List of practice Questions

दिए गए संस्कृत गद्यांश का संदर्भ सहित हिन्दी में अनुवाद कीजिए। गद्यांश 1 –
एषा नगरी भारतीय संस्कृतेः संस्कृत भाषायाः केन्द्रस्थानम् अस्ति। इत एव संस्कृतवाङ्मयस्य संस्कृतेः आलोकः सर्वत्र प्रसृतः। मुघलयुवराजः दाराशिकोहः अग्रगण्य भारतीय दर्शन – शास्त्राणां अध्ययनम् अकरोत्। स तेजो ज्ञानं तथा प्राभामिवित्। भवतः, यत् तेन उपनिषदाम् अनुवादः पारसी भाषायां कृतः।

A particle of mass 100 g is projected at time \(𝑡=0\) with a speed \(20\,ms^{−1}\) at an angle \(45°\) to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time \(𝑡=2 s\) is found to be \(\sqrt{K}\  kgm^2/s.\) The value of \(K\) is ________. (Take \(g=10\) \(ms^{−2}\))

If polynomial \(g(x) = 3x^2 - 7x + 2\), then the value of \(g(-1)\) is

If \(\alpha\) and \(\beta\) are zeroes of the polynomial \(p(x) = x^2 - 3x + 5\), then the value of \(4(\alpha + \beta)\) is

If \( p(x) = 3x^{3} + x^{2} + 2x + 5 \) is divided by \( q(x) = x^{2} + 2x + 1 \), then the degree of the quotient will be:

Evaluate \( \dfrac{\sin^{2}(90^\circ-\theta)+\sin^{2}\theta}{\csc^{2}(90^\circ-\theta)-\tan^{2}\theta} \).

If \((\tan\theta+\cot\theta)=6\), then the value of \(\tan^{2}\theta+\cot^{2}\theta\) is

If \(\sec\theta+\tan\theta+1=0\), then the value of \(\sec\theta-\tan\theta\) is

If \(\sin\theta=\dfrac{\sqrt{3}}{2}\), then the value of \(\csc\theta+\cot\theta\) is

If \(\sin\theta=\cos\theta,\ 0^\circ\le \theta\le 90^\circ\), then the value of \(\theta\) is

\(\displaystyle \frac{\sin 30^\circ+\cos 45^\circ-\tan 60^\circ}{\cot 30^\circ-\sin 45^\circ-\cos 60^\circ}=\)

\(\tan30^\circ\cdot \sin30^\circ\cdot \cot60^\circ\cdot \csc30^\circ=\)

Which relationship is true for Mean, Median and Mode?

If the mean of \(x+2, 2x+3, 4x+5, 5x+2\) is 18, then the value of \(x\) is

If point \(R(a,b)\) lies on the line segment joining \(P(0,0)\) and \(Q(0,2)\), which of the following is true?

The point of intersection of the straight lines \(x=2\) and \(y=-3\) is

If \(\tan\theta=\dfrac{15}{8}\), then the value of \(\sin\theta\) will be

The perimeter of a semicircle whose radius is \(3r\) is

Which of the following numbers is not the probability of any event?

If \(E'\) is the complementary event of an event \(E\), then which of the following is true?

In throwing a die one time, what is the probability of not appearing 2?

A card is drawn at random from a well-shuffled deck of 52 cards. What is the probability of getting a black king?

If the median of \(24,27,28,31,34,x,37,40,42,45,50\) is 35, then the value of \(x\) is

The cumulative frequency table is useful in the determination of the following?