y=5 \ \text{ and } z=7 For a=9  and d=−2\mathrm{a}=9 \ \text{ and } \mathrm{ d}=-2, x=7,y=5  and z=3⇒xyz=7×5×3=105x=7, \mathrm{y}=5 \ \text{ and } \mathrm{z}=3\Rightarrow \quad x y z=7 \times 5 \times 3=105
Practice Sequences and Series on Quantrex Academy →

More from Sequences and Series

Let p , q and r be three unequal numbers such that p , q and r are in AP. If (q-p)… NDA 2026If p^ th term of an AP is k , then what is the sum of p^ th term, (p+q)^ th term and… NDA 2026If p , g_1 , g_2 and q are in GP and m is the arithmetic mean of p and q , then… NDA 2026The sum of the first n terms of an AP is 3n^2+5n . If the m^ th term of the AP is 68… NDA 2026Passage: Let X(a,p) , Y(b,q) and Z(c,r) be the points such that a , b and c are in AP.… NDA 2026If (10 + _ 10 x) , (10 + _ 10 y) and (10 + _ 10 z) are in AP, then consider the following… NDA 2025How many terms of the series 1 + 3 + 5 + 7 + … amount to a sum equal to 12345678987654321… NDA 2025For the following two (02) items: Let (6 + 10 + 14 + … up to m terms) = (1 + 3 + 5 + 7 +… NDA 2025For the following two (02) items: Let (6 + 10 + 14 + … up to m terms) = (1 + 3 + 5 + 7 +… NDA 2025How many terms are identical in the two APs 19, 21, 23, … up to 110 terms and 19, 22, 25… NDA 2025If p , 1 , q are in AP and p , 2 , q are in GP, then which of the following statements… NDA 2025The sum of the first 8 terms of a GP is five times the sum of its first 4 terms. If r ≠ 1… NDA 2025If 5th, 7th and 13th terms of an AP are in GP, then what is the ratio of its first term… NDA 2025The sum of the first k terms of a series S is 3k^2 + 5k . Which one of the following is… NDA 2025What is the harmonic mean of the numbers C(10,3) , C(10,4) , C(10,5) , C(10,6) and… NDA 2025If p times the p^ th term of an AP is equal to q times the q^ th term (p ≠ q) , then what… NDA 2024 Full Sequences and Series list Sequences and Series JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs