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10th Standard Mathematics English Medium Free Online Test 1 Mark Questions with Answer Key 2020 - 2021 Part - 6

Published on: 04/12/2020

Download Tamil Nadu 10th Standard Maths question papers, model tests, one-mark questions, important questions, and public exam papers in PDF format. Free study materials and answer keys for TN State Board students.

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Std: 10th Standard - Maths

chapter: - Model Question paper

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Questions:

Multiple Choice Question

25 x 1 = 25

A ladder of length 14m just reaches the top of a wall. If the ladder makes an angle of 60^o with the horizontal, then the height of the wall is ____________

(a)

\(14\sqrt { 3 } \)

(b)

\(28\sqrt { 3 } \)

(c)

\(7\sqrt { 3 } \)

(d)

\(35\sqrt { 3 } \)

(sec A + tan A)(1 - sin A) is equal to ___________

(a)

sec A

(b)

sin A

(c)

cosec A

(d)

cos A

In a competition containing two events A and B, the probability of winning the events A and B are \(\frac { 1 }{ 3 } \) and \(\frac { 1 }{ 4 } \) respectively and the probability if winning both events is ___________

(a)

\(\frac { 1 }{ 12 } \)

(b)

\(\frac { 5 }{ 12 } \)

(c)

\(\frac { 1 }{ 12 } \)

(d)

\(\frac { 7 }{ 12 } \)

The radius of a wire is decreased to one-third of the original. If volume the same, then the length will be increased _______of the original.

(a)

3 times

(b)

6 times

(c)

9 times

(d)

27 times

The y-intercept of the line 3x - 4y + 8 = 0 is ___________

(a)

\(-\frac { 8 }{ 3 } \)

(b)

\(\frac { 8 }{ 3 } \)

(c)

(d)

\(\frac { 1 }{ 2 } \)

The four vertices of a quadrilateral are (1, 2), (5, -6), (7, -4) and (k, -2) taken in order. If the area of quadrilateral is zero then find the value of k.

(a)

(b)

-2

(c)

(d)

In the given figure if OC = 9 cm and OB = 15 cm then OB + BD is equal to ____________

(a)

23 cm

(b)

24 cm

(c)

27 cm

(d)

30 cm

If P and Q are matrices, then which of the following is true?

(a)

PQ ≠ QP

(b)

(P^T)^T≠ P

(c)

P + Q ≠ Q + P

(d)

All are true

If \(\frac { p }{ q } =a\) then \(\frac { { p }^{ 2 }+{ q }^{ 2 } }{ { p }^{ 2 }-{ q }^{ 2 } } \) ___________

(a)

\(\frac { { a }^{ 2 }+1 }{ { a }^{ 2 }-1 } \)

(b)

\(\frac { 1+{ a }^{ 2 } }{ 1-{ a }^{ 2 } } \)

(c)

\(\frac { 1-{ a }^{ 2 } }{ 1-{ +a }^{ 2 } } \)

(d)

\(\frac { { a }^{ 2 }-1 }{ { a }^{ 2 }+1 } \)

10.

Sum of first n terms of the series \(\sqrt { 2 } +\sqrt { 8 } +\sqrt { 18 } +...\) is ____________

(a)

\(\frac { n(n+1) }{ 2 } \)

(b)

\(\sqrt { n } \)

(c)

\(\frac { n\left( n+1 \right) }{ \sqrt { 2 } } \)

(d)

11.

The difference between the remainders when 6002 and 601 are divided by 6 is ____________

(a)

(b)

(c)

(d)

12.

The function t which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined Fahrenheit degree is 95, then the value of C \(t(C)=\frac { 9c }{ 5 } +32\) is ___________

(a)

(b)

(c)

(d)

13.

The mean of a observation x₁, x₂, x₃, ......... x_n is \(\bar { x } \). If each observation is multiplied by p, there the mean of the new observations is ___________

(a)

\(\frac { \bar { x } }{ p } \)

(b)

p\(\bar { x } \)

(c)

\(\bar { x } \)

(d)

P+\(\bar { x } \)

14.

The maximum value of sin θ is ___________

(a)

\(\frac{1}{2}\)

(b)

\(\frac{\sqrt{3}}{2}\)

(c)

(d)

\(\frac{1}{\sqrt2}\)

15.

If cos9∝ = sin∝ and 9∝ < 90^o, then the value of tan t∝ is

(a)

\(\frac{1}{\sqrt{3}}\)

(b)

\({\sqrt{3}}\)

(c)

(d)

16.

Which of the following is incorrect?

(a)

P(A) > 1

(b)

0 ≤ P(A) ≤ 1

(c)

P(ф) = 0

(d)

P(A) + P(\(\bar { A } \)) = 1

17.

