If θ>0 , be an acute angle , then the value of θ in degrees satisfying $\frac{\cos^{2}θ-3\cosθ+2}{\sin^{2}θ}$ =1 is1). 90° 2). 30°3). 45°4). 60°
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1. If $\frac{x}{3} - \frac{ \left[5\left(\frac{7x}{5} - \frac{4}{3}\right)\right]}{2}= -\frac{x}{6}$, then what is the value of x?
2. In the following question, two equations numbered I and II are given. You have to solve both the equations and mark your answer as: I. x² - 7x + 12 = 0 II. 9y² - 29y + 22 = 0
3. What is the value of $\frac{(4a^{2} + 8b + 14c + 2)}{2}$ ?
4. In $\triangle ABC$, D is the mid-point of BC. Length AD is 27 cm. N is a point in AD such that the length of DN is 12 cm. The distance of N from the centroid of $\triangle ABC$ is equal to
5. If a + b + c = 6 and ab + bc + ca = 11, then the value of bc(b + c) + ca(c + a) + ab(a + b) + 3abc is
6. In the following question two equations are given in variables x and y. You have to solve these equations and determine relation between x and y. I. \({\rm{}}\frac{{32}}{{\sqrt {\rm{x}} }} + \sqrt {\rm{x}} = 5\sqrt {\rm{x}} \) II. \({\rm{}}3y + \frac{{{y^2} + \;64}}{{\rm{y}}} = 5y\)
7. In the following question two equations are given. You have to solve these equations and determine relation between x and y. I. x2 + 19x – 120 = 0 II. y2 – 14y + 45 = 0
8. The 5th and 9th term of an arithmetic progression are 7 and 13 respectively. What is the 15th term?
9. A man travels 434 km, partly by rail and partly by steamer, He spends 8 hours more time on steamer, If the velocity of the steamer is 25 km/hr and the velocity of rail is 65 km/hr, how much distance does he cover by steamer?
10. If \({\rm{x\;}} = {\rm{\;}}\frac{{8{\rm{ab}}}}{{{\rm{a\;}} + {\rm{\;b}}}}\) then the value of\({\rm{\;}}\frac{{{\rm{x\;}} + {\rm{\;}}4{\rm{a}}}}{{{\rm{x\;}} - {\rm{\;}}4{\rm{a}}}}{\rm{\;}} + {\rm{\;}}\frac{{{\rm{x\;}} + {\rm{\;}}4{\rm{b}}}}{{{\rm{x\;}} - {\rm{\;}}4{\rm{b}}}}\) is equal to
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