If x = 1 and y = 3 is a solution of 3x + 5y = k, then k =
- Pencils cost
Rs 2 each; pens cost Rs 7 each. John spends Rs 20 on these items.
Then the linear equation for the given data is:
A. 2x + 7y = 20
B. x + 7y = 20
C. 2x + y = 20
D. 2x – 7y = 20
- In a quadrilateral, if the opposite sides are equal and the diagonals
are also equal, then the quadrilateral is a:
- If three
angles of a quadrilateral measure 100°, 50° and
70°, then the fourth angle measures:
- The base of a
parallelogram is 14 cm, and its distance from the opposite side is
8 cm. Then its area is:
A. 144 cm2
B. 64 cm2
C. 76 cm2
D. 112 cm2
- The part of a
plane enclosed by a simple closed figure is called:
A. Volume of the figure
B. Planar region
C. Angular region
D. Area of the figure
- In the
figure given here, the value of x is:
- In the
figure given here, ABCD is a parallelogram. A circle through A, B
and C meets CD produced at E. Then AE =
- The total
surface area of a hemisphere of radius 14 cm is:
A. 942 cm2
B. 2464 cm2
C. 1375 cm2
D. 2104 cm2
- If the mean of 25, 27,
19, 29, 21, 23, p, 30, 28 and 20 is 24.7, then p =
- In the equation 3(x
– 3) – 3(y – 1) = 10, if x = 3, then find the
value of y.
ABCD is a parallelogram. Diagonals AC and BD intersect at O.
If ∠ADB = 40°, ∠ABD
25° and ∠DAC = 30°, then find ∠DOC.
the figure given here, if ABCD, ABFE and CDEF are parallelograms,
then prove that ar(ΔADE) = ar(ΔBCF).
- Diagonals AC and BD of
quadrilateral ABCD intersect at O such that ar (ΔBOC) = ar
(ΔAOD). Then show that ABCD is a trapezium.
- Prove that equal chords
of a circle subtend equal angles at its centre.
- Find the area of a
triangle whose sides measure 20 cm, 30 cm and 40 cm.
- A rectangular sheet of
paper 44 cm × 18 cm is rolled along its length and a cylinder
is formed. Find the volume of the cylinder.
- A dice is
thrown once. Find the probability of getting
(i) a number greater than 2 (ii) a number less than
- Draw the
graph of the equation 3x – 2y = 4. From the graph, find the
coordinates of the point when:
(i) x = 2
(ii) y = 7
- A railway half ticket costs half the full fare. The
reservation charges are the same for both half and full
tickets. A family of three adults and five children pay Rs 1200 for
their travel from Hyderabad to Bengaluru. If the basic fare is Rs x
and reservation charge is Rs y, then find the linear equation that
represents the given information.
figure given here, ABCD is a parallelogram. Compute the values of x
figure given here, ABCD is a parallelogram. AE ⊥ DC and CF
⊥ AD. If CD = 12 cm, AE = 8 cm and CF = 10 cm, find AD.
a triangle ABC in which BC = 8 cm, ∠B = 45° and AB –
AC = 3.5 cm.
- Find the
area of quadrilateral ABCD in which AB = 7 cm, BC = 6 cm, CD = 12
cm, DA = 15 cm and AC = 9 cm.
thickness of a hollow wooden cylinder is 2 cm. It is 35 cm long and
its inner radius is 12 cm. Find the volume of the wood required to
make the cylinder, assuming it is open at either end.
scored 75, 82 and 90 in three Mathematics tests. How many marks
must she obtain in the next test to get an average of exactly 85
for the four tests?
weather forecast from a news channel shows that out of the past 300
consecutive days, its weather forecast was correct 210 times.
(i) What is the probability that on a given day, it was
(ii) What is the probability that on a given day, it was not
coins are tossed simultaneously 200 times with the following
frequencies of different outcomes:
If the three coins are tossed simultaneously again, compute the
probability of two heads coming up.
- Draw the
graph of the equation 2x + y = 8. Read two solutions from the graph
and verify the same by actual substitution. Also find the points
where the line meets the two axes.
- Show that
the quadrilateral formed by joining the mid-points of the
consecutive sides of a rectangle is a rhombus.
AC and BD of cyclic quadrilateral ABCD intersect at right angles at
E. Line l through E and perpendicular to AB meets CD at F. Prove
that F is the mid-point of CD.
- E, F, G
and H are the mid-points of the sides of parallelogram ABCD. Show
- A cone of
height 24 cm has a curved surface area of 550 cm2. Find
its volume (take
- A die is
thrown 500 times with the frequencies for the outcomes 1, 2, 3, 4,
5, 6 as given in the following table:
Find the probability of getting each outcome.