(1 + tan \(\theta \) + sec\(\theta \)) (1 + cot\(\theta \) - cosec\(\theta \)) is equal to

(a)

(b)

(c)

(d)

-1

18.

An A.P. consists of 31 terms. If its 16^th term is m, then the sum of all the terms of this A.P. is

(a)

16 m

(b)

62 m

(c)

31 m

(d)

\(\frac { 31 }{ 2 } \) m

19.

If A is a point on the Y axis whose ordinate is 8 and B is a point on the X axis whose abscissae is 5 then the equation of the line AB is

(a)

8x + 5y = 40

(b)

8x - 5y = 40

(c)

x = 8

(d)

y = 5

20.

In figure if PR is tangent to the circle at P and O is the centre of the circle, then \(\angle PQR\) is

(a)

120^o

(b)

100°

(c)

110°

(d)

90°

21.

The volume (in cm³) of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is

(a)

\(\frac{4}{3}\pi\)

(b)

\(\frac{10}{3}\pi\)

(c)

\(5\pi\)

(d)

\(\frac{20}{3}\pi\)

22.

The height of a right circular cone whose radius is 5 cm and slant height is 13 cm will be

(a)

12 cm

(b)

10 cm

(c)

13 cm

(d)

5 cm

23.

Let f and g be two functions given by
f = {(0,1), (2,0), (3,-4), (4,2), (5,7)}
g = {(0,2), (1,0), (2,4), (-4,2), (7,0)} then the range of f o g is

(a)

{0,2,3,4,5}

(b)

{–4,1,0,2,7}

(c)

{1,2,3,4,5}

(d)

{0,1,2}

24.

If A = \(\left( \begin{matrix} 1 & 2 & 3 \\ 3 & 2 & 1 \end{matrix} \right) \), B = \(\left( \begin{matrix} 1 & 0 \\ 2 & -1 \\ 0 & 2 \end{matrix} \right) \) and C = \(\left( \begin{matrix} 0 & 1 \\ -2 & 5 \end{matrix} \right) \), Which of the following statements are correct?
(i) AB + C = \(\left( \begin{matrix} 5 & 5 \\ 5 & 5 \end{matrix} \right) \)
(ii) BC = \(\left( \begin{matrix} 0 & 1 \\ 2 & -3 \\ -4 & 10 \end{matrix} \right) \)
(iii) BA + C = \(\left( \begin{matrix} 2 & 5 \\ 3 & 0 \end{matrix} \right) \)
(iv) (AB)C = \(\left( \begin{matrix} -8 & 20 \\ -8 & 13 \end{matrix} \right) \)

(a)

(i) and (ii) only

(b)

(ii) and (iii) only

(c)

(ii) and (iv) only

(d)

all of these

25.

The square root of \(\frac { 256{ x }^{ 8 }{ y }^{ 4 }{ z }^{ 10 } }{ 25{ x }^{ 6 }{ y }^{ 6 }{ z }^{ 6 } } \) is equal to

(a)

\(\frac { 16 }{ 5 } \left| \frac { { x }^{ 2 }{ z }^{ 4 } }{ { y }^{ 2 } } \right| \)

(b)

\(16\left| \frac { { y }^{ 2 } }{ { x }^{ 2 }{ z }^{ 4 } } \right| \)

(c)

\(\frac { 16 }{ 5 } \left| \frac { y }{ x{ z }^{ 2 } } \right| \)

(d)

\(\frac { 16 }{ 5 } \left| \frac { x{ z }^{ 2 } }{ y } \right| \)

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Answers Key:

Multiple Choice Question

25 x 1 = 25

(d)
cos A

(a)
\(\frac { 1 }{ 12 } \)

(a)
4

(d)
All are true

(a)
\(\frac { { a }^{ 2 }+1 }{ { a }^{ 2 }-1 } \)

10.

11.

(b)
1

12.

13.

(b)
p\(\bar { x } \)

14.

15.

16.

(a)
P(A) > 1

17.

18.

(i) To check if h is one – one, we assume that h(b₁) = h(b₂)
Then we get 2.47 b₁+ 54.10 = 2.47 b₂ + 54.10
2.47b₁ = 2.47b₂ ⇒ b₁ = b₂
Thus, h(b₁) = h(b₂) ⇒ b₁ = b₂, So, the function h is one – one.
(ii) If the length of the thigh bone b = 50, then the height is
h(50) = (2.47 x 50) + 54.10 = 177.6 cms
(iii) If the height of a person is 147.96 cms, then h(b) = 147.96 and so the length of the thigh bone is given by 2.47b + 54.10 = 147.96.
b = \(\frac { 93.86 }{ 2.47 } \)
Therefore, the length of the thigh bone is 38 cms.