SSC CHSL 10 July 2019 Shift-1

The simplified value of $$\left[1\frac{1}{5}  of  \left\{\frac{3}{7} - \left(1\frac{4}{15}-\frac{13}{15}\right) \times \frac{5}{7}\right\}\right] \div \left(\frac{6}{7} \div 5\right)$$ is:

The point A of a triangle ABC moves parallel to the straight line BC. Which one amongthe following also moves along a straightline parallel to BC?
(a) The circumcentre (b) the centroid (c) the incentre (d) the orthocentre.

If $$\frac{\cos \alpha}{\sin \alpha + \cos \beta} + \frac{\cos \beta}{\sin \beta - \cos \alpha} = \frac{x}{\sin \alpha - \cos \beta} + \frac{\cos \beta}{\sin \beta + \cos \alpha}$$ then '$$x$$' is equal to:

Three successive discounts on the marked price of an article turns out to be equivalent to a single discount of 19%.If the rates of the first and second discountare 10% and 4% respectively, what is the rate of the third discount?

The given Bar Graph presents the runs scored (A) and strike rate (B) of a batsman in five matches. Strike Rate is the number of runs scored per 100 balls faced. The strike rate (B) is taken on record only when the batsman scores at least 30 runs in a match.

What is the average strike rate of the batsman?

Ina $$\triangle$$ABC, AD is perpendicular to BC from A. if $$\angle BAC = 90^\circ,  then  AB^2 : AC^2$$ is equal to:

The total cost price of two articles is ₹2,000. Oneofthem is sold at a profit of 12% and the other at a loss of 12%. The overall gain in the transaction is 1.2%. The costprice of the article for which there wasa profit was:

For $$\theta$$ being an acute angle, $$4(2 \sin^2 \theta + 7 \cos^2 \theta) = 13$$. What is the value of $$\theta$$?

A boy standing by the side of a railway track finds that an Up train crosses him in 8 seconds and a Down train of twice the length of that of the Up train crosses him in 20 seconds. How long (in seconds) will the two trains take to cross each other?

$$a, b, c$$ are three positive numbers, such that, $$(a + b + c) = 20, a^2 + b^2 + c^2 = 152$$. The value of $$(ab + bc + ca)$$ is equal to: