MODEL PAPER 4 (STANDARD) - CBSE STD 10 Maths Questions

Consider the frequency distribution of the heights of 60 students of a class:

Height (in cm)	No. of Students	Cumulative Frequency
150-155	16	16
155-160	12	28
160-165	9	37
165-170	7	44
170-175	10	54
175-180	6	60

The sum of the lower limit of the modal class and the upper limit of the median class is

A
320
✓
315
C
330
D
310

Answer: B.

View full solution →

Q 2M.C.Q (1 Marks)1 Mark

A bag contains $5$ red balls and n green balls. If the probability of drawing a green ball is three times that of a red ball, then the value of n is:

A
$20$
B
$18$
✓
$15$
D
$10$

Answer: C.

View full solution →

Q 3M.C.Q (1 Marks)1 Mark

In the given figure. JKLM is a square with sides of length 6 units. Points $A$ and $B$ are the mid-points of sides KL and LM respectively. If a point is selected at random from the interior of the square. What is the probability that the point will be chosen from the interior of $\triangle JAB$ ?

A
$\frac{5}{8}$
✓
$\frac{3}{8}$
C
$\frac{7}{8}$
D
$\frac{3}{4}$

Answer: B.

View full solution →

Q 4M.C.Q (1 Marks)1 Mark

Area of a segment of a circle of radius $r$ and central angle $90^{\circ}$ is:

A
$\frac{2 \pi r}{4}-\frac{1}{2} r^2$
✓
$\frac{\pi r^2}{4}-\frac{1}{2} r^2$
C
$\frac{\pi r ^2}{2}-\frac{1}{2} r ^2$
D
$\frac{2 \pi r}{4}-r^2 \sin 90^{\circ}$

Answer: B.

View full solution →

Q 5M.C.Q (1 Marks)1 Mark

$O$ is the centre of a circle of diameter $4 \ cm$ and $\text{OABC}$ is a square, if the shaded area is $\frac{1}{3}$ area of the square, then the side of the square is $....... .$

✓
$\sqrt{3 \pi} \ cm$
B
$\pi \sqrt{3} \ cm$
C
$3 \pi \ cm$
D
$3 \sqrt{\pi} \ cm$

Answer: A.

View full solution →

Q 6Assertion (A) & Reason (B) MCQ1 Mark

Assertion $(A):$ Sum of first $10$ terms of the arithmetic progression $-0.5,-1.0,-1.5, \ldots$ is $27.5$
Reason $(R):$ Sum of n terms of an $A.P.$ is given as $S _{ n }=\frac{n}{2}[2 a+(n-1) d]$ where $a =$ first term, $d =$ common difference.

✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
C
$A$ is true but $R$ is false.
D
$A$ is false but $R$ is true.

Answer: A.

View full solution →

Q 7Assertion (A) & Reason (B) MCQ1 Mark

Assertion (A): The given figure represents a hemisphere surmounted by a conical block of wood. The diameter of their bases is 6 cm each and the slant height of the cone is 5 cm . The volume of the solid is $196 cm^3$

Reason (R): The volume hemisphere is given by $\frac{2}{3} \pi r^3$

A
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is not the correct explanation of A.
C
A is true but R is false.
✓
A is false but R is true.

Answer: D.

View full solution →

Q 82 Marks Questions2 Marks

A car has two wipers which do not overlap. Each wiper has a blade of length $25 \ cm$ sweeping through an angle of $115^{\circ}$. Find the total area cleaned at each sweep of the blades.

View full solution →

Q 92 Marks Questions2 Marks

Prove that: $\frac{1-\cos A}{1+\cos A}=(\cot A-\operatorname{cosec} A)^2$

View full solution →

Q 102 Marks Questions2 Marks

Find the area of the segment shown in Fig., if radius of the circle is $21 \ cm$ and $\angle A O B=120^{\circ}$ $($Use $\pi=\frac{22}{7} )$

View full solution →

Q 112 Marks Questions2 Marks

Prove that: $\sin ^4 A-\cos ^4 A=\sin ^2 A-\cos ^2 A=2 \sin ^2 A-1=1-2 \cos ^2 A$

View full solution →

Q 122 Marks Questions2 Marks

If a circle touches the side $B C$ of a triangle $A B C$ at $P$ and extended sides $A B$ and $A C$ at $Q$ and $R$, respectively, prove that $AQ=\frac{1}{2}(BC+CA+AB)$

View full solution →

Q 133 Marks Question3 Marks

In the given figure, $O$ is the centre of a circle. PT and PQ are tangents to the circle from an external point $P$. If $\angle T P Q=70^{\circ}$, find $\angle T R Q$.

View full solution →

Q 143 Marks Question3 Marks

Find median for the following data:

Class Interval	Frequency
$10 - 19$	$2$
$20 - 29$	$4$
$30 - 39$	$8$
$40 - 49$	$9$
$50 - 59$	$4$
$60 - 69$	$2$
$70 - 79$	$1$

View full solution →

Q 153 Marks Question3 Marks

If $1+\sin ^2 \theta=3 \sin \theta \cos \theta$, then prove that $\tan \theta=1$, or $\frac{1}{2}$.

View full solution →

Q 163 Marks Question3 Marks

Two tangents $TP$ and $TQ$ are drawn to a circle with centre $O$ from an external point $T$ . Prove that $\angle PTQ =2\ \angle O P Q$.

View full solution →

Q 173 Marks Question3 Marks

Graphically, solve the following pair of equations:
$2 x+y=6$
$2 x-y+2=0$
Find the ratio of the areas of the two triangles formed by the lines representing these equations with the $x-$ axis and the lines with the $y-$ axis.

View full solution →

Q 185 Marks Questions5 Marks

Rasheed got a playing top $($lattu$)$ as his birthday present, which surprisingly had no colour on it. He wanted to colour it with his crayons. The top is shaped like a cone surmounted by a hemisphere. The entire top is $5 \ cm$ in height and the diameter of the top is $3.5 \ cm$ . Find the area he has to colour. $($Take $\pi=\frac{22}{7} )$.

View full solution →

Q 195 Marks Questions5 Marks

If the roots of the quadratic equation $(x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0$ are equal. Then show that $a=b$ $=c$

View full solution →

Q 205 Marks Questions5 Marks

Find the missing frequencies in the following distribution, if the sum of the frequencies is $120$ and the mean is $50.$

Class	$0-20$	$20-40$	$40-60$	$60-80$	$80-100$
Frequency	$17$	$f_1$	$32$	$f_2$	$19$

View full solution →

Q 215 Marks Questions5 Marks

A rocket is in the form of a right circular cylinder closed at the lower end and surmounted by a cone with the same radius as that of cylinder. The diameter and height of cylinder are $6 \ cm$ and $12 \ cm ,$ respectively. If the slant height of the conical portion is $5 \ cm,$ then find the total surface area and volume of rocket. $($Use $\pi=3.14)$

View full solution →

Q 225 Marks Questions5 Marks

In the following figure, $\triangle \text{FEC} \cong \triangle \text{GBD}$ and $\angle 1=\angle 2$ Prove that $\triangle \text{ADE} \cong \triangle \text{ABC}$.

View full solution →

Q 23Case study (4 Marks)4 Marks

Read the text carefully and answer the questions:
Skysails is the genre of engineering science that uses extensive utilization of wind energy to move a vessel in the seawater.
The 'Skysails' technology allows the towing kite to gain a height of anything between $100$ metres $- 300$ metres.
The sailing kite is made in such a way that it can be raised to its proper elevation and then brought back with the help of a 'telescopic mast' that enables the kite to be raised properly and effectively.
Based on the following figure related to sky sailing, answer the following questions:

$(a)$ In the given figure, if $\sin \theta=\cos \left(\theta-30^{\circ}\right)$, where $\theta$ and $\theta-30^{\circ}$ are acute angles, then find the value of $\theta$.
$(b)$ What should be the length of the rope of the kite sail in order to pull the ship at the angle $\theta$ $($calculated above$)$ and be at a vertical height of $200 m$ ?
OR
What should be the length of the rope of the kite sail in order to pull the ship at the angle $\theta \ ($calculated above$)$ and be at a vertical height of $150 m$ ?
$(c)$ In the given figure, if $\sin \theta=\cos \left(3 \theta-30^{\circ}\right),$ where $\theta$ and $3 \theta-30^{\circ}$ are acute angles, then find the value of $\theta$.

View full solution →

Q 24Case study (4 Marks)4 Marks

Read the text carefully and answer the questions :
In order to facilitate smooth passage of the parade, movement of traffic on certain roads leading to the route of the Parade and Tableaux ah rays restricted. To avoid traffic on the road Delhi Police decided to construct a rectangular route plan, as shown in the figure.

(a) If Q is the mid point of BC, then what are the coordinates of Q?
(b) What is the length of the sides of quadrilateral PQRS?
OR
What is the length of route ABCD?
(c) What is the length of route PQRS?

View full solution →

Q 25Case study (4 Marks)4 Marks

Read the text carefully and answer the questions:
Deepa has to buy a scooty.
She can buy scooty either making cashdown payment of $₹ 25,000$ or by making $15$ monthly instalments as below.
Ist month $- ₹ 3425, II^{nd}$ month $- ₹ 3225, III^{rd}$ month $- ₹ 3025, IV^{th}$ month $ - ₹ 2825$ and so on

$(a)$ Find the amount of $6^{th}$ instalment.
$(b)$ Total amount paid in $15$ instalments.
OR
If Deepa pays $₹ 2625$ then find the number of instalment.
$(c)$ Deepa paid $10^{th}$ and $11^{th}$ instalment together find the amount paid that month.

View full solution →

MODEL PAPER 4 (STANDARD) question types

MODEL PAPER 4 (STANDARD) questions

Generate a MODEL PAPER 4 (STANDARD) paper free

MODEL PAPER 4 (STANDARD) Maths - MODEL PAPER 4 (STANDARD)

MODEL PAPER 4 (STANDARD) question types

MODEL PAPER 4 (STANDARD) questions

Generate a MODEL PAPER 4 (STANDARD) paper free