TS EAMCET · Maths · Functions
Consider the following statements: I. The number of positive integral solutions of \(x_1+x_2+x_3+x_4=10\) is 286 . II. If \(25 !=10^n \times k,(k \in \mathbf{N})\), then \(n=6\) Which one of the following options is true?
- A Only I is true
- B Only II is true
- C Both I and II are true
- D Both I and II are false
Answer & Solution
Correct Answer
(B) Only II is true
Step-by-step Solution
Detailed explanation
The number of positive integral solution of \(x_1+x_2+x_3+x_4=10 \text { is }{ }^9 C_3=\frac{9 \times 8 \times 7}{1 \times 2 \times 3}=84\) \(\therefore\) Statement I is false. The exponent of 2 in 25 ! is…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- A variable straight-line \(L\) with negative slope passes through the point \((4,9)\) and cuts the positive coordinate axes in A and B. If O is the origin, then the minimum value of \(\mathrm{OA}+\mathrm{OB}\) isTS EAMCET 2025 Medium
- If \(p\) th, \(q\) th, \(r\) th terms of a geometric progression are the positive numbers \(a, b\) and \(c\) respectively, then the angle between the vectors \(\left(\log a^2\right) \mathbf{i}+\left(\log b^2\right) \mathbf{j}+\left(\log c^2\right) \mathbf{k} \quad\) and \((q-r) \mathbf{i}+(r-p) \mathbf{j}+(p-q) \mathbf{k}\) isTS EAMCET 2012 Hard
- Let \(A(1,1), B(1,-1), C(-1,1)\) be the vertices of \(\triangle A B C\). Let \(S\) be the circum-centre, \(O\) be the orthocentre and \(I\) be the incentre of the \(\triangle A B C\). Then \(I S+O S=\)TS EAMCET 2020 Medium
- Consider the following
Assertion (A): The two lines \(\bar{r}=\bar{a}+t(\bar{b})\) and \(\bar{r}=\bar{b}+s(\bar{a})\) intersect each other.
Reason (R): The shortest distance between the lines \(\bar{r}=\bar{p}+t(\bar{q})\) and \(\bar{r}=\bar{c}+s(\bar{d})\) is equal to the length of projection of the vector \((\bar{p}-\bar{c})\) on \((\bar{q} \times \bar{d})\)
The correct answer isTS EAMCET 2025 Hard - The lines are chords of the hyperbola and they subtend a right angle at the centre of the hyperbola. The locus of the poles of these lines with respect to the given hyperbola isTS EAMCET 2021 Hard
- The system of linear equations \((\sin \theta) x+y-2 z=0,2 x-y+(\cos \theta) z=0\) and \(-3 x+(\sec \theta) y+3 z=0\), where \(\theta \neq(2 n+1) \frac{\pi}{2}\), has non-trivial solution forTS EAMCET 2025 Medium
More PYQs from TS EAMCET
- \(0.16 \mathrm{~g}\) of an organic compound containing sulphur produces \(0.233 \mathrm{~g}\) of \(\mathrm{BaSO}_4\). Percentage of sulphur in the compound isTS EAMCET 2011 Easy
- Numerically greatest term in the expansion of \((3 x-4 y)^{23}\) when \(x=\frac{1}{6}\) and \(y=\frac{1}{8}\) isTS EAMCET 2025 Medium
- If a gas contains only three molecules that move with velocities of \(100,200,500 \mathrm{~ms}^{-1}\). What is the rms velocity of that gas in \(\mathrm{ms}^{-1}\) ?TS EAMCET 2003 Easy
- If \(\tan \beta=\frac{n \sin \alpha \cos \alpha}{1-n \cos ^2 \alpha}\), then \(\tan (\alpha+\beta) \cdot \cot \alpha=\)TS EAMCET 2023 Easy
- The equation of the straight line passing through the point of intersection of \(5 x-6 y-1, \quad 3 x+2 y+5=0 \quad\) and perpendicular to the line \(3 x-5 y+11=0\) isTS EAMCET 2017 Medium
- An angle between the curves \(x^2-y^2=4\) and \(x^2+y^2=4 \sqrt{2}\) isTS EAMCET 2018 Medium