How many diagonals are there in an octagon?
- A24
- B28
- C20
- D36
Question types
Model Paper 4 question types
45 questions across 6 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.
45
Questions
6
Question groups
5
Question types
01
M.C.Q (1 Marks)
18 Q→022 Marks Questions
7 Q→033 Marks Question
9 Q→045 Marks Questions
6 Q→05Assertion (A) & Reason (B) MCQ
2 Q→06Case study (4 Marks)
3 Q→Sample Questions
Model Paper 4 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Mark the correct answer for: $i ^{-38}=$ ?
- Ai
- B-i
- C-1
- D1
If $A$ and $B$ are two sets, then $A \cap(A \cup B)$ equals
- AB
- B$\phi$
- CA
- D$A \cap B$
If a, b, c are real numbers such that a > b, c < 0
- Aac > bc
- Bac < bc
- C$a c \geq b c$
- D$ac \neq bc$
If $\sin x=\frac{-2 \sqrt{6}}{5}$ and $x$ lies in quadrant III, then $\cot x$ ?
- A$\frac{3}{2 \sqrt{6}}$
- B$\frac{1}{2 \sqrt{6}}$
- C$\frac{-1}{2 \sqrt{6}}$
- D$\frac{-3}{2 \sqrt{6}}$
Find the equation of hyperbola having Foci $( \pm 3 \sqrt{5}, 0)$, the latus rectum is of length 8 .
View full solution →If $A =(1,2,3), B =\{4\}, C =\{5\}$, then verify that $A \times(B-C)=(A \times B)-(A \times C)$.
View full solution →Find the lengths of major and minor axes, coordinates of foci, vertices and the eccentricity: $3 x^2+2 y^2=6$.
View full solution →Three vertices of a parallelogram, taken in order, are (-1, -6), (2, -5) and (7, 2). Write the coordinates of its fourth vertex.
For all sets A, B and C
Is $(A \cap B) \cup C=A \cap(B \cup C)$ ?
Justify your statement.
View full solution →Is $(A \cap B) \cup C=A \cap(B \cup C)$ ?
Justify your statement.
Find the distance between the following pairs of points:
(i) (2, 3, 5) and (4, 3, 1)
(ii) (-3, 7, 2) and (2, 4, -1)
(iii) (-1, 3, -4) and (1, -3, 4)
(iv) (2, -1, 3) and (-2, 1, 3)
(i) (2, 3, 5) and (4, 3, 1)
(ii) (-3, 7, 2) and (2, 4, -1)
(iii) (-1, 3, -4) and (1, -3, 4)
(iv) (2, -1, 3) and (-2, 1, 3)
The longest side of a triangle is 3 times the shortest side and the third side is 2 cm shorter than the longest side. If the perimeter of the triangle is at least 61 cm. Find the minimum length of the shortest side.
$\begin{array}{l}\text { If } u =\{1,2,3,4,5,6,7,8,9,10,12,24\} \\ A =\{ x : x \text { is prime and } x \leq 10\} \\ B =\{ x : x \text { is a factor of } 24\}\end{array}$
Verify the following result
i. $A - B = A \cap B^{\prime}$
ii. $(A \cup B)^{\prime}=A^{\prime} \cap B^{\prime}$
iii. $(A \cap B)^{\prime}=A^{\prime} \cup B^{\prime}$
View full solution →Verify the following result
i. $A - B = A \cap B^{\prime}$
ii. $(A \cup B)^{\prime}=A^{\prime} \cap B^{\prime}$
iii. $(A \cap B)^{\prime}=A^{\prime} \cup B^{\prime}$
If $(x+i y)^{1 / 3}=a+i b$, where $x, y$, $a, b \in R$, then show that $\frac{x}{a}-\frac{y}{b}=-2\left(a^2+b^2\right)$.
View full solution →Show that a real value of x will satisfy the equation $\frac{1-i x}{1+i x}=a-i$ if $a ^2+ b ^2=1$ where a and b are real
View full solution →Two dice are thrown. The events A, B, C, D, E and F are described as follows: A = Getting an even number on the first die.
B = Getting an odd number on the first die.
C = Getting at most 5 as a sum of the numbers on the two dice.
D = Getting the sum of the numbers on the dice greater than 5 but less than 10.
E = Getting at least 10 as the sum of the numbers on the dice.
F = Getting an odd number on one of the dice.
Describe the following events: A and B, B or C, B and C, A and E, A or F, A and F.
B = Getting an odd number on the first die.
C = Getting at most 5 as a sum of the numbers on the two dice.
D = Getting the sum of the numbers on the dice greater than 5 but less than 10.
E = Getting at least 10 as the sum of the numbers on the dice.
F = Getting an odd number on one of the dice.
Describe the following events: A and B, B or C, B and C, A and E, A or F, A and F.
Prove that: $4 \sin A \sin \left(60^{\circ}- A \right) \sin \left(60^{\circ}+ A \right)=\sin 3 A$.
Hence deduce that: $\sin 20^{\circ} \times \sin 40^{\circ} \times \sin 60^{\circ} \times \sin 80^{\circ}=\frac{3}{16}$
View full solution →Hence deduce that: $\sin 20^{\circ} \times \sin 40^{\circ} \times \sin 60^{\circ} \times \sin 80^{\circ}=\frac{3}{16}$
Prove that $\cos \frac{2 \pi}{15} \cdot \cos \frac{4 \pi}{15} \cdot \cos \frac{8 \pi}{15} \cdot \cos \frac{16 \pi}{15}=\frac{1}{16}$
View full solution →The Sum of two no. is 6 times their geometric mean, show that no. are in the ratio $(3+3 \sqrt{2}):(3-2 \sqrt{2})$
View full solution →Assertion (A): The expansion of $(1+ x )^{ n }=n_{c_0}+n_{c_1} x+n_{c_2} x^2 \ldots+n_{c_n} x^n$.
Reason (R): If $x=-1$, then the above expansion is zero.
Reason (R): If $x=-1$, then the above expansion is zero.
- ABoth A and R are true and R is the correct
- BBoth A and R are true but R is not the explanation of A . correct explanation of A.
- CA is true but $R$ is false.
- DA is false but $R$ is true.
Consider the following data
Assertion (A): The variance of the data is 45.8.
Reason (R): The standard deviation of the data is 6.77.
| $x _{ i }$ | 4 | 8 | 11 | 17 | 20 | 24 | 32 |
| $f _{ i }$ | 3 | 5 | 9 | 5 | 4 | 3 | 1 |
Reason (R): The standard deviation of the data is 6.77.
- ABoth A and R are true and R is the correct explanation of A.
- BBoth A and R are true but R is not the correct explanation of A.
- CA is true but R is false.
- DA is false but R is true.
An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results:
i. Which firm A or B shows greater variability in individual wages? (1)
ii. Find the standard deviation of the distribution of wages for frim B. (1)
iii. Find the coefficient of variation of the distribution of wages for firm A. (2)
OR
Find the amount paid by firm A. (2)
| Particulars | Firm A | Firm B |
| No. of wage earners | 586 | 648 |
| Mean of monthly wages | ₹ 5253 | ₹ 5253 |
| Variance of the distribution of wages | 100 | 121 |
i. Which firm A or B shows greater variability in individual wages? (1)
ii. Find the standard deviation of the distribution of wages for frim B. (1)
iii. Find the coefficient of variation of the distribution of wages for firm A. (2)
OR
Find the amount paid by firm A. (2)
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