Find the value of a and b if (x-1) and (x+1) are factors of x⁴+ax³-3x²+2x+b

Sanjay invested Rs. 48000 in two different parts one at 10% CI (Compounded half yearly) and another one at 15% SI. At the end of the year he received total interest Rs. 5490, then find the amount invested in SI?

If ( 2x – y): ( 5x+3y)=3 : 8 then ( x² + y²) : ( x² – y²)=?

Find the value tanθ-cosθ in the given figure.

Find the value of given expression.

30 – [40 – {56 – (25 – 13 – 12)}]

Study the information carefully to answer the question that follow.
In a college there are 900 students who are doing Post Graduation (PG) in any one of the subjects, out of five different subjects, out of the five different subjects viz. Zoology, Botany, Mathematics, Physics and Statistics. The ratio between the boys and the girls among those is 5:4 respectively, 20% of the total girls are doing PG in Zoology and 25% of the total girls are doing PG in Statistics. Total number of students doing PG in Botany is 220. Total students who are doing PG in Mathematics is 150. Respectively ratio between the number of girls and the number of boys doing PG in statistics is 2:3. Twenty percent of the total number of boys are doing PG in Mathematics is 1:2 respectively. There are equal number of boys and girls who are doing PG in PG in Physics. 180 students are doing PG in Zoology.
What is the respective ratio between the boys doing PG in Mathematics and the number of girls doing PG in Botany?

A 160-meter-long train running at a speed of 90 km/h crosses a platform is 18 s. What is the length of the platform in metre?

Excluding stoppages, the speed of a train is 120 kmph and including stoppage, it is 50 kmph. For how many minutes does the train stop per hour?