Given ∣a∣=2, ∣b∣=3, and a⋅b=4
For any two vectors, the magnitude of their difference is:
∣a−b∣2=∣a∣2+∣b∣2−2(a⋅b)
Substituting the given values:
∣a−b∣2=(2)2+(3)2−2(4)
∣a−b∣2=4+9−8
∣a−b∣2=5
Taking the square root:
∣a−b∣=5
Therefore, ∣a−b∣=5
Which of the following statements are correct about the Compound Annual Growth Rate (CAGR)?
(A) It can be used to compare historical returns on different investment portfolios.
(B) It helps smooth returns when growth rates are expected to be volatile and inconsistent.
(C) It is unable to track the performance of various business measures of one or multiple companies alongside one another.
(D) It can be used to calculate the average growth of a single investment.
Choose the correct answer from the options given below:
Held on 13 May 2025 · Verified 13 Jul 2026.
(A), (B) and (D) only
(A), (B) and (C) only
(A), (C) and (D) only
(B) and (D) only
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The behavior and pattern of the data in a time series is NOT based on which of the following component?
Which of the following is not correct about the Compound Annual Growth Rate (CAGR)?
An automobile dealer wishes to buy four luxury cars of different brands given in the table below with some down payment and balance in equal monthly installments (EMI) for 10 years. The bank charges 9% interest per annum compounded monthly. $\left( {Given } \frac{0.0075 \times(1.0075)^{120}}{(1.0075)^{120}-1} = 0.01266\right)$ | Luxury Car | Price of the Car (in Rs.) | Down payment (in Rs.) | |---|---|---| | P | 25,00,000 | 5,00,000 | | Q | 35,00,000 | 12,00,000 | | R | 45,00,000 | 15,00,000 | | S | 42,00,000 | 15,00,000 | Match List-I with List-II | List-I | List-II | |---|---| | Luxury Car | EMI (in Rs.) | | (A) P | (I) 34,182 | | (B) Q | (II) 37,980 | | (C) R | (III) 29,118 | | (D) S | (IV) 25,320 | Choose the correct answer from the options given below:
What sum of money is needed to invest now, so as to get ₹5000 at the beginning of every month forever, if the money is worth 6% per annum compounded monthly?
Mr. X wishes to purchase a flat for Rs. 44,65,000 with a down payment of Rs. 10,00,000 and balance in equated monthly installments (EMI) for 25 years. If the bank charges 6 % per annum compounded monthly, the EMI is: [Given: $(1.005)^{300} =4.4650$]
Work through every CUET UG Statistics & Applications PYQ, year by year.