Simplify $ \frac{(x^2 – 9)}{x+3}$ Options a) x – 9b) x + 3c) x – 3d) $ \sqrt{x^2 – 9} $ Solution As per question$ \frac{(x^2 – 9)}{x+3}$ $ \frac{x^2 – 3^2}{x+3}$ $ \frac{(x – 3) (x + 3)}{x+3} = (x – 3)$ Ans is ) x – 3
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The value of cos229o + cos261o is: Optionsa) $ \frac {\sqrt 3}{2}$b) 2c) 0d) 1 Solution As per questioncos229 + cos261ocos229 + (cos 61o)2cos229 + (cos (90 – 29)o)2cos229 + (Sin 29)2 Formula :- $ Sin \theta $ = cos (90 – $ \theta)$cos229 + sin229 = 1Formula :- $ sin^2 \theta + cos^2 \theta
The value of cos2 29o + cos2 61o is: Read More »
What is the value of sec (t), if tan (t) = $ \frac{1}{3}$ ? Optionsa) $ \frac{ \sqrt3}{3}$b) $ \frac{2 \sqrt2}{3}$c) $ \frac{ \sqrt10}{3}$d) $ \frac{ \sqrt10}{9}$ Solution As per question tan Q = $ \frac {BC}{AC} = \frac 13 $(AB)2 = (AC)2 + (BC)2(AB)2 = (3)2 + (1)2(AB)2 = 9 + 1 = 10AB
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The value of sin2 30 – sin2 40 + sin2 45 – sin2 55 – sin2 35 + sin2 45 – sin2 50 + sin2 60 is: Optionsa) 4b) 0c) 1d) 2 Solution As per question sin2 30 – sin2 40 + sin2 45 – sin2 55 – sin2 35 + sin2 45 – sin2
Simplify $ \dfrac{x^3 + 15x^2 + 75x + 125}{x^2 – 25} (x – 5)$. Optionsa) x2 + 5x + 25b) x2 – 25c) x2 + 10x + 25d) x2 + 25 Solution As per question$ \dfrac{x^3 + 15x^2 + 75x + 125}{x^2 – 25} (x – 5)$ $ \dfrac{x^3 + 15x^2 + 75x + 125
Simplify x3 + 15×2 + 75x + 125/x2 – 25 (x – 5). Read More »
If $ cosec \theta = \frac 53 $ , then evaluate ($ sec^2 \theta – 1) \times cot^2 \theta \times (1 + cot^2 \theta)$. Optionsa) $ \frac {9}{16}$b) $ \frac {25}{9}$c) $ \frac {25}{16}$d) $ \frac {4}{5}$ Solution As per questionFormula :- $ sec^2 \theta – 1 = tan^2 \theta $$ 1 + cot^2 \theta
If cosec theta = 5/3 , then evaluate (sec2 theta – 1) x cot2 theta x (1 + cot2 theta). Read More »
Pipe A usually fills a tank in 6 hours. But due to a leak at the bottom of the tank, it takes extra 2 hours to fill the tank. If the tank is full, then how much time will it take to get emptied due to the leak? Optionsa) 16 hoursb) 12 hoursc) 24 hoursd)
A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km/h and 11 km/h, respectively. What is the distance (in metres) between them after 9 minutes? Optionsa) 50b) 40c) 60d) 30 Solution
Simplify $ 4 \frac{4}{5} \times \frac{3}{8} + (3 \frac{1}{2} + \frac{2}{3}) \times \frac{4}{5}$ Optionsa) $ \frac{3}{10}$b) $ \frac{77}{15}$c) $ \frac{15}{77}$d) $ \frac{10}{3}$ Solution As per question$ 4 \frac{4}{5} \times \frac{3}{8} + (3 \frac{1}{2} + \frac{2}{3}) \times \frac{4}{5}$$ 4 \frac{4}{5} \times \frac{3}{8} + ( \frac{7}{2} + \frac{2}{3}) \times \frac{4}{5}$$ 4 \frac{4}{5} \times \frac{3}{8} + (\frac{21+4}{6}) \times
Simplify 4 4/5 x 3/8 + (3 1/2 + 2/3) x 4/5 Read More »
Replace * by the smallest digit so that 723 *56* is divisible by 6. Optionsa) 1b) 2c) 3d) 4 Solution As per question723 *56*Divisible by 6 (2 x 3) divisible by both 2 and 3Divisible by 2 = Last digit is evenFrom options : Number may be 2 and 4Divisible by 3 = sum of
Replace * by the smallest digit so that 723 *56* is divisible by 6. Read More »