JEE Advanced · Mathematics · 18. Matrices

Paragraph:
Read the following passage and answer the questions.
Question:
The value of $|U|$ is

A
3
B
$-3$
C
$\frac{3}{2}$
D
2

Verified Solution

Answer & Solution

Correct Answer

(A)
3

Step-by-step Solution

Detailed explanation

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Paragraph:

Football teams $T_{1}$ and $T_{2}$ have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of $T_{1}$ winning, drawing and losing a game against $T_{2}$ are $\frac{1}{2}, \frac{1}{6}$ and $\frac{1}{3}$, respectively. Each team gets $3$ points for a win, $1$ point for a draw and $0$ point for a loss in a game. Let $X$ and $Y$ denote the total points scored by teams $T_{1}$ and $T_{2}$, respectively, after two games.

Question:

$P(X=Y)$ is

JEE Advanced 2016 Easy

Consider the given data with frequency distribution

\begin{array}{l} x_{i} & 3 & 8 & 11 & 10 & 5 & 4 \\ f_{i} & 5 & 2 & 3 & 2 & 4 & 4 \end{array}

Match each entry in List-I to the correct entries in List-II.

	List-I		List-II
$(P)$	The mean of the above data is	$(1)$	$2.5$
$(Q)$	The median of the above data is	$(2)$	$5$
$(R)$	The mean deviation about the mean of the above data is	$(3)$	$6$
$(S)$	The mean deviation about the median of the above data is	$(4)$	$2.7$
		$(5)$	$2.4$

The correct option is

JEE Advanced 2023 Easy

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From JEE Advanced

Columns 1, 2 and 3 contain conics, equations of tangents to the conics and points of contact, respectively.

Column 1	Column 2	Column 3
(I) $x^{2} + y^{2} = a^{2}$	(i) $m y = m^{2} x + a$	(P) $(\frac{a}{m^{2}}, \frac{2 a}{m})$
(II) $x^{2} + a^{2} y^{2} = a^{2}$	(ii) $y = m x + a \sqrt{m^{2} + 1}$	(Q) $(\frac{- m a}{\sqrt{m^{2} + 1}}, \frac{a}{\sqrt{m^{2} + 1}})$
(III) $y^{2} = 4 a x$	(iii) $y = m x + \sqrt{a^{2} m^{2} - 1}$	(R) $(\frac{- a^{2} m}{\sqrt{a^{2} m^{2} + 1}}, \frac{1}{\sqrt{a^{2} m^{2} + 1}})$
(IV) $x^{2} - a^{2} y^{2} = a^{2}$	(iv) $y = m x + \sqrt{a^{2} m^{2} + 1}$	(S) $(\frac{- a^{2} m}{\sqrt{a^{2} m^{2} - 1}}, \frac{- 1}{\sqrt{a^{2} m^{2} - 1}})$

For

a = \sqrt{2}

, if a tangent is drawn to a suitable conic (Column 1) at the point of contact

(- 1, 1)

, then which of the following options is the only Correct combination for obtaining its equation?

JEE Advanced 2017 Hard

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Paragraph:
Read the following passage and answer the questions.
Question:
The value of \(|U|\) is

Answer & Solution

Step-by-step Solution

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Paragraph:Read the following passage and answer the questions.Question:The value of \(|U|\) is

Step-by-step Solution

Paragraph:
Read the following passage and answer the questions.
Question:
The value of \(|U|\) is