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2026 16 questions

Q72026 · 8 Apr 2026 · Shift 2
A set of four observations has mean 1 and variance 13. Another set of six observations has mean 2 and variance 1. Then, the variance of all these 10 observations is equal to :
1. A. $5.96$
2. B. $6.14$
3. C. $6.04$
4. D. $6.24$
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Answer: C
Q92026 · 6 Apr 2026 · Shift 1
A data consists of 20 observations $x_{1}, x_{2}, \dots, x_{20}$ . If $\sum_{i = 1}^{20} (x_{i} + 5)^{2} = 2500$ and $\sum_{i = 1}^{20} (x_{i} - 5)^{2} = 100$ , then the ratio of mean to standard deviation of this data is:
1. A.2:1
2. B.3:1
3. C.3:2
4. D.4:1
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Answer: B
Q82026 · 6 Apr 2026 · Shift 2
1. A. $x^{2} - 35 x + 306 = 0$
2. B. $x^{2} - 41 x + 420 = 0$
3. C. $x^{2} - 45 x + 506 = 0$
4. D. $x^{2} - 37 x + 342 = 0$
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Answer: B
Q82026 · 5 Apr 2026 · Shift 1
The mean deviation about the mean for the data $x_{i} f_{i} 587692102122156$ is equal to:
1. A. $\frac{40}{13}$
2. B. $\frac{42}{13}$
3. C. $\frac{44}{13}$
4. D. $\frac{46}{13}$
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Answer: C
Q102026 · 5 Apr 2026 · Shift 2
A variable $X$ takes values $0, 0, 2, 6, 12, 20, \dots, n (n - 1)$ with frequencies $^{n} C_{0},^{n} C_{1},^{n} C_{2},^{n} C_{3},^{n} C_{4},^{n} C_{5}, \dots,^{n} C_{n}$ respectively. If the mean of this data is $60$ , then its median is :
1. A. $56$
2. B. $42$
3. C. $72$
4. D. $90$
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Answer: A
Q102026 · 4 Apr 2026 · Shift 1
Suppose that the mean and median of the non-negative numbers $21, 8, 17, a, 51, 103, b, 13, 67$ , ( $a > b$ ), are 40 and 21, respectively. If the mean deviation about the median is 26, then $2 a$ is equal to:
1. A.109
2. B.117
3. C.161
4. D.131
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Answer: D
Q82026 · 4 Apr 2026 · Shift 2
For 10 observations $x_{1}, x_{2}, \dots, x_{10}$ , if $\sum_{i = 1}^{10} (x_{i} + 2)^{2} = 180$ and $\sum_{i = 1}^{10} (x_{i} - 1)^{2} = 90$ , then their standard deviation is:
1. A.2
2. B. $3$
3. C. $22$
4. D.3
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Answer: D
Q82026 · 2 Apr 2026 · Shift 1
If the mean of the data $Class Frequency 5 - 10 2 10 - 15 k 15 - 20 28 20 - 25 54 25 - 30 k + 1 30 - 35 5$ is $21$ , then $k$ is one of the roots of the equation :
1. A. $2 x^{2} - 23 x - 10 = 0$
2. B. $4 x^{2} - 35 x + 24 = 0$
3. C. $2 x^{2} - 19 x - 10 = 0$
4. D. $2 x^{2} - 35 x + 98 = 0$
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Answer: C
Q92026 · 2 Apr 2026 · Shift 2
Given below are two statements : Statement I: The second ionization enthalpy of B, Al and Ga is in the order of B > Al > Ga. Statement II: The correct order in terms of first ionization enthalpy is Si < Ge < Pb < Sn. In the light of the above statements, choose the correct answer from the options given below :
1. A.Both Statement I and Statement II are true
2. B.Both Statement I and Statement II are false
3. C.Statement I is true but Statement II is false
4. D.Statement I is false but Statement II is true
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Answer: D
Q42026 · 28 Jan 2026 · Shift 1
The mean and variance of $10$ observations are $9$ and $34.2$ , respectively. If $8$ of these observations are $2, 3, 5, 10, 11, 13, 15, 21$ , then the mean deviation about the median of all the $10$ observations is
1. A.7
2. B.4
3. C.5
4. D.6
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Answer: C
Q182026 · 24 Jan 2026 · Shift 1
The mean and variance of a data of 10 observations are 10 and 2 , respectively. If an observations $α$ in this data is replaced by $β$ , then the mean and variance become 10.1 and 1.99 , respectively. Then $α + β$ equals
1. A.15
2. B.10
3. C.5
4. D.20
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Answer: D
Q82026 · 23 Jan 2026 · Shift 1
Let the mean and variance of 8 numbers $- 10, - 7, - 1, x, y, 9, 2, 16$ be $\frac{7}{2}$ and $\frac{293}{4}$ , respectively. Then the mean of 4 numbers $x, y, x + y + 1, ∣ x - y ∣$ is :
1. A.11
2. B.9
3. C.10
4. D.12
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Answer: A
Q252026 · 23 Jan 2026 · Shift 1· Numerical answer
The number of 4-letter words, with or without meaning, which can be formed using the letters PQRPQRSTUVP, is ____ .
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Answer: 1422
Q92026 · 23 Jan 2026 · Shift 2
If the mean and the variance of the data $Class Frequency 4 - 8 3 8 - 12 λ 12 - 16 4 16 - 20 7$ are $μ$ and 19 respectively, then the value of $λ + μ$ is :
1. A.21
2. B.19
3. C.18
4. D.20
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Answer: B
Q12026 · 21 Jan 2026 · Shift 1
Let the mean and variance of 7 observations $2, 4, 10, x, 12, 14, y, x > y$ , be 8 and 16 respectively. Two numbers are chosen from ${1, 2, 3, x - 4, y, 5}$ one after another without replacement, then the probability, that the smaller number among the two chosen numbers is less than 4 , is :
1. A. $\frac{4}{5}$
2. B. $\frac{3}{5}$
3. C. $\frac{2}{5}$
4. D. $\frac{1}{3}$
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Answer: A
Q172026 · 21 Jan 2026 · Shift 2
A random variable X takes values 0, 1, 2, 3 with probabilities $\frac{2 a + 1}{30}, \frac{8 a - 1}{30}, \frac{4 a + 1}{30}, b$ respectively, where $a, b \in R$ . Let $μ$ and $σ$ respectively be the mean and standard deviation of $X$ such that $σ^{2} + μ^{2} = 2$ . Then $\frac{a}{b}$ is equal to:
1. A.12
2. B.60
3. C.30
4. D.3
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Answer: B