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Question 521
StructuredStandard5 marks
CBSE Class 11 Mathematics · Probability · Probability of events

One card is selected from a standard 52-card deck. Give

(a)
the sample-space size
(b)
probabilities of the ace of spades
(c)
any ace
(d)
a black card.
Question 522
StructuredStandard5 marks
CBSE Class 11 Mathematics · Statistics · Mean deviation

Marks classes 0–10,...,50–60 have frequencies 6,8,14,16,4,2. Find mean deviation about the grouped median.

Question 523
StructuredStandard5 marks
CBSE Class 11 Mathematics · Limits and Derivatives · Algebraic limits

Evaluate lim(x→1)(ax²+bx+c)/(cx²+bx+a), assuming a+b+c≠0.

Question 524
StructuredStandard5 marks
CBSE Class 11 Mathematics · Introduction to Three Dimensional Geometry · Section formula and loci

Find all three median lengths of the triangle A(0,0,6), B(0,4,0), C(6,0,0).

Question 525
StructuredStandard5 marks
CBSE Class 11 Mathematics · Conic Sections · Circles

Find the circle through (2,3) and (−1,1) whose centre lies on x−3y−11=0.

Question 526
StructuredStandard5 marks
CBSE Class 11 Mathematics · Straight Lines · Slope and inclination

A line of slope m contains (x_1,y_1) and (h,k). Derive the relation among these five quantities.

Question 527
StructuredStandard4 marks
CBSE Class 11 Mathematics · Permutations and Combinations · Permutations

Complete every requested part of exercise 6.2, question 5: ( ) Evaluate n − r ! , when (i) n = 6, r = 2 (ii) n = 9, r = 5. 6.3.3 Derivation of the formula for nPr n n! Pr = ,0≤r≤n ( r )! n − Let us now go back to the stage where we had determined the listed cases formula: n Pr = n (n – 1) (n – 2) . . . (n – r + 1) Multiplying numerator and denomirator by (n – r) (n – r – 1) . . . 3 × 2 × 1, we get n ( n − 1) ( n − 2 ) ...( n − r + 1)( n − r )( n − r − 1) ...3 × 2 × 1 n! n Pr = = , ( n − r )( n − r − 1) ... 3 × 2 × 1 ( n − r )! n! n Pr = Thus ( n − r )! , where 0 < r ≤ n This is a much more convenient expression for nPr than the previous one. n! In particular, when r = n, n Pn = = n! 0! Counting permutations is merely counting the number of ways in which some or all objects at a time are rearranged. Arranging no object at all is the same as leaving behind all the objects and we know that there is.

Question 528
StructuredStandard4 marks
CBSE Class 11 Mathematics · Linear Inequalities · One-variable inequalities

Complete every requested part of exercise 5.1, question 11: ≤

Question 529
StructuredStandard4 marks
CBSE Class 11 Mathematics · Trigonometric Functions · Trigonometric functions

Complete every requested part of exercise 3.2, question 4: sec x = , x lies in fourth quadrant. 5 5

Question 530
StructuredStandard4 marks
CBSE Class 11 Mathematics · Relations and Functions · Relations

On \(A=\{1,2,\ldots,14\}\), let \(R=\{(x,y):

(a)
3x-y=0\}\). Give its domain
(b)
codomain
(c)
range.