Paragraph: Read the following passage and answer the questions. Question: The value of the elements of U^{-1} is

Paragraph: Read the following passage and answer the ques…

	List – I		List – II
(A)	The number of polynomials f(x) with non – negative integer coefficients of degree $\leq 2,$ satisfying f(0) =0 and $\int_{0}^{1} f (x) d x = 1, i s$	(P)	8
(B)	The number of point in the interval $[- \sqrt{13}, \sqrt{13}]$ at which $f (x) = \sin (x^{2}) + \cos (x^{2})$ attains its maximum value, is	(Q)	2
(C)	$\int_{- 2}^{2} \frac{3 x^{2}}{(1 + e^{x})} d x$ equals	(R)	4
(D)	$\frac{(\int_{- \frac{1}{2}}^{\frac{1}{2}} \cos 2 x . \log (\frac{1 + x}{1 - x}) d x)}{(\int_{0}^{\frac{1}{2}} \cos 2 x . \log (\frac{1 + x}{1 - x}) d x)}$	(S)	0

JEE Advanced 2014 Hard

If

3^{x} = 4^{x - 1}

, then x =

JEE Advanced 2013 Medium

Consider the hyperbola

H : x^{2} - y^{2} = 1

and a circle S with center

N (x_{2}, 0) .

Suppose that H and S touch each other at point

P (x_{1}, y_{1})

with

x_{1} > 1 a n d y_{1} > 0 .

The common tangent to H and S at P intersects the x - axis at point M. If

(l, m)

is the centroid of the triangle

Δ P M N,

then the correct expression(s) is(are)

JEE Advanced 2015 Medium

Consider the

6 \times 6

square in the figure. Let

A_{1}, A_{2}, \dots, A_{49}

be the points of intersections (dots in the picture) in some order. We say that

A_{i}

and

A_{j}

are friends if they are adjacent along a row or along a column. Assume that each point

A_{i}

has an equal chance of being chosen.

(There are two questions based on

PARAGRAPH " II "

, the question given below is one of them)

Let

p_{i}

be the probability that a randomly chosen point has

i

many friends,

i = 0, 1, 2, 3, 4

. Let

X

be a random variable such that for

i = 0, 1, 2, 3, 4

, the probability

P (X = i) = p_{i}

. Then the value of

7 E (X)

is

JEE Advanced 2023 Hard

Let

M

be a

3 \times 3

invertible matrix with real entries and let

I

denote the

3 \times 3

identity matrix.

M^{- 1} = a d j (a d j M)

, then which of the following statements is/are ALWAYS TRUE?

JEE Advanced 2020 Easy

Let

a, b, x

and

y

be real numbers such that

a - b = 1

and

y \neq 0

. If the complex number

z = x + i y

satisfies

I m (\frac{a z + b}{z + 1}) = y,

then which of the following is (are) possible value (s) of

x ?

JEE Advanced 2017 Medium

Paragraph:
Read the following passage and answer the questions.
Question:
The value of the elements of \(U^{-1}\) is

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Paragraph:Read the following passage and answer the questions.Question:The value of the elements of \(U^{-1}\) is

Step-by-step Solution

Paragraph:
Read the following passage and answer the questions.
Question:
The value of the elements of \(U^{-1}\) is