SSC CGL MATHS QUIZ-43

$\mathrm{ABCD}$ is a cyclic quadrilateral. Diagonals BD and AC intersect each other at $\mathrm{E} .$ If $\angle \mathrm{BEC}=$ $123^{\circ}$ and $\angle \mathrm{ECD}=32^{\circ}$, then what is the measure of $\angle \mathrm{BAC} ?$

If the amount received at the end of 2nd and 3rd year at compound interest compounded annually on a certain sum is Rs. 21000 and Rs. 22470 respectively then find the rate of interest (in %)?

In a circle centre at $\mathrm{O}$, a tangent $\mathrm{AP}$ is drawn from an external point $\mathrm{A}$. If $\mathrm{OA}=61 \mathrm{~cm}$ and $\mathrm{OP}=11 \mathrm{~cm}$, then the lengthof tangent AP is:

Mohan spends $76 \%$ of his income. If her income increases by $12 \%$ and savings increases by $15 \%$, then what is the approximate increase in his expenditure (in %)?

A and B can separately do a piece of work in 20 and 15 days respectively. They worked together for 6 days after which B was replaced by C. The work was finished in next 4 days. The number of days in which C alone could do the work is :

A shopkeeper buys a washing machine and a television together for Rs. 57,400 . He sold the washing machine at a profit of $25 \%$ and TV at a loss of $20 \%$. If he sold both the articles at the same price. Then the CP of the dearer article.(in rupees)

From each of two given numbers, half the smaller number is subtracted. After such subtraction, the larger number is 4 times as large as the smaller number. What is the ratio of the numbers?

$\mathrm{AB}$ is the diameter of a circle with centre $\mathrm{O} . \mathrm{C}$ and $\mathrm{D}$ are two points on the circumference of the circle on either side of $\mathrm{AB}$, such that $\angle C A B=43^{\circ}$ and $\angle A B D=58^{\circ}$. What is difference (in degrees) between the measures of $\angle C A D$ and $\angle C B D$ ?