West Bengal Board - Class 12 (WBCHSE Uchha Madhyamik) previous year questions (PYQ)

Paragraph & Story Writing: What is the proper opening sentence for a story about 'Biomolecules (Carbohydrates, Proteins, Nucleic Acids)'?

Directions: In the question below, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option:

Assertion (A): The quadratic equation $x^2 - 6x + 9 = 0$ has real and equal roots.

Reason (R): A quadratic equation $ax^2 + bx + c = 0$ has real and equal roots if and only if its discriminant $D = b^2 - 4ac = 0$.

Directions: In the question below, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option:

Assertion (A): The quadratic equation $x^2 - 6x + 9 = 0$ has real and equal roots.

Reason (R): A quadratic equation $ax^2 + bx + c = 0$ has real and equal roots if and only if its discriminant $D = b^2 - 4ac = 0$.

ভগ্নাংশ ও দশমিক (Fractions - 5th Standard): 'Differential Equations (Order, Degree, Variable Separable, Linear D.E.)'-এর সমতুল্য ভগ্নাংশ বা দশমিক রূপ কী?

Advanced Research & Methodology: In scholarly analysis of 'Relations and Functions (Equivalence Relations, Invertible Functions)', which methodological approach ensures reproducibility and minimizes systematic bias?

Directions: In the question below, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option:

Assertion (A): The electrical conductivity of an intrinsic semiconductor increases with rise in temperature.

Reason (R): With increase in temperature, covalent bonds rupture, generating additional free conduction electrons and mobile holes.

Directions: In the question below, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option:

Assertion (A): The square root of 2 ($\sqrt{2}$) is an irrational real number.

Reason (R): The square root of any positive prime integer is an irrational number.

Vocabulary: Find the correct antonym or rhyming word for 'Current Electricity (Ohm's Law, Kirchhoff's Laws, Wheatstone Bridge, Potentiometer)':

গ.সা.গু. ও ল.সা.গু. (৫ম শ্রেণি বৃত্তি মান): 'Indefinite and Definite Integrals (Standard Formulas, Substitution, Parts)' সংখ্যাগুলির ল.সা.গু. বা গ.সা.গু. কত?

Directions: In the question below, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option:

Assertion (A): The electrical conductivity of an intrinsic semiconductor increases with rise in temperature.

Reason (R): With increase in temperature, covalent bonds rupture, generating additional free conduction electrons and mobile holes.

Directions: In the question below, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option:

Assertion (A): Danger signals on communication towers and traffic posts are always illuminated in red color.

Reason (R): Red light has the longest wavelength in the visible spectrum and suffers minimum Rayleigh scattering ($I \propto 1/\lambda^4$) through fog and smoke.

স্থানীয় মান ও প্রকৃত মান: 'Inverse Trigonometric Functions (Principal Value Branches)' সংখ্যাটিতে অঙ্কের স্থানীয় মান কত?

Directions: In the question below, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option:

Assertion (A): Heavy water ($D_2O$) is utilized as a moderator in thermal nuclear power reactors.

Reason (R): Deuterium nuclei slow down energetic fission neutrons through elastic collisions without substantial parasitic neutron absorption.

Paragraph & Story Writing: What is the proper opening sentence for a story about 'Organic Compounds Containing Nitrogen (Amines, Diazonium Salts)'?

Refer to the Case Study 'Case Study: Optical Fibers and Total Internal Reflection in Medical Endoscopy' to answer:

Calculate the critical angle $\theta_c$ for the optical fiber described in the passage ($n_1 = 1.52, n_2 = 1.48$).

Directions: In the question below, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option:

Assertion (A): Heavy water ($D_2O$) is utilized as a moderator in thermal nuclear power reactors.

Reason (R): Deuterium nuclei slow down energetic fission neutrons through elastic collisions without substantial parasitic neutron absorption.

Directions: In the question below, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option:

Assertion (A): The electrical conductivity of an intrinsic semiconductor increases with rise in temperature.

Reason (R): With increase in temperature, covalent bonds rupture, generating additional free conduction electrons and mobile holes.

Directions: In the following question, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option:

Assertion (A): The quadratic equation $2x^2 - 4x + 3 = 0$ has no real roots.

Reason (R): The discriminant $D = b^2 - 4ac$ for this equation is $(-4)^2 - 4(2)(3) = 16 - 24 = -8 < 0$.