New Mathematics for Class X>Chapter 16 - Model Test Paper>SECTION>Q 7

EASY

10th CBSE

IMPORTANT

Earn 100

Can two numbers have $18$ as their HCF and $380$ as their LCM. Give reasons.

Important Questions on Model Test Paper

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 16 - Model Test Paper>SECTION>Q 8

α, β

are zeros of the polynomial

p (x) = x^{2} - (k + 6) x + 2 (2 k - 1)

. Find the value of

k

if

α + β = \frac{1}{2} α β

.

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 16 - Model Test Paper>SECTION>Q 9

Write the set of values of

k

for which the quadratic equation

2 x^{2} + k x + 8 = 0

has real roots.

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 16 - Model Test Paper>SECTION>Q 10

If

x = r sinAcosC

,

y = r sinAsinC

and

z = r cosA

, prove that

x^{2} + y^{2} + z^{2} = r^{2}

.

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 16 - Model Test Paper>SECTION>Q 11

If

A, B

and

C

are interior angles of a triangle

A B C

, then show that

\sin (\frac{B + C}{2}) = \cos (\frac{A}{2})

.

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 16 - Model Test Paper>SECTION>Q 12

A chord of a circle of radius

12 cm

subtends an angle of

120 °

at the centre. If the area of the corresponding segment of the circle is

k {cm}^{2}

, find

k

.
(Use

π = 3.14

and

\sqrt{3} = 1.73

)

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 16 - Model Test Paper>SECTION>Q 13

Three sets of English, Hindi and Mathematics books have to be stacked in such a way that all the books are stored topic wise and the height of each stack is the same. The number of English books is

96

, the number of Hindi books is

240

and the number of Mathematics book is

336

. Assuming that the books are of the same thickness, determine the number of stacks of English, Hindi and Mathematics books.

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 16 - Model Test Paper>SECTION>Q 13

A sweet seller has

420

kaju barfis and

130

badam burfis. She wants to stack them in such a way that each stack has the same number and they take up the least area of the tray. What is the number of barfis that can be placed in each stack for this purpose?

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 16 - Model Test Paper>SECTION>Q 14

If one zero of the polynomial

3 x^{2} - 8 x - (2 k + 1)

is seven times the other, find both zeros of the polynomial and the values of

k

.