If A ≡ 2i + 3j, B ≡ pi + 9j and C ≡ i − j Are Collinear, Then the Value of p Is
Points A=2i+3j, B=pi+9j, C=i−j are collinear. Find p by setting the vectors AB and AC parallel using the 2D cross-product (determinant) condition.
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Two Dice Rolled — P(Even on First Die or Total of 8)
Two dice are rolled once. Find the probability of getting an even number on the first die or a total of 8, using the addition rule for probability.
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Proof: P(A∪B) = 1 − P(A′)·P(B′) for Independent Events
A derivation of P(A∪B)=1−P(A’)P(B’) for independent events A and B, from NCERT Example 14, using the standard union and complement rules.
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A Wheel Makes 360 Revolutions in 1 Minute. Find the Number of Radians It Turns Through in 1 Second
A wheel makes 360 revolutions in one minute. Find how many radians it turns through in 1 second, converting revolutions per minute into radians per second.
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Find the Positive Square Root of 3+√5
Find the positive square root of 3+√5 by expressing it as √x+√y, splitting the equation into a rational and irrational part, and solving for x and y.
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Direction Cosines of the Line 5x−3=15y+7=3−10z
Find the direction cosines of 5x−3=15y+7=3−10z and a point through which it passes, by converting to symmetric form with equal-magnitude denominators.
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The Monthly Incomes of Aryan and Babban Are in the Ratio 3:4 and Their Monthly Expenditures Are in the Ratio 5:7. If Each Saves ₹15,000 per Month, Find Their Monthly Incomes Using the Matrix Method
The monthly incomes of Aryan and Babban are in the ratio 3:4 and expenditures in the ratio 5:7. If each saves ₹15,000, find their incomes using the matrix method.
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The Value of (sin 70°)(cot 10° cot 70° − 1) Is Equal To
A short JEE Main 2025 trigonometry problem solved by converting cotangents to cosines and sines, then applying the cos(A+B) identity.
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3-Digit Numbers Divisible by 2 and 3, Not 4 and 9
How many 3-digit numbers are divisible by both 2 and 3, but not by 4 or 9? Solved using LCMs and arithmetic progressions, JEE Main 2025 style.