Question
Two circles intersect in points P and Q. A secant passing through P intersects the circles in Aand B respectively. Tangents to the circles at A and B intersect at T. Prove that A, Q, B and T lie on a circle.
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The following histogram shows the ages of teachers in a school.
Read the histogram and answer the questions that follow:
(a) How many teachers are in the age group of 45 – 50 years?
(b) How many teachers are 40 years or above 40 years of age?
(c) How many teachers are below 35 years of age?
(d) Which age group has the maximum number of teachers?
(e) Which age group has the minimum number of teachers?
Read the histogram and answer the questions that follow:
(a) How many teachers are in the age group of 45 – 50 years?
(b) How many teachers are 40 years or above 40 years of age?
(c) How many teachers are below 35 years of age?
(d) Which age group has the maximum number of teachers?
(e) Which age group has the minimum number of teachers?
A manufacturer in Noida (UP) sold a carton of hair oil to a dealer in Raipur (Chhattisgarh) for ₹ $22,000$. The dealer in Raipur sold it to a consumer in Bastar (Chhattisgarh) at a profit of ₹ $5,000$ . If the rate of GST is $18 \%$, find :
(i) the net IGST, CSGT, and SGST payable by the dealer in Raipur.
(ii) the cost price of the hair oil for the consumer.
→(i) the net IGST, CSGT, and SGST payable by the dealer in Raipur.
(ii) the cost price of the hair oil for the consumer.
ABC is a triangle whose vertices are A(-4, 2), B(O, 2) and C(-2, -4). D. E and Fare the midpoint of the sides BC, CA and AB respectively. Prove that the centroid of the Δ ABC coincides with the centroid of the Δ DEF.
Construct an isosceles triangle ABC such that AB = 6cm, BC = AC = 4cm. Bisect ∠C internally and mark a point P on this bisector such that CP = 5 cm. Find the points Q and R which are 5 cm from P and also 5 cm from the line AB.
A Mathematics aptitude test of 50 students was recorded as follows:
Draw a histogram for the above data using a graph paper and locate the mode.
| Marks | No. of Students |
| 50 - 60 | 4 |
| 60 - 70 | 8 |
| 70 - 80 | 14 |
| 80 - 90 | 19 |
| 90 - 100 | 5 |
Find the value of the middle most term(s) of the $AP -11,-7,-3$, $\ldots\ldots$ 49.
→On what sum of money will the compound interest for $2$ years at $10\%$ p.a. compounded half-yearly amount to $Rs.3,448.10?$
→On what sum will the difference between compound interest and the simple interest for $3$ years at $12\%$ be $Rs.1,123.20?$
→Draw a circle at a radius of 3 cm. Take a point at 5.5 cm from the center at the circle. From point P, draw two tangents to the circle.
Calculate the mean of the distribution given below using the short cut method.
→| Marks | $11 - 20$ | $21 - 30$ | $31 - 40$ | $41 - 50$ | $51 - 60$ | $61 - 70$ | $71 - 80$ |
| No. of students | $2$ | $6$ | $10$ | $12$ | $9$ | $7$ | $4$ |