In how many ways can the letters of the word 'APPLE' be arranged?
- A90
- B6
- C120
- D60
Question types
Model Paper 6 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 6 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If z is any complex number, then $\frac{z-\bar{z}}{2 i}$ is
- Aeither 0 or purely imaginary
- Bpurely imaginary
- Cpurely real
- Deither 0 or purely real
$\cos \theta+\sin \left(270^{\circ}+\theta\right)-\sin \left(270^{\circ}-\theta\right)+\cos \left(180^{\circ}+\theta\right)$ is equal to
- A$2 \cos \theta$
- B$0$
- C$2 \sin \theta$
- D1
If $A$ and $B$ are two given sets, then $A \cap(A \cap B)^C$ is equal to
- AB
- BA
- C$A \cap B ^{ C }$
- D$\phi$
The solution set for $(x + 3) + 4 > -2x + 5:$
- A$(-\infty, 2)$
- ✓$\left(\frac{-2}{3}, \infty\right)$
- C$(-\infty,-2)$
- D$(2, \infty)$
Answer: B.
View full solution →Assertion (A): The proper measure of dispersion about the mean of a set of observations i.e. standard deviation is expressed as positive square root of the variance.
Reason (R): The units of individual observations $x _{ i }$ and the unit of their mean are different that of variance.
Reason (R): The units of individual observations $x _{ i }$ and the unit of their mean are different that of variance.
- 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 explanation of $A.$
- ✓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: B.
View full solution →The intercept cuts$-$off by a line from $y-$axis is twice than that from $x-$axis and the line passes through the point $(1, 2).$ Find the equation of the line.
View full solution →Write $E = (14, 21, 28, 35, 42, ..., 98)$ in set$-$builder form.
View full solution →Find the vertex, focus, axis, directrix and latus$-$rectum of the following parabolas $y^2-4 y+4 x=0$
View full solution →Find the equation of the hyperbola, referred to its principal axes as axes of coordinates, in the following cases:
Vertices at $( \pm 5,0)$, Foci at $( \pm 7,0)$.
View full solution →Differentiate $\sin ^3 x \cos ^3 x\ \ w.r.t\ x$
View full solution →Let $A=\{a, e, i, o, u\}, B=\{a, d, e, o, v)$ and $C=\{e, o, t, m]$. Using Venn diagrams, verify that: $A \cup(B \cap C)=$ $(A \cup B) \cap(A \cup C)$
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 the square roots $: 7 - 24i.$
View full solution →Find the coefficient of $x^5$ in the product $(1+2 x)^6(1-x)^7$ using binomial theorem.
View full solution →Given that $, P (5,4,-2), Q (7,6,-4)$ and $R (11,10,-8)$ are collinear points. Find the ratio in which Q divides PR.
View full solution →
A teacher conducted a surprise test of Mathematics, Physics and Chemistry for class XI on Monday. The mean and standard deviation of marks obtained by 50 students of the class in three subjects are given below:
i. Which of the three subjects shows the highest variability? (1)
ii. What is the coefficient of variation of marks obtained by the students in Chemistry? (1)
iii. What is the coefficient of variation of marks obtained by the students in Physics? (2)
OR
What is the coefficient of variation of marks obtained by the students in Mathematics? (2)
| Subject | Mathematics | Physics | Chemistry |
| Mean | 42 | 32 | 40.9 |
| Standard deviation | 12 | 15 | 20 |
i. Which of the three subjects shows the highest variability? (1)
ii. What is the coefficient of variation of marks obtained by the students in Chemistry? (1)
iii. What is the coefficient of variation of marks obtained by the students in Physics? (2)
OR
What is the coefficient of variation of marks obtained by the students in Mathematics? (2)
Arun is running in a racecourse note that the sum of the distances from the two flag posts from him is always $10 m$ and the distance between the flag posts is $8 m. $
$i.$ Path traced by Arun represents which type of curve. Find the length of major axis? $(1)$
$ii.$ Find the equation of the curve traced by Arun? $(1)$
$iii.$ Find the eccentricity of path traced by Arun? $(2)$
OR
$iv.$ Find the length of latus rectum for the path traced by Arun. $(2)$
View full solution →$i.$ Path traced by Arun represents which type of curve. Find the length of major axis? $(1)$
$ii.$ Find the equation of the curve traced by Arun? $(1)$
$iii.$ Find the eccentricity of path traced by Arun? $(2)$
OR
$iv.$ Find the length of latus rectum for the path traced by Arun. $(2)$
If $\alpha, \beta$ are two different values of $x$ lying between $0$ and $2 \pi$ which satisfy the equation $6 \cos x +8 \sin x =9$, find the value of $\sin (\alpha+\beta)$
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 →Find four numbers in $GP,$ whose sum is $85$ and product is $4096.$
View full solution →Differentiate log sin $x$ from first principles.
View full solution →Solve: $\lim _{x \rightarrow 1} \frac{x^4-3 x^3+2}{x^3-5 x^2+3 x+1}$
View full solution →Generate a Model Paper 6 paper free
Pick question groups from the list above, set marks and difficulty, and export a branded PDF with step-by-step answer keys. First 3 chapters free — no signup.