Vardaan Learning Institute
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NCERT MATHS TEST 02
General Instructions: All questions are compulsory. Questions are strictly from
Even
Chapters.
SECTION A (Multiple Choice Questions) - 1 Mark Each
1.
The zeroes of the quadratic polynomial x² + 7x + 10 are:
[1]
2.
The discriminant of the quadratic equation 2x² - 4x + 3 = 0 is:
[1]
3.
If ∆ABC ~ ∆DEF and the ratio of their corresponding sides is 4:9, then the ratio of their areas is:
[1]
4.
The value of (1 - tan² 45°) / (1 + tan² 45°) is:
[1]
5.
From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre
is
25 cm. The radius of the circle is:
[1]
6.
A cylinder and a cone are of the same base radius and of the same height. The ratio of their volumes
is:
[1]
7.
If P(E) = 0.05, what is the probability of 'not E'?
[1]
8.
A quadratic polynomial whose zeroes are -3 and 4 is:
[1]
9.
The nature of roots of the quadratic equation x² + 4x + 5 = 0 is:
[1]
10.
In a right triangle ABC, right-angled at B, if AB = 24 cm, BC = 7 cm, determine sin A.
[1]
11.
In Figure, if DE || BC, find EC. Given AD = 1.5 cm, DB = 3 cm, AE = 1 cm.
[1]
12.
The tangents drawn at the ends of a diameter of a circle are:
[1]
13.
The Total Surface Area of a solid hemisphere of radius r is:
[1]
14.
A die is thrown once. The probability of getting a prime number is:
[1]
15.
The degree of the polynomial p(x) = (x + 1)(x² - x + 1) is:
[1]
16.
Find the value of k for which the quadratic equation 2x² + kx + 3 = 0 has two real equal roots.
[1]
17.
The value of sin 60° cos 30° + sin 30° cos 60° is:
[1]
18.
If the perimeter and the area of a circle are numerically equal, then the radius of the circle is:
[1]
19.
Which of the following cannot be the probability of an event?
[1]
20.
A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q
so
that OQ = 12 cm. Length PQ is:
[1]
SECTION B (Very Short Answer Questions) - 2 Marks Each
21.
Find the zeros of the quadratic polynomial x² - 2x - 8 and verify the relationship
between the zeros and the coefficients.
[2]
22.
Find the roots of the quadratic equation 2x² - x + 1/8 = 0 by factorization.
[2]
23.
ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the
point O. Show that AO/BO = CO/DO.
[2]
24.
If tan 2A = cot (A - 18°), where 2A is an acute angle, find the value of A.
[2]
25.
One card is drawn from a well-shuffled deck of 52 cards. Calculate the probability
that
the card will be (i) an ace, (ii) not be an ace.
[2]
SECTION C (Short Answer Questions) - 3 Marks Each
26.
Find two consecutive odd positive integers, sum of whose squares is 290.
[3]
27.
Prove that the parallelogram circumscribing a circle is a rhombus.
[3]
28.
Prove the identity: √[(1 + sin A)/(1 - sin A)] = sec A + tan A.
[3]
29.
Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively, are melted to form a
single solid sphere. Find the radius of the resulting sphere.
[3]
30.
BL and CM are medians of a triangle ABC right angled at A. Prove that 4(BL² + CM²) =
5BC².
[3]
31.
A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at
random
from the box, find the probability that it bears (i) a two-digit number (ii) a perfect square
number.
[3]
SECTION D (Long Answer Questions) - 5 Marks Each
32.
A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it
would have taken 3 hours more to cover the same distance. Find the speed of the train.
[5]
33.
State and prove the Basic Proportionality Theorem (Thales Theorem).
[5]
34.
A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the
cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the
area
of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of
₹
500 per m². (Note that the base of the tent will not be covered with canvas.)
[5]
35.
Prove that: (sin A + cosec A)² + (cos A + sec A)² = 7 + tan² A + cot² A.
[5]
SECTION E (Case Study Based Questions) - 4 Marks Each
36.
Case Study 1: A rollercoaster ride is an exciting activity at an amusement park.
The
shape of the track often follows a parabolic path. Suppose the path of a part of the roller coaster
is
given by the polynomial p(x) = x² - 2x - 8.
(i) What is the shape of the graph of a quadratic polynomial? [1]
(ii) Find the zeroes of the given polynomial p(x). [1]
(iii) If α and β are the zeroes, find the value of α + β + αβ. [2]
(i) What is the shape of the graph of a quadratic polynomial? [1]
(ii) Find the zeroes of the given polynomial p(x). [1]
(iii) If α and β are the zeroes, find the value of α + β + αβ. [2]
[4]
37.
Case Study 2: A vertical pole of length 6 m casts a shadow 4 m long on the ground
and
at the same time a tower casts a shadow 28 m long.
(i) Are the two triangles formed (Pole-Shadow and Tower-Shadow) similar? By which criterion? [1]
(ii) Write the ratio of corresponding sides if the triangles are similar. [1]
(iii) Find the height of the tower. [2]
(i) Are the two triangles formed (Pole-Shadow and Tower-Shadow) similar? By which criterion? [1]
(ii) Write the ratio of corresponding sides if the triangles are similar. [1]
(iii) Find the height of the tower. [2]
[4]
38.
Case Study 3: A gulab jamun, contains sugar syrup up to about 30% of its volume.
Find
approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two
hemispherical ends with length 5 cm and diameter 2.8 cm.
(i) Find the volume of the cylindrical part. [1]
(ii) Find the volume of two hemispherical ends. [1]
(iii) Find the total volume of one gulab jamun and the syrup in 45 gulab jamuns. [2]
(i) Find the volume of the cylindrical part. [1](ii) Find the volume of two hemispherical ends. [1]
(iii) Find the total volume of one gulab jamun and the syrup in 45 gulab jamuns. [2]
[4]