JEE (Advanced) 2009 Paper-1

Instructions

For the following questions answer them individually

JEE (Advanced) 2009 Paper-1 - Question 31


Let
$$L = \lim_{x \rightarrow 0}\frac{a - \sqrt{a^2 - x^2} - \frac{x^4}{4}}{x^4}, a>0$$. If L is finite, then

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JEE (Advanced) 2009 Paper-1 - Question 32


If $$\frac{\sin^4x}{2}+\frac{\cos^4x}{3} = \frac{1}{5}$$ then

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Instructions

Let A be the set of all $$3 \times 3$$ symmetric matrices all of whose entries are either 0 or 1. Five of these entries are 1 and four of them are 0.

JEE (Advanced) 2009 Paper-1 - Question 33


The number of matrices in A is

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JEE (Advanced) 2009 Paper-1 - Question 34


The number of matrices A in A for which the system of linear equations
$$A\begin{bmatrix}x\\y\\z \end{bmatrix} = \begin{bmatrix}1\\0\\0 \end{bmatrix}$$
has a unique solution, is

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JEE (Advanced) 2009 Paper-1 - Question 35


The number of matrices A in A for which the system of linear equations
$$A\begin{bmatrix}x\\y\\z \end{bmatrix} = \begin{bmatrix}1\\0\\0 \end{bmatrix}$$
is inconsistent, is

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Instructions

A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required.

JEE (Advanced) 2009 Paper-1 - Question 36


The probability that X = 3 equals

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JEE (Advanced) 2009 Paper-1 - Question 37


The probability that $$X \geq 3$$ equals

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JEE (Advanced) 2009 Paper-1 - Question 38


The conditional probability that $$X \geq 6$$ given $$X > 3$$ equals

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Instructions

This section contains 2 questions. Each questions contains statements given in two columns, which have to be matched. The statements in Column I are labelled A, B, C and D, while the statements in Column II are labeled p, q, r, s and t. Any given statement in Column I can have correct matching with ONE OR MORE statement(s) in Column II. The appropriate bubbles corresponding to the answers to these questions have to be darkened as illustrated in the following example:

If the correct matches are A - p, s and t; B - q and r; C -p and q ; and D -s and t; then the correct darkening of bubbles will look like the following.

JEE (Advanced) 2009 Paper-1 - Question 39


Match the statements/ expressions in Column I with the open intervals in Column- II

Backspace
789
456
123
0.-
Clear All
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JEE (Advanced) 2009 Paper-1 - Question 40


Match the conics in Column I with the statements/ expressions in Column- II

Backspace
789
456
123
0.-
Clear All
Video Solution
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