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→02Assertion (A) & Reason (B) MCQ
2 Q→032 Marks Questions
7 Q→043 Marks Question
9 Q→05Case study (4 Marks)
3 Q→065 Marks Questions
6 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 $\sin x=\frac{-2 \sqrt{6}}{5}$ 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$\frac{-3}{2 \sqrt{6}}$
If $A$ and $B$ are two sets, then $A \cap(A \cup B)$ equals
- A$B$
- B$\phi$
- ✓$A$
- D$A \cap B$
Answer: C.
View full solution →If a, b, c are real numbers such that a > b, c < 0
- Aac > bc
- Bac < bc
- C$a c \geq b c$
- D$ac \neq bc$
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.
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
- ✓Both $A$ and $R$ are true but $R$ is not the explanation of $A$. correct explanation of $A.$
- C$A$ is true but $R$ is false.
- D$A$ is false but $R$ is true.
Answer: B.
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.
View full solution →For all sets $A, B$ and $C$ Is $(A \cap B) \cup C=A \cap(B \cup C)$ ? Justify your statement.
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 →Find the equation of hyperbola having Foci $( \pm 3 \sqrt{5}, 0)$, the latus rectum is of length $8 .$
View full solution →Evaluate: $\lim _{x \rightarrow \frac{1}{2}} \frac{8 x^3-1}{16 x^4-1}$.
View full solution →$\text { If } u =\{1,2,3,4,5,6,7,8,9,10,12,24\}$
$A =\{ x : x \text { is prime and } x \leq 10\}$
$B =\{ x : x \text { is a factor of } 24\}$
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 →$A =\{ x : x \text { is prime and } x \leq 10\}$
$B =\{ x : x \text { is a factor of } 24\}$
Verify the following result
$i. A - B = A \cap B^{\prime}$
$ii. (A \cup B)^{\prime}=A^{\prime} \cap B^{\prime}$
$iii. (A \cap B)^{\prime}=A^{\prime} \cup B^{\prime}$
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 →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 →Find $a , b$ and n in the expansion of $( a + b )^{ n }$ if the first three terms of the expansion are $729,7290$ and $30375$ respectively.
View full solution →Expand the given expression $\left(\frac{2}{x}-\frac{\pi}{2}\right)^5$
View full solution →A permutation is an act of arranging the objects or numbers in order. Combinations are the way of selecting the objects or numbers from a group of objects or collections, in such a way that the order of the objects does not matter.
How many words, with or without meaning can be made from the letters of the word, $\text{MONDAY,}$ assuming that no letter is repeated if
$(i) 4$ letters are used at a time
$(ii)$ all letters are used at a time
View full solution →How many words, with or without meaning can be made from the letters of the word, $\text{MONDAY,}$ assuming that no letter is repeated if
$(i) 4$ letters are used at a time
$(ii)$ all letters are used at a time
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 $A. \ (2$)
View full solution →| 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 $A. \ (2$)
The girder of a railway bridge is a parabola with its vertex at the highest point, $10\ m$ above the ends. Its span is $100 \ m$.
$i$. Find the coordinates of the focus of the parabola. $(1)$
$ii$. Find the equation of girder of bridge and find the length of latus rectum of girder of bridge.$ (1)$
$iii$. Find the height of the bridge at $20\ m$ from the mid $-$ point. $(2)$
OR
Find the radius of circle with centre at focus of the parabola and passes through the vertex of parabola. $(2)$
View full solution →$i$. Find the coordinates of the focus of the parabola. $(1)$
$ii$. Find the equation of girder of bridge and find the length of latus rectum of girder of bridge.$ (1)$
$iii$. Find the height of the bridge at $20\ m$ from the mid $-$ point. $(2)$
OR
Find the radius of circle with centre at focus of the parabola and passes through the vertex of parabola. $(2)$
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 →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 →$i$. If $f(x)=\left\{\begin{array}{cl}|x|+1, & x<0 \\ 0, & x=0 \\ |x|-1, & x>0\end{array}\right.$, for what values $(s)$ of a does $\lim _{x \rightarrow a} f(x)$ exist?
$ii$. Find the derivative of the function $\cos \left(x-\frac{\pi}{8}\right)$ from the first principle.
View full solution →$ii$. Find the derivative of the function $\cos \left(x-\frac{\pi}{8}\right)$ from the first principle.
Find the derivative of $(\sin x + \cos x)$ from first principle.
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