WB JEE 2011 | Permutations and Combinations Question 9 | Mathematics | WB JEE - ExamSIDE.Com

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Algebra

Sets and Relations

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Logarithms

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Sequence and Series

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Quadratic Equations

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Permutations and Combinations

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Mathematical Induction and Binomial Theorem

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Mathematical Induction

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Binomial Theorem

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Matrices and Determinants

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Vector Algebra

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Three Dimensional Geometry

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Probability

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Complex Numbers

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Statistics

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Trigonometry

Trigonometric Functions & Equations

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Inverse Trigonometric Functions

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Properties of Triangle

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Coordinate Geometry

Straight Lines and Pair of Straight Lines

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Circle

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Parabola

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Ellipse

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Hyperbola

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Calculus

Functions

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Limits, Continuity and Differentiability

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Differentiation

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Application of Derivatives

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Indefinite Integrals

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Definite Integration

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Application of Integration

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Differential Equations

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1

WB JEE 2011

MCQ (Single Correct Answer)

+1

-0.25

$${}^{15}{C_3} + {}^{15}{C_5} + \,\,......\,\, + {}^{15}{C_{15}} = $$

A

$${2^{14}}$$

B

$${2^{14}} - 15$$

C

$${2^{14}} + 15$$

D

$${2^{14}} - 1$$

2

WB JEE 2012

MCQ (Single Correct Answer)

+1

-0.33

A vehicle registration number consists of 2 letters of English alphabet followed by 4 digits, where the first digit is not zero. Then, the total number of vehicles with distinct registration numbers is

A

26² $$\times$$ 10⁴

B

$${}^{26}{P_2}$$ $$\times$$ $${}^{10}{P_4}$$

C

$${}^{26}{P_2}$$ $$\times$$ 9 $${}^{10}{P_3}$$

D

26² $$\times$$ 9 $$\times$$ 10³

3

WB JEE 2025

MCQ (Single Correct Answer)

+1

-0.25

If ${ }^9 P_5+5 \cdot{ }^9 P_4={ }^{10} P_r$, then the value of '$r$' is

A

4

B

8

C

5

D

7

4

WB JEE 2025

MCQ (Single Correct Answer)

+1

-0.25

The value of the expression ${ }^{47} C_4+\sum\limits_{j=1}^5{ }^{52-j} C_3$ is

A

${ }^{52} C_3$

B

${ }^{51} C_4$

C

${ }^{52} C_4$

D

${ }^{51} C_3$

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