For what value of K is the equation \(\frac{0.009}{K}\) = 0.1 true?
To find the value of \(K\), we need to rearrange the given equation to isolate \(K\). This involves basic algebraic manipulation of decimal numbers.
To make the division easier, we can multiply the numerator and the denominator by 10 to remove the decimal from the denominator:
\[ K = \frac{0.009 \times 10}{0.1 \times 10} = \frac{0.09}{1} = 0.09 \]Alternatively, we can think of dividing by 0.1 as multiplying by 10. So, \(0.009 \times 10 = 0.09\).
Substitute \(K = 0.09\) back into the original equation:
\[ \frac{0.009}{0.09} = \frac{9 \times 10^{-3}}{9 \times 10^{-2}} = 10^{-3 - (-2)} = 10^{-1} = 0.1 \]Since this is true, our value for \(K\) is correct.
Correct Option: B) 0.09
The question asks for the correct definition of pollination. We need to evaluate each option based on the biological process of plant reproduction.
Correct Option: A) Pollination is transfer of pollen grains from stamen to stigma.
Simplify the expression: \(\sqrt{\frac{1+\cos\theta}{1-\cos\theta}}\) is:
secθ + cotθ
cosecθ − cotθ
secθ − cotθ
cosecθ + cotθ
To simplify the given trigonometric expression, we will use trigonometric identities to transform the terms inside the square root into a perfect square, allowing us to remove the square root. The key identities are the half-angle formulas for sine and cosine, and the reciprocal and ratio identities for cosecant and cotangent.
The given expression is:
\[ \sqrt{\frac{1+\cos\theta}{1-\cos\theta}} \]We know the double angle identities:
Applying these with \( x = \frac{\theta}{2} \), we get:
Substitute these into the expression:
\[ \sqrt{\frac{2\cos^2\left(\frac{\theta}{2}\right)}{2\sin^2\left(\frac{\theta}{2}\right)}} \]Cancel out the 2s:
\[ \sqrt{\frac{\cos^2\left(\frac{\theta}{2}\right)}{\sin^2\left(\frac{\theta}{2}\right)}} \]Simplify the fraction inside the square root:
\[ \sqrt{\left(\frac{\cos\left(\frac{\theta}{2}\right)}{\sin\left(\frac{\theta}{2}\right)}\right)^2} \]We know that \( \frac{\cos x}{\sin x} = \cot x \). So, the expression becomes:
\[ \sqrt{\cot^2\left(\frac{\theta}{2}\right)} \]Taking the square root, we get:
\[ \left|\cot\left(\frac{\theta}{2}\right)\right| \]Assuming \( \theta \) is in a range where \( \cot\left(\frac{\theta}{2}\right) \) is positive (e.g., \( 0 < \theta < \pi \)), we can write it as:
\[ \cot\left(\frac{\theta}{2}\right) \]Now, we need to express \( \cot\left(\frac{\theta}{2}\right) \) in terms of \( \csc\theta \) and \( \cot\theta \). We use the half-angle formulas for cotangent:
Using the first identity:
\[ \cot\left(\frac{\theta}{2}\right) = \frac{1+\cos\theta}{\sin\theta} \]Separate the terms:
\[ \frac{1}{\sin\theta} + \frac{\cos\theta}{\sin\theta} \]Recall the reciprocal and ratio identities:
Substitute these back:
\[ \csc\theta + \cot\theta \]D) cosecθ + cotθ is the correct simplification of the given expression.
The 63rd National Open Athletics Championship was conducted in the city of ____________.
The question asks for the city where the 63rd National Open Athletics Championship was held. This is a factual question related to current affairs or sports events. To answer correctly, one needs to recall the venue of this specific event.
Correct Option: C) Bengaluru
This question tests knowledge of recent appointments in the Indian government. Such appointments are common topics in current affairs sections of competitive exams. The approach is to recall or identify the correct ministry associated with the mentioned individual's appointment.
Correct Option: A) Power and New and Renewable Energy
The question asks to identify the specific mission that will facilitate India's first human presence on the International Space Station (ISS). This requires knowledge of recent developments and collaborations in space exploration, particularly involving India's Gaganyaan program and international partnerships.
Correct Option: A) Axiom-4 is the mission identified for India's first human presence on the International Space Station, as announced by NASA and ISRO.
The question asks to identify the rapper from Dharavi known for the indie album 'Halaat' who has become prominent in Indian hip hop. This requires knowledge of prominent Indian hip hop artists, their origins, and their notable works.
Correct Option: B) MC Altaf is the rapper from Dharavi known for the indie album 'Halaat' and has risen to prominence in Indian hip hop. His music often reflects his experiences growing up in Dharavi.
This is a blood relations question where symbols represent relationships. We need to decode the given expression 'P × Q ÷ R − S + T' step-by-step to determine the relationship between Q and T.
A) Mother's father — As derived, Q is the father of S, and S is the mother of T. Thus, Q is T's mother's father (maternal grandfather).
The question asks to identify an example of uniform circular motion. Uniform circular motion is defined as the motion of an object moving in a circular path at a constant speed. While the speed is constant, the velocity is continuously changing because the direction of motion is always changing.
D) Motion of clock hands. The hands of a clock move in a circular path at a constant speed, fulfilling the definition of uniform circular motion.