A) \( \Large 4 \sin^{2} 4 \alpha \) |
B) \( \Large 4 \cos^{2} 4 \alpha \) |
C) \( \Large 4 cosec^{2} 4 \alpha \) |
D) \( \Large 4 \sec^{2} 4 \alpha \) |
C) \( \Large 4 cosec^{2} 4 \alpha \) |
Therefore, \( \Large \because P^{2}_{1}+P^{2}_{2}=\frac{4a^{2}}{\sec^{2} \alpha + cosec^{2} \alpha } + \frac{a^{2} \cos^{2} 2 \alpha }{\cos^{2} \alpha + \sin^{2} \alpha }\)
= \( \Large a^{2} \left(\frac{4 \cos 2 \alpha \sin^{2} \alpha }{\cos^{2
} \alpha + \sin^{2} \alpha }\right) + \frac{\cos^{2} 2 \alpha }{1} \)
= \( \Large a^{2} \left(\sin 2 \alpha + \cos^{2} 2 \alpha \right) = a^{2} \)
and \( \Large P^{2}_{1} \times P^{2}_{2}=a^{4} \sin^{2} 2 \alpha \cos^{2} 2 \alpha \)
= \( \Large \left(\frac{1}{4} a^{4}\sin^{2} 4 \alpha \right) \)
Therefore, \( \Large \left(\frac{P_{1}}{P_{2}}+\frac{P_{2}}{P_{1}}\right)^{2} = \frac{ \left(P^{2}_{1}+P^{2}_{2}\right)^{2} }{P^{2}_{1}P^{2}_{2}} \)
=> \( \Large \frac{4}{\sin^{2} 4 \alpha } = 4 cosec^{2} 4 \alpha \)
1). lf every point on the line \( \Large \left(a_{1}-a_{2}\right)x+ \left(b_{1}-b_{2}\right)y=c \) is equidistant from the points \( \Large \left(a_{1},\ b_{1}\right) \) then 2c is equal to:
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2). If two vertices of a triangle are \( \Large \left(-2,\ 3\right)\ and\ \left(5,\ -1\right) \) orthocentre lies at origin and centroid on the line x + y = 7, then the third vertex lies at:
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3). The locus of a points p which moves such that 2PA = 3PB, where \( \Large A \left(0,\ 0\right)\ and\ B \left(4,\ -3\right) \) are points is:
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4). If \( \Large A \left(-a,0\right) \) and \( \Large B \left(a,0\right) \) are two fixed points, then the locus of the point at which AB subtends a right angle is;
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5). If \( \Large a+b+c=0 \), then \( \Large a^{3}+b^{3}+c^{3} \) is equal to
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6). Largest number among \( \Large 2^{2^{2}},\ 2^{22},\ 222,\ \left(22\right)^{2} \) is
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7). Both addition and multiplication of numbers are operations which are
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8). The positive square root of \( \Large \left(x^{2}+2x-1\right)+\frac{1}{x^{2}+2x+1} \) is
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9). The simplified value of the decimal fraction \( \Large \frac{1.59 \times 1.59-.41 \times .41}{1.59-.41} \)
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10). The fraction \( \Large 101\frac{27}{100000} \) in decimal form is
